1. Introduction:
The Birth of a New Art Form
The advent of the digital computer represents a
rare event in the fine arts: the birth of an entirely new creative process.
This process is distinguished by its deep conceptual roots in areas normally
held as alien to the arts and by its peculiar deterministic mechanism of
expression, which is wholly novel to the practice of artistic creation.
In this process the computer acts as a potent engine of interpretation,
reifying in images the dry but austerely beautiful abstractions of formal
scientific models of the universe we inhabit. The images so created may
in turn become artworks, spun from a process based upon philosophy, mathematics
and the physical sciences, and entraining the rigor, beauty, and intellectual
depth of those fields. Art and science, so often viewed as mutually inimical
and irreconcilable, come together in pursuit of the common goal of visual
aesthetics.
In the seventeenth century Rene Descartes and Isaac
Newton, as natural philosophers, fleshed out a world view so compelling
that, if the average educated person in our society today stops and thinks
about it, it seems to be "the obvious way that things are": In the Cartesian
universe with Newtonian dynamics, if we knew A) the position and velocity
of every particle in a closed system and B) the rules for their interactions,
and we had sufficient power to compute all those interactions, we would
have the power to predict the future, forever, for that system. If the
closed system in question were the entire universe, this would have profound
philosophical implications: There could be no free will; it would imply
that we are all witless automatons, mere puppets in some sort of deterministic,
already-written cosmic script. It would affirm the nihilistic philosophy
of fatalism, and undermine the basis of human morality: that we have a
choice in matters, and that what we choose to do--and not to do--makes
some kind of a difference.
In a broad view, the new artistic process we describe
here juxtaposes formal logic with human self-expression. The former is
founded upon determinism; a philosophical assumption that denies the possibility
of free will. Self expression, on the other hand, is an ultimate manifestation
of free will. I emphasize these two extremes, to highlight what is interesting
in this new process. One may substitute "aesthetic judgment" for "self
expression" throughout the text, but I will maintain the latter usage,
in the interest of contrast.
As a practitioner of the new process, I will attempt to illuminate both
its specific concerns and the significance of its links to the fields of
formal logic, the natural sciences, and computer science. While the arguments
presented are necessarily technical at turns, I will make every attempt
to keep them comprehensible to the intelligent layperson. As well, I will
attempt along the way to point out some of the implications of the advent
of this new way of working, and how they relate to current trends in the
visual arts.
1. 1. The Thesis
The thesis I propose is this: Self-expression in
representational imagery may be obtained strictly through formal logic;
and the practice of doing so marks a discontinuity of significant import
in the history of the creative process. In addition, I claim that the resulting
artworks are conceptually enriched by the intellectual underpinnings of
this approach: When an artwork represents the unaltered result of a deterministic
logical derivation, it entrains a conceptual depth and richness not commonly
achieved in the realm of visual arts.
Only time and our culture can determine the validity
of the first two claims I make. The last I can illuminate; that is what
this essay attempts to do.
1. 2. Foundations
Science is the discipline of observing Nature and
deriving potent and internally consistent descriptions (models)
of systems observed therein. Mathematics is the language of science; it
provides both a terse notation and a logically consistent framework in
which to couch such descriptions. Computer science is the study of the
complex logical system that is the computer; it is largely based on the
discipline of mathematical logic: The operation of the modern digital computer
is described completely by, and at the lowest level is literally implemented
in terms of, the predicate calculus of formal logic.
It is worth pointing out that it is a specific sub-branch
of computer science,
numerical analysis, which concerns itself
with the problems of performing mathematical computations with a digital
"computer. "Note the sudden appearance of quotes around the word computer--it
turns out that this appellation is a misnomer: a (digital) computer is
more rightly viewed as a symbol manipulator, a string re-arranger,
[1]
than as a mathematical calculating device. I point this out because this
"string re-arranger" model of the computer will be essential to my treatment
of the computer as an artistic tool and process.
1. 2. 1 Formal Logic and Formal Systems
Our arguments are based on the discipline of formal
logic, the study of logic in its pure form. Interestingly, a first
college course in logic will typically be taught in the philosophy department--logic
being, of course, the foundation of reasoning and reasoning being the foundation
of most precisely communicable human understanding. A first course in formal
logic may also be taught in the philosophy department. Formal logic
is codified in the predicate calculus, which explicitly lays out
the valid and invalid forms of logical inference as well as the minimal
set of rules required for full logical reasoning. More advanced courses
in formal logic are likely to be taught in the mathematics department,
under the moniker
mathematical logic. Mathematicians are intimately
involved with formal logic, as all of their work is in the domain of the
logical framework provided by formal systems, the reasoning systems
of formal logic. Finally, formal logic is also taught in computer science
departments, as computers are implemented in terms of logical operations;
thus all theoretical models of computation reduce to the study of formal
logic and formal systems. We see then that formal logic is already a highly
interdisciplinary field; in this essay we will extend its scope by establishing
a direct linkage to the visual arts.
A
formal system is a sort of game;
it is a fundamental concept of mathematical, or formal logic.
[2]
For
our purposes we may think of a formal system as a set of given input strings,
called
axioms, along with a set of rules for performing transformations
on, or changes to, those strings. The latter are called
rules of
production or
rules of inference. Consecutive application of
the rules of production to the axioms constitutes the derivation of a
theorem
in the system. The specific sequence of application of rules of production
in the derivation constitutes a
formal proof of the theorem.
A simple, illustrative example of a formal system
is Hofstadter's MIU system. [4] In this system, the only recognized
symbols from which to compose strings are the characters M, I,
and U. The only axiom, or starting (i. e. , input) string is MI.
There are four rules of production that may be applied to the axiom and
its successors:
Rule I: If a string ends in I, you may add a U
to the end.
Rule II: If you have Mx, where x is an MIU string,
you may add Mxx to your collection.
Rule III: If III occurs in a string, it may be replaced with
U.
Rule IV: If UU occurs inside a string, you may drop it.
Every string derived from the axiom by these rules of production may be
added to your collection of valid strings. Hofstadter challenges the reader
to derive the string
MU from the given axiom
MI, using the
rules of production given for the formal system. Note that there is no
ambiguity in these rules, no "maybes" or "kind-of-likes. "The results of
an application of a rule are deterministic; but there is free choice in
the order of application of the rules.
This is a very simple formal system, but it reflects exactly the behavior
to which a computer is constrained: modifying strings by the application
of well defined deterministic rules of production.
Why do we bring up this rigmarole? Because this is exactly how a computer
operates. We can describe the functioning of a computer completely through
this kind of formal treatment; all other "higher level" functions of a
computer are built on top of, and implement different instances of, such
formal systems. Formal systems have, in turn, been studied intensively.
Early in this century, Bertrand Russell and Alfred North Whitehead [13]
set out to map all of mathematics into a single, unifying formal system;
their difficulties were shown to be theoretically insurmountable by Kurt
Godel in his famous Incompleteness Theorem. (This theorem demonstrates
that, for any 'sufficiently powerful' formal system, there exist statements
that are neither inconsistent with the system nor provable or disprovable
within the system; in short, the system has nothing to say about them.
MU
is such a statement in the MIU system. ) In short, great minds of
our century and before have worked on the ramifications of the machinations
of formal systems; in fact, many smart mathematicians and logicians continue
to do so today.
The consequence to us, of all the above, is that when we are using formal
logic (i. e. , formal systems) we are "standing on the shoulders of giants,"
intellectually. There is a rich, preexisting mathematical and philosophical
body of knowledge in this area, which we are implicitly drawing upon when
we use the computer.
1. 2. 2 Artwork as Theorem
How does this concern us, artistically? As it turns
out, all computer programs can be mapped into formal systems. Thus, when
we use a computer, we are using a formal system; we are utilizing formal
logic. Every time we execute a computer program, we are causing the derivation
of a theorem in a formal system. "So what?" you might ask. This observation
might seem to trivialize, to render vacuous, any claim that the derivation
of a theorem in a formal system is in any way something special or intellectually
weighty--after all, computers do it all the time, day in and day out, all
around us.
But how often do we call the result art? ("Too often,"
indeed. ) How often is the artist cognizant of these arcane machinations?
How often can the artist claim to have consciously engineered the entire
procedure? When the formal system involved is a computer program written
specifically by the artist for the purpose of producing the artwork, when
the program itself embodies much or even most of the power to create the
work, when the artwork represents something that could not have come into
being in any other way, then these observations vis a vis formal
logic become interesting. Indeed, they gain great import.
1. 2. 3 Theorem as Self Expression
It is one thing to label a theorem derived in a
formal system a work of art; it is another to claim that work of art represents
self-expression on the part of the artist. Scientifically, such a claim
is weak, as it can be verified only by the artist; no independent formal
verification is possible. I maintain that the claim can nevertheless
be valid, and is even readily verifiable in many cases, if only qualitatively
(as opposed to quantitatively). There exist examples of such artworks--the
pure output of a computer program--wherein it is readily evident that something
of the artist's soul has been bared. As an example I offer "Blessed State,"
Plate
1.
Claiming self-expression purely through formal logic
obviously involves massive constraints on what constitutes successful practice
and an acceptable result in the artistic process. Yet another significant
set of constraints is generated by the requirement that the works be representational.
Abstract expressionism is an honored aesthetic in its own right, and formal
systems and the computer can be--and have been--used in this context. But
the requirement of literal realism in formal imagery spawns a host of problems
and concerns that are only starting to be addressed, primarily in the research
literature of computer graphics. Representationalism in synthetic imagery
remains, in general, an open problem.
Many of the problems of generating realistic looking
synthetic imagery have been solved, albeit sometimes in ad hoc ways;
many such problems yet await satisfactory solution. For example, specular
reflection from glossy surfaces has been handled to nearly everyone's satisfaction
by ray tracing; however, general realistic lighting models--including
atmospheric scattering of light and interreflection between semi-glossy
surfaces--are still under active development. In short, there are some
things we can do very well with the current techniques of computer graphics;
others that are imminently doable but not yet done; and some which are,
and are expected to remain, refractory. As an active researcher in the
field of computer graphics, I am involved in the effort to move more phenomena
from the category of "doable" to that of "done. "As a result, my own artworks
more often than not serve simultaneously as a form of aesthetic self-expression
and as illustrations of techniques new to the field of computer graphics.
This adds a dimension of technical significance to the works; however,
I generally intend this to be transparent to the uninformed observer.
In fact, one of my key intentions as an artist is to keep this entire esoteric
process that I am describing transparent, to make it invisible to the viewer.
There are a variety of reasons for this: First, I do not wish to immediately
and automatically invoke the instinctive fear of mathematics that the average
person is prone to feeling (myself included). Second, it is a research
goal to have the image look as natural, i. e. , non-computer generated,
as possible; thus the formal process should be thoroughly sublimated in
the result. Third, and most important, is that it would be no better than
arrogant and obfuscatory to require the audience to confront and grapple
with these issues--the images should be able to stand on their own as aesthetic
visual statements, outside of this technical context. I say: "Let them,
or let them fail. "
1. 3. Deterministic Formalism and the Creative Process
An artist requires constraints, if for no other
reason than to narrow down the "search space" (to put it in computer science
terminology) wherein the desired result is sought. The formal logic approach
certainly provides a rigorous set of constraints on the creative process.
It also provides some interesting side-effects.
The determinism of the logic involved means that
the result is reproducible: repeated runs of the same program with the
same input provide, modulo the occasional hardware glitch, precisely the
same output. The artwork is reproduced
exactly. (Or at least
the numerical metarepresentation of it is; more on this later. ) This is
true despite the fact that randomness is an essential element in all my
images--the randomness employed is a deterministic randomness; it is not
"truly" random, but what we computer scientists refer to as "pseudo-random.
"
[3] Pseudo-random processes are
simple yet sophisticated constructions from the mathematical discipline
of
number theory that are, for practical purposes, fully
random (i. e. , they lack discernible order or structure) yet which are
simultaneously fully deterministic and therefore exactly reproducible.
The fact that I constrain my artworks to be purely
the output of a computer program insures that they feature this peculiar
reproducibility. This could never be true of a painting, for instance,
as a brush stroke is not an exactly reproducible act, on the microscopic
scale at least. In the case of a computation the result is a string or,
at the lowest level, a number or sequence of numbers or digits. This string
or number can be checked character by character, digit by digit, for exact
fidelity; there is no ambiguity or latitude for imprecision in the representation.
Viewed in the light of computational result as artwork, and artwork as
representational self-expression, this determinism and exact reproducibility
are rather bizarre.
2. Distinguishing the Process
It is worthwhile to take a little time to point
out what distinguishes this process from the more traditional practices
of fine arts such as painting, sculpture and photography.
2. 1. Dimensionality
The product of this process is a two-dimensional
image; this characteristic it shares with painting and photography. Like
a painter or photographer, the artist is responsible for choosing an interesting
point of view and framing for the image. As with a camera, a geometrically
precise projection of the three-dimensional world onto the image plane
is performed; painters have much greater latitude here. Like a photographer,
one is free to roam the three-dimensional world, even to employ cinematography
to add motion in a temporal exploration.
In this new process, though, the artist is responsible
for the creation of the entire world being imaged: there are no preexisting
objects "out there to be found" and creatively imaged; all objects and
all interesting visual detail must be created explicitly. The elegant means
we have for creating such visual complexity are at the heart of what makes
this process successful and interesting.
2. 2. Visual Complexity: Fractal Models
Fractal geometry [7] is the key to generating potentially
unlimited visual complexity in my work, and in computer graphics in general.
Fractal geometry is a language of shape, similar to the language of planes,
circles, spheres, triangles, cones and cylinders of the more familiar Euclidean
geometry. But as Benoit Mandelbrot has observed [7]:
Clouds are not spheres, mountains are not cones, coastlines
are not circles, and bark is not smooth, nor does lightening travel in
a straight line. . .
|
The vocabulary of shape
of fractal geometry provides, can describe such complex natural shapes
with striking elegance.
There are two key aspects to fractal descriptions
of natural forms: self-similarity, or the repetition of similar
shapes at different scales, and randomness in the model. The first
means that we need only describe one fundamental shape plus the relationship
of its manifestation to the scale at which it is manifest--a very simple
description indeed, for an object of potentially unlimited complexity.
(The complexity is simply a function of the number of different scales
at which we manifest the basic shape; the shape itself is typically simple,
e. g. , a triangle or a sine wave. ) The second aspect, randomness,
is the key to having the resulting shapes look natural, rather than man-made
or (worse still) computer-made. Control then takes the form of shaping
statistical distributions in random processes, rather than explicit specification
of exact form. Thus we exchange exact control over form, for power in automatic
generation of complex shapes. [2]
2. 3. Purity of Algorithmic Process
Of course, I could employ my omnipotent powers in
this synthetic universe to intervene and make specific, local changes wherever
I saw fit. In adherence to a self-imposed constraint of process, however,
I do not allow myself to do this. This often proscribes the shortest route
to a desired result (as in obtaining a desired hue in a given highlight)
by disallowing local intrusions and modifications to the world or the image
that would, in practice, be relatively easy to execute. What is gained
in exchange, however, is purity of algorithmic process. Creation of an
image becomes a dance with the opportunities and serendipity granted by
the powerful, random fractal models that I create, embellish and (more
or less) control. By disallowing post-process meddling with the results
of various algorithmic processes I employ, I gain two compelling benefits:
legitimacy in illustrating the descriptive power of these abstract fractal
models, and claim to an elegance in the creative process--the image is
indeed a theorem proved, in one pass, in a formal system.
[4]
Adherence to principles of algorithmic purity legitimizes one of the
key claims I make about the significance of this process: that it entrains
the intellectual depth of logic, mathematics and computer science as its
foundations. In practice, it entails the pure use of formal logic to obtain
the desired result. If I were to indulge in local meddling, this claim
would be compromised and/or invalidated.
Again, another (more or less arbitrary) constraint
I impose upon the process is that the results represent self-expression.
Expressionism is a practice the popularity of which perhaps waxes and wanes
through the history of the fine arts; I do not claim that it makes my work
in any way "better," I only note that it constitutes a significant constraint
upon what I, as an artist, consider to be a successful result.
2. 4. Proceduralism
These concerns lead us to proceduralism.
[2,12] Proceduralism is the practice of abstracting complex behaviors into
relatively terse functions or algorithms that do not contain
specific information about details of the phenomenon, but rather encode
a given behavior in a formal set of instructions that specify the behavior
everywhere it might manifest itself, and which may be evaluated only when
and where such information is desired (what we charmingly call "lazy evaluation"
in computer science).
Thus, in the procedural approach, a "virtual world"
is abstracted into a compact procedure or set of procedures. These procedures
are in turn controlled by a relatively few parameters which affect (only)
global
control. Alvy Ray Smith [15] called this database amplification;
I refer to the process of creating landscape images within this paradigm
"playing God in a found Universe"--I may have God-like powers over these
worlds, but in practice, because of the randomness they embody, they behave
as if they have a will of their own. Furthermore, they have an ineffable
sense of having existed a priori; of somehow being inherent in the
timeless, universal formal procedures that specify them and of always having
existed there as an aspect of Nature, or at least of Mathematics, just
waiting to be discovered. As an artist, I simply interpret these forms
visually. Thus they may represent, at least in part, "found art." But there
nevertheless remains enormous latitude for the exercise of aesthetic judgment
in the development of any given image. It is, after all, but one out of
an unimaginably huge, if finite, multitude of images that might have been
selected (more on this later).
2. 4. 1 Functions and Algorithms
Proceduralism in practice consists of devising functions
which in turn are implemented as algorithms, or unambiguous sequences
of instructions telling the computer exactly what to do, for a given input.
Functions are a mathematical concept. They may be viewed very simply as
contraptions that change values given as input, to other values--the output.
The input and output values might be very different: input may be numbers
and output colors, or other stranger and more subtle mappings.
Mathematically, we refer to the action of a function
f
like
this:
f:D->R
which simply says that function
f sends (
maps) input values
from
D (the
domain) to values in R (the
range). It
is useful to distinguish the set of possible input values
D from
the set of possible output values
R as they may be quite different
kinds of things.
The simplest kind of function is a scalar valued function of a single
variable, denoted f(x) = y. (We use lower case letters
to refer to specific values, upper case to refer to the entire set from
which those values may be chosen. ) A scalar value is just
a single number. A function of one variable has only one input value.
Most interesting functions are the more complex vector valued functions
of several variables, denoted f(x1, x2, Ö,
xn) = [y1, y2, Ö, ym].
This particular function takes a number (n) of input values, and
maps them to another number (m) of output values. Such functions
are more common in my images. They typically take more than three values
as input: the three spatial coordinates of the location where the function
is being evaluated (as the function is usually defined over all of space)
plus a set of variables controlling the behavior of the function. They
output some small number of values, such as the primary color components
of a certain color and a spatial vector used to modify the apparent orientation
of a surface (as with the water in Plate 1).
It is the concoction of functions like this with interesting visual
behaviors, which constitutes the first step in this formal creative process.
These functions are small parts of a much larger program that orchestrates
the overall creation of the picture. Examples of such functions in action
can be seen in the ripples in the water in Plate
1, as well as in the roughness of the moon and the coloring of the
mountains. Each of these effects issues entirely from the functions evaluated
on the surfaces there. (Believe it or not, the water is a perfectly flat
plane, and the moon is a perfectly smooth sphere!) The fact that
the functions are defined over all of space allows us to evaluate them
anywhere we desire. Thus the moon is carved out of an infinite block of
"moon-ness," the mountains out of an infinite virtual block of snow, rock
and greenery, and the water out of an infinite expanse of abstract "sea.
"
2. 4. 2 Global Parametric Control
The values
xi (
i denoting the numbers 1 through
n)
which serve as input to our functions are known as
parameters. The
parameters beyond the three spatial coordinates at which the function is
being evaluated, are used to determine the overall behavior of the function.
The way these functions are usually constructed, the parameter values affect
the function's output
everywhere in space. This amounts to
global
parametric control of the function's behavior.
In practice this means that, for instance, I may exactly specify a color
for a light source; if I dislike the resulting hue in a particular highlight
(a local effect) I may change the color of the light source accordingly,
but this changes tones everywhere that light falls in the scene. Similarly,
if I dislike the shape or location of a given wave in the water or mountain
peak in the terrain, I may change it, but this change will also affect
all other waves or peaks and valleys. The randomness at the heart of the
fractal models I use grants both enormous flexibility and expressive power,
but it also entails complete abdication of control over specific details
in relation to their global context. While this global parametric
control represents a profound creative constraint, it also entails an enormous
(and often elegant) simplification of the final stage in the creation of
the image: After the program is written, all that is to be done is to select
values for these parameters.
2. 5. Representationalism and Conceptualism
When manual renderings were the only source of pictures, artists were deeply
concerned with accurate representation; they developed a full set of techniques
for realistic rendering. Since the invention of the camera, representationalism
has not generally been a vital issue in the visual arts. Our new process,
however, reopens the problem of representationalism: We simply do not yet
know, in general, how to reproduce the visual appearance and complexity
of the everyday world in computer synthesized imagery. It may thus push
us back several steps in the cycle of aesthetic evolution (or is it simply
forward, one step?)
Recently, conceptualism has sometimes given the ideas behind an artwork
work precedence over the artwork's physical manifestation. For that reason,
I wish to emphasize throughout this essay the depth of the conceptualism
inherent in this process, and to cast a faint glimmer of light into those
depths.
2. 6. Lighting
The artist's responsibility for lighting in synthetic scenes brings this
process into relation with lighting as used for photography and stage performances.
Direct responsibility for lighting is something new for landscape rendering,
where artists have traditionally relied on serendipity in Nature to provide
striking effects. As the author of a synthetic world, we will find nothing
that we do not explicitly create. And of course, due to the nascence of
the process, we have yet to approach the kinds of diverse, subtle and spectacular
effects captured by the masters of more mature art forms like Bierstadt,
Monet, Turner and Adams.
The process of providing synthetic lighting is exactly analogous to
stage lighting. We have light sources with color, brightness, direction,
and area of influence. We can position those lights wherever we want. We
can have as many of them as we like (though in practice I rarely use more
than two--a warm sunlight and a cool skylight). In addition, we are responsible
for specifying, mathematically, the interaction of light with surfaces
in the scene: are those surfaces mirror like, glossy, or matte? Or
something different, perhaps completely unnatural? There are no set
limits here. This mathematical treatment of light and color also marks
a new practice in the visual arts; we will expand upon it later.
2. 7. A Model of the Creative Process
A particularly fascinating view of the parametrically controlled creative
process is that of
searching n-space for local maxima of an aesthetic
gradient. Let me explain: We have created a procedural, parametrically-controlled
model of a synthetic microcosm. Say there are
n independent parameters
in that model and the specification of its projection onto the image plane.
As these parameters are independent, we can think of each as representing
a
degree of freedom, or an additional
dimension
or direction in which we may move. Taken together, the
n parameters
define an
n-dimensional space or
n-space for short. In this
space we are free to move not just up and down, right and left, or forward
and back, but in a whole lot of other abstract directions as well. This
may seem abstruse to the layperson, but mathematicians, scientists and
engineers never hesitate to work in spaces with many more dimensions than
the familiar three of our everyday world.
The task of the artist then is first to create these
n parameters
(n being usually around two to five hundred in my own images) and
their (deterministic) meaning through creating the procedures or functions
that they drive, then to "tweak" the values of these parameters to obtain
a satisfactory result or image. The creation of the parameters in formulating
the formal system corresponds to defining the n-space; the process
of refining the parameter values, or choosing the axioms to start with,
corresponds to searching that n-space for local maxima
of an aesthetic gradient. A
local maximum is location
in the space from which all directions lead "downhill," that is, it is
a kind of hilltop in n-space. "Downhill" is defined by the aesthetic
gradient function--the completely subjective (non-deterministic) assessment
on the part of the artist of what constitutes a "better" image, in terms
of the parameter values. Obviously, this so-called "function" is not unambiguous:
Its value will depend on the criterion by which the image is being assessed,
and even upon the mood of the artist at the moment of evaluation. [5]
The
local maximum is then a point in n-space from which a small move
in any direction would result in a "less good" image.
Ambiguity notwithstanding, this n-space gradient ascent model
is more than just entertaining: It points out that a given image represents
merely a local maximum of the aesthetic gradient field. Other, more
global maxima ("higher hilltops," corresponding to "better" pictures or
possibly "better" self-expression) undoubtedly exist elsewhere in the rich
abstract n-space of potential images defined by the formal system.
This is very much akin to noting that a photographer might have gotten
a better shot by choosing a different vantage point or time, except that
we have much, much more control here. Creating and searching this n-space
is, I submit, a singular way of obtaining self-expression.
2. 7. 1 Searching N-Space for Aesthetic Maxima
What does this process look like, in practice? I have a bunch of
numbers, usually about two to five hundred, which define the entire scene
I'm creating (other than the landscape itself, which consists of thousands
of numbers that, again, I don't allow myself to change or fiddle with).
This is a lot of numbers to deal with. And it turns out that if you change
more than one or two at a time, the effects are usually conflated, and
you can't be sure which change accomplished what effect. Thus I spend long
hours massaging the values one or two at a time, until I am sufficiently
satisfied or exhausted to "call it a picture."
This is a very tedious process. It is also very obscure: No one else
can hope to use my programs--the meanings of the parameters are simply
too obscure for another artist to practically deal with. In fact, I am
only really cognizant of their intended effects when I create the functions;
this intent is quickly forgotten in the complexities of my work and daily
life. If later I need to reconstruct that meaning, I generally have to
go back and look at the computer code that I've written to implement the
functions, and figure it out by inspection, reverse engineering, and the
memories of my original intent that the inspection triggers.
This is not a highly desirable interface or working methodology. When
people ask me "Can other people use your programs, too?" I have to answer
"No." (I certainly lack the time and patience to explain or document all
of these things. ) This deplorable state of affairs I would attribute to
the youth of the method--it is certain to be improved over time. Powerful
mathematical methods can be brought to bear in such endeavors. Principle
components analysis may be used, for instance, to reduce the dimensionality
of the parameter space, and to maximize the effects of changes in parameter
values (though the resulting reorientation of parameter vectors in n-space
may destroy any original intuition as to parameter meaning).
2. 7. 2 Genetic Programming
One very promising method for managing the creation and search of the high
dimensional parameter space is
genetic programming. In the
genetic approach, we borrow some concepts from biology, namely
genotype,
phenotype,
mutation,
and
sexual reproduction.
Genotype is the encoding
of an organism's form in its DNA, while
phenotype is the physical
manifestation of that coded form in an actual organism.
Mutation
is the spontaneous change in the encoding itself, and
sexual reproduction
is the recombination of genotype information from two individuals, by "mixing
and matching" parts of their genetic code. This is a powerful approach
to creation--after all, it appears to have gotten us to where we are today,
as intelligent sentient beings.
Richard Dawkins popularized the genetic approach in his book "The Blind
Watchmaker." [1] Several artists are using genetic algorithms to create
striking works (though they are not representational, in the sense that
I am using here). Karl Sims creates wonderful abstract images very rapidly
with his genetic software, running on a massively parallel supercomputer.
[14] My personal experience with his system showed it be an astonishingly
fecund process. And it is as simple as can be: The computer puts up a sequence
of images, you pick one you like which the computer then proceeds to mutate
for you, or you pick two which the computer then "breeds" for your pleasure.
Mutation is random, and "natural" and sexual selection are performed by
you, the user. William Latham uses similar genetic methods in creating
his fantastic sculptural forms of Cambrian beasts that never were. [16]
While this genetic approach to the management of procedural models is
incredibly promising, it is currently limited to the creation of such free-form
objects and images as Latham's and Sims'. Indeed, one of the points that
Dawkins stresses is that evolution (of life on Earth) never has any goals
as such. Rather, its only "values" are propagation and persistence; organisms
satisfying those two criteria are "successful," those which do not are
"failures." Unfortunately, it is therefore not immediately apparent how
to apply the genetic methods of selection and random mutation to the evolution
of models of non-biological natural phenomena or, more generally, to the
problem of converging on any highly specific and complex a priori
goal.
2. 7. 3 A Biological Analogue
Roman Verostko [17] has likened software that embodies an artist's aesthetic
judgment to the genotype, and the resulting artwork to the phenotype. Program
execution then corresponds to
epigenesis, the biological process
of the development of an undifferentiated cell, as a spore or an egg, into
a complex organism.
The work of Verostko, Sims, Rooke and others is closely related to the
process I am describing here; we may be regarded as being of the same school
of algorithmic art. Yet our processes are not identical. Verostko's "Hodos"
system has a deterministic front end: the computer driving the plotter.
The back end, the plotter, is no more deterministic than any paintbrush.
As a result, none of the phenotypes is exactly reproducible (not that that
is a desired trait, it is simply a distinction between the processes).
The main distinction between Verostko's process and the one I am describing
is that Hodos creates an artwork, while my process creates only a metarepresentation
(again, more on this later). In this sense, Hodos is more mature and complete;
as we will see, our new process as yet lacks a satisfactory medium in which
to manifest the final piece.
3. What the Process Is Not
To further distinguish the process, it is worthwhile to point out certain
aspects of what the process is
not, to clarify by defining the negative
space around it.
3. 1. A 2-D Canvas
One thing this process is not, is a flat canvas. While the final image
is indeed two dimensional, its creation takes place in three dimensions
(excluding time). We are responsible for the creation of an entire three
dimensional world, which we proceed to image by projecting it onto a film
plane like a photographer, only doing so with mathematics.
[6]
The potential of the process will be expanded when we gain the capability
of rendering scenes at video frame rates--then the viewer will no longer
need be passive, but will be able to enter the synthetic world and explore
it, much as one moves about to inspect a piece of sculpture or a physical
environment. In an immersive VR environment, this is foreseen to be quite
an exciting development, though one better suited to entertainment than
art, perhaps.
It is important to me, as an artist, to emphasize a certain point: The
really interesting uses of the computer in the creation of artworks will
not be in the traditional role of a canvas and paintbrush. Certainly, the
computer can function as such and offers some unique capabilities, such
as infinite erasure and reworking capabilities, not possible with paints.
But that does not mark a significant conceptual breakthrough, merely incremental
progress for an established process. Not that there is anything wrong with
using the computer in this way--most of the best computer art has been,
and will continue to be, produced in this way. I simply wish to emphasize
that the process I am describing has very little in common with that, aside
from using some common hardware devices and their common aesthetic disciplines
of composition, color usage, and so forth. The means of creation are utterly
different, and it is only the new process that is truly significant as
an intellectual event in the history of art, I maintain.
3. 2. Local Control
Almost every established process in the visual arts involves local control:
details are manipulated in isolation from the whole. Any given brush stroke,
for instance, while it certainly may indirectly affect, and be indirectly
affected by, its global context, represents an absolutely local act. It
does not directly affect anything beyond the area where the paint is applied.
Changing a global parameter, in contrast, immediately and directly affects
everything, everywhere its function has influence. Thus I again wish to
emphasize the contrast with, for instance, painting and sculpture, where
the work is usually realized incrementally by a series of fundamentally
local actions. When working with global control only, we have a much less
precise control over details, but gain in return something akin to the
power of "painting with a broad brush"--we cover a lot of territory with
a single action.
3. 3. "Of the Hand"
As the only access to expression is through the formal logic of the computer
program, there is no "evidence of the hand" in the final work (or if there
appears to be, it is illusory). Some may find this anathema, but it is
important to point it out as a distinction of the process. The mechanism
of creation that I use is extraordinarily abstract and removed from the
product. This is part of what is interesting and bizarre about the process:
that such prosaic imagery comes about through such indirection and abstraction.
I claim that this is significant in itself.
3. 4. Pure Mathematics
I am often mistaken for a mathematician. That I am not. While all the models
employed are based on logic, and many are mathematical models of natural
phenomena, the mathematics I employ is generally quite simple compared
to what a "real" research mathematician would be involved with.
Pure mathematics, after all, assiduously shuns applications and other
associations with "reality." And what I am up to, is recreating reality
as we see it.
3. 5. Computer as Creator
Finally, and most importantly, this process does
not represent
creative action on the part of the computer. A computer, given no instructions,
will just sit there dumb as a rock, if a little warmer. A computer (on
a good day) will cheerfully do exactly what you tell it to do, with blinding
speed and precision. It will never do anything useful that you, the human
operator, did not describe explicitly and in excruciating detail precisely
how to do (this is the tedious art of computer programming). Remember:
the computer operates as a formal system, and that admits no ambiguity
and no choice, only deterministic cut and dried yes or no instructions
and conditionals. Certainly, the complexity of the instructions we hand
the computer rapidly surpasses our human ability to track every detail
thereof, while the computer never loses track of one iota. But the computer
remains a simpleton; a very fast and capable simpleton, but a simpleton
nevertheless. If we puny humans were given eons of time and inhuman patience,
we could track, produce, and reproduce every tiny detail of what the computer
does--only we'd make a lot more mistakes along the way.
The point is, the computer acts as a powerful tool, maybe even like
a semi-intelligent slave/apprentice in practice, but is in no way the creator,
the author of the product. It simply did as it was manipulated to do, as
with a paintbrush in the hand of a painter. The main difference is that
the form of the manipulation is highly abstract and rigorous, and very
different from the physical manipulation of tangible media that we are
more familiar with in the visual arts.
4. The Process in Action
How does one proceed to create an image through this process? First,
we have to posit an abstract model of a world; then we must map that model
into a formal system--a computer program. Next we devise axioms, or input
to the program. Finally, we run the program to create the output, which
we will interpret as an image. This output is, like the input, in the form
of a string of symbols or values (i. e. , numbers; ones and zeros). Such
a string is hardly an image; therefore we call this the
metarepresentation
of the image. This metarepresentation still requires a considerable array
of sophisticated machinery and methodology of interpretation, to translate
it into the intended image.
We can then further subdivide the process of image creation into two
separate undertakings: creating the metarepresentation and interpreting
it. This essay concerns itself primarily with the first; it is here that
the bulk of the intellectual content resides. The second represents primarily
an engineering problem, though there is a considerable dose of color science
involved and that is none too simple in itself. [19] In artistic
terms, these two parts correspond to process and medium:
the first concerns itself with the machinations of artistic creation while
the second is about producing a physical manifestation. After the first
part is done, all we have generated is a still highly abstract and intangible
form. It is the second step that maps this abstraction into something that
can be perceived in a sensible way, and maybe even felt, held, or hung
on a wall. It is interesting that the two, process and medium, are so neatly
partitioned in this new way of working.
4. 1. Creating a Metarepresentation
Again, the first phase is the creation of the metarepresentation: the theorem,
the string, the sequence of digits, the one huge number, the signature
on a magnetic or optical storage medium, or the image file; however you
care to view it.
4. 1. 1 Creating the Formal System
We begin the process unconsciously as a young child: observing and cataloging
sights, phenomena, and behaviors in Nature. Over time we build some potent
and internally consistent models of Nature and the behavior and visual
manifestations of phenomena there: clouds, mountains, water, light and
color, to name but a few. Some training in the sciences teaches us the
practice of mapping this intuition into formal, mathematical models of
the behavior of natural systems, and the practice of empirical testing
and verification of those models. We become familiar with many such formal
models that scientists before us have devised and refined, and we learn
where to find descriptions of such models--in the scientific literature.
Becoming a practitioner of computer graphics, we learn the practice of
mapping such models into formal systems that the computer can efficiently
use to generate pictures. Note the qualification "efficiently," as the
scientific literature consists mainly of picayune and non-general models,
along with some very elegant and general ones that are simply not well
suited to the practice of image synthesis: Witness the wave model of light.
This is a potent, elegant model of Nature that the computer just can't
practically deal with for image synthesis, as it involves too much complex
calculation. What we require are models with potent descriptive capabilities,
which also admit to reasonable computational implementations.
It is this formulation of a model of Nature and its mapping it into
a computer program that constitutes the first phase of the process. It
is in the act of creating the functions, in the writing of the program,
that we create the parameters and give them their functional "meaning"
(the program semantics). The program, again, represents the rules
of production in the formal system, which will be repeatedly applied to
the axioms, or the input, in the process of deriving the theorem that is
the result or image metarepresentation.
Our tools at this stage are such abstractions as shaping functions,
e. g. , polynomials with continuity in a desired number of derivatives,
numerical integration methods, logic in the form of conditional "if/then"
statements, and algebra as applied to color (more on that later). Largely
by combination and recombination of a series of standard building blocks,
such as fractal functions, bump maps, color maps, etc. , we construct a
relatively small set of functions with which we intend to generate a world,
and the given image of that world.
The process of generating the formal system is so involving that, in
practice, almost all of my own images have come about as verifications
of some abstract idea that I was attempting to map into such a system.
In this sense they represent illustration of the model being developed;
I use the word "illustration" deliberately, despite the stigma that may
be attached to it in the visual arts. Keep in mind that in our new paradigm,
representationalism is no longer a "pedestrian concern"--it is again an
unsolved problem, and we are actively working towards solving it. Thus
the work cannot be dismissed as "mere illustration" or "simply representational";
these are highly honorable labels in our context. This may mark an inversion
of contemporary thinking in the visual arts.
There is one inevitable and undesirable side effect of this stage of
the process: parameter proliferation. In the process of developing
a potent model of complex phenomena, we almost always end up introducing
a large number of parameters that control the behavior of our models or
functions. This means that the artist will be faced with a bewildering
array of values which must be fixed, to create an image, and refined, to
create an artwork. Again, we currently know of no way around this, but
that may just be another symptom of the youth of our endeavor.
4. 1. 2 Generating Axioms
The next step is to formulate values for those multifarious parameters.
This is not quite as bleak a prospect as it may sound, as the same intuition
that drove the formulation of the model and the functions, also informs
the choice of values for the parameters. Thus we are not groping in complete
darkness; we generally have a good idea of where to start and how to change
the values to obtain the desired effects.
Nevertheless, as described before, fixing these values is a long and
tedious process in practice. The goal is the creation of an input file,
to be fed to the program upon its execution, which in turn results in an
image. The process in practice consists of sitting in front of a terminal,
working in a text editor to change the strings in the input file, running
the program with the modified file, inspecting the results, going back
into the editor to make changes, running again, and so forth. I generally
spend the equivalent of about two to six weeks of full time work in this
loop, for each of my finished images.
But it is important to note that the procedure isn't quite as neat and
sequential as I've presented it to be so far. These first two stages are
not really so distinct--while I am refining the parameters to the functions,
I am generally simultaneously developing, extending and refining the functions
themselves. Since the ultimate theorem proved is determined by both the
axioms and the rules of production, we naturally massage both the axioms
and the rules more or less simultaneously as we develop that theorem into
the image we desire. Furthermore, even the author of the formal system
would not generally care to be confronted with the need to explicitly specify
every
single parametric value in the model in the input file--there are simply
too many hundreds of them. For this reason, many of the axiomatic values
are hard coded as constants in the program and thus are not part of the
input file. (This constitutes poor programming practice, from a computer
science standpoint, but is nevertheless necessary from a practical, user's
standpoint. ) Thus the separation of axioms into input and rules
of production into program is not very precise. It would actually be easy
to be very thorough about so partitioning the system, but in practice it
is neither necessary nor desirable.
4. 1. 3 Deriving the Theorem: Epigenesis
Once we have a set of production rules and axioms--a complete formal system--we
may proceed to derive a theorem, to create an image. Again, this means
firing up the program and running it with the given input file. Execution
time for the program varies widely for my own images, from a minimum of
about a minute to a maximum of several weeks. This at a rate of tens or
hundreds of millions of operations per second
[7]--there
are obviously many, many steps in the derivation of the theorem, far more
than any human being could ever hope to perform or even follow.
Again, each of these operations (other than, perhaps, memory accesses)
represents a transformation to a string: One sequence of ones and zeros
is translated, deterministically, into another. The sum total transformation
is that of translating the input file into an image, an image that may
represent self-expression in an artwork to the person orchestrating the
execution of the program.
The formal system embodies the aesthetic judgment of the artist; those
judgments are implicit in its construction. Execution of the program, derivation
of the theorem, corresponds to the epigenesis discussed by Verostko [17]
and Waddington. [18] A successful result reflects the artist's aesthetic
judgment and may represent self-expression for the artist, derived through
deterministic mechanism. Again, this juxtaposition of determinism and free
will is at the heart of what makes the process interesting, from a philosophical
standpoint. Determinism ultimately precludes free will, yet here it is
used as the vehicle of expressing free will and the latitude for expression
of individual judgment which free will grants.
4. 1. 4 The Loop of Scientific Discovery
Gregory Nielson points out [11] that this process embodies the basic loop
of scientific discovery: One posits a formal model, observes the behavior
of the model in comparison to Nature, then refines the model and makes
further observations, proceeding in an iterative loop. Perhaps the main
difference between mainstream science and this practice in computer graphics,
is the time required for a single iteration of the loop: For a scientist,
it may be decades, even a lifetime or longer, whereas in computer graphics
it is typically measured in minutes.
4. 1. 5 The Role of Intuition
Both science and art are ultimately driven by intuition. No scientist derives
potent models of Nature through exhaustive search of all the possibilities
provided by first principles. Neither does any mathematician originally
get to the proof a hard theorem by simple extrapolation of logical principles.
Rather, they both retrofit their (originally) intuitive
conjectures
with a deterministic logical derivation to advance them to the state of
logical conclusions. These logical derivations then become what both mathematics
and the physical sciences base their clams of irrefutable legitimacy upon.
And indeed, when well-formed, these arguments are (logically) irrefutable
and because of this, when they are fully comprehended they may have a truly
compelling and seductive character of somehow reifying, or at least reflecting,
the self-evident design of the universe.
[8]
But
if not for the role of
intuition in positing the original conjecture
and in formulating the logical derivation, computers would immediately
leave us all in the dust, intellectually, because we could program them
to do the same far faster and more accurately than we humans. Curiously,
though--and to the great detriment of the field of "artificial intelligence"--it
turns out that, ultimate expositions in deterministic proof notwithstanding,
no mathematician or scientist can explain exactly
how they originally
conjectured the result, or even how they arrived at the formal derivation
finally presented. No, in the creative process scientists, mathematicians,
and artists all rely on intuition to the same degree and in exactly the
same way. It is in only aspects of their final respective products that
they so differ: Scientists' and mathematicians' final product is the logical
edifice itself; the artist's final product is a physical object or temporal
event,. the accurate apprehension of which is often highly dependent on
dynamic intangibilities such as cultural context.
The point is, none of us knows precisely how to get where we want to
go a priori, but we all conjecture worthwhile goals and eventually
intuit some path that indeed gets us to our desired ends. Such is the magic
of human intelligence, and this is what continues to distinguish us from
any "artificial intelligence" yet devised.
4. 1. 6 The Role of Serendipity
Finally, we must note the role of serendipity in this formal process. The
fact is, we don't always know exactly what the results of our derivations
will be, and we can't realistically expect to always be able to accurately
foresee the behavior of our deterministic models (the emerging science
of chaos is making that abundantly clear).
Serendipity emerges from the unforeseeable, as with random models; from
the unforeseen, as with a model that has not yet been subjected to thorough
intellectual scrutiny; and from errors and mistakes, as with typos and
program bugs. Each of these factors has played an important role in the
genesis of my own images. Plate 1, for example,
did not come from a preconceived idea for a visual composition. Rather
it came from the unforeseen, or a sort of bug: I had moved the program
that I expected to generate a thoroughly familiar mountain range, to another
computer. This new computer had a different random number generator, which
I had not foreseen in writing and porting my program. Thus when I ran the
program I was confronted with a wholly unexpected landscape, which serendipitously
harmonized with the large moon I had put in the sky, but not yet scaled
own to a reasonable size. Perhaps every artist can tell similar tales,
but here it is important to see that, though we work through a formal,
deterministic process we are still in an intimate dance with chance, the
unknown, and the unpredictable.
4. 2. Interpreting the Metarepresentation
As I said before, the theorem we derive is nothing more than a string of
symbols in the computer's memory. Nothing tangible or image-like about
that, yet. But we do intend an image, and we have (thankfully) a preexisting
machinery of interpretation for that metarepresentation. I will now outline
that machinery, and sketch how that machinery is currently woefully inadequate
to the creation of works of art. This, too, is a symptom of immaturity
of the process and medium, and will change for the better with time.
The problem at hand is how to map the formal metarepresentation, i.
e. , the string or sequence of numbers, to a certain appearance in a physical
manifestation. Obviously, we have enormous latitude in this transformation,
as the metarepresentation has no intrinsic meaning: It is merely the deterministic
result of applying a series of abstract transformations to some input symbols;
there is no meaning in that other than what we (more or less arbitrarily)
ascribe to it. [9] Also obviously,
we always had a certain interpretation in mind for the result, throughout
the process.
Unfortunately, when we leave the idealized, uncertainty-free world of
formal logic and its embodiment in the computer to enter the "meat" world
of physical manifestations, we lose the grace and precision of Boolean
digital representation and enter the fickle, imprecise, and heinously ill-defined
world of things analog, physical, and continuous. The real, "analog" world
is far less well behaved than the formal and deterministic world in which
have been dwelling. We face a whole new, different, and largely unrelated
set of problems, problems usually without the clean, irrefutable solutions
we've been using. This is the world of color monitors, color printers,
and photographic reproduction. This is where we do well to hand our theorem
over to the artisans skilled in working with such things, and beg, cajole,
plead with and threaten them to do our bidding.
Such is the real world, with which our abstract idealizations must eventually
interface.
4. 2. 1 Numbers as Colors
We have a huge string, usually of hundreds of millions of symbols, or
megabytes
of data, which we wish to interpret as a picture. "How?" one might ask.
Well, again fortunately, there are conventions for this interpretation
that we can follow to make our lives easier.
The primary convention is to regard the string as a sequence of numbers,
usually comprised of eight 0/1 symbols or digits each. Such an eight bit
string can, by logical and mathematical convention, encode a single number
between 0 and 255, inclusive (those 256 values correspond to the 28
possible distinct combinations of eight ones and zeros). According to the
tristimulus
[6]
model of human vision, we can encode all perceptible colors into combinations
of exactly three primary colors. [10]
By
more or less arbitrary convention, we may interpret our string of eight
bit numbers as representing consecutive triplets of eight bit values for
those primary colors. Thus we know what the derived string "means": It
is a sequence of color values for pixels (pixels being the atomic
colored dots of which our final image is composed). These color values
proceed in a canonical order, as do the pixels they are meant to represent.
(There is a wide variety of standard digital image file formats which specify
the actual form and sequence of data elements, such as GIF, TIFF, TARGA,
etc. , but they all simply represent different conventions for encodings
of the same information. )
This interpretation is arbitrary, but then so is
any interpretation
of an intrinsically meaningless formalism. By being as specific as we can
be about the intended meaning or interpretation of the metarepresentation,
we take on another arbitrary set of constraints that greatly simplify our
task.
4. 2. 2 The Finite Number of Possible Outcomes
As each pixel is represented by three eight bit numbers, it can have exactly
one of 2
8 x 2
8 x 2
8 = 2
24 =
16 million values. If we have, say, 2
20 = 1 million pixels in
the image then the entire image can take on exactly one of 2
24
x 2
20 = 2
44 values. While 2
44 is a very
large number, it is finite. Thus, at a given number of pixels (or image
resolution) and a given number of possible colors, there is a large but
finite number of pictures that can be represented.
[11]
The
actual number will be considerably less than 2
44, of course,
as no human observer would be able to distinguish between the different
visual representations of many slightly different metarepresentations.
We can then view our elaborate logical formalisms and derivations as
simply selectors that choose for one out of a truly vast, but finite, set
of possible outcomes. That this set exists, perfectly defined a priori,
adds to the sense that this is all "found art" that exists, and always
has existed, in the immutable formalism of that predefined set. The simplicity
of the definition of that set--as all possible combinations of 244
ones and zeros--is part of the compelling beauty of the mathematical logic
that underlies the artistic processes we are illuminating here.
4. 2. 3 Additive vs. Subtractive Color
Another factor that distinguishes working with the computer from most other
visual media, is that we work in an
additive colorspace, versus
the more familiar
subtractive colors. The difference is that when
using pigments, one is
subtracting color energy out of the impinging
light that illuminates the work. If there is no illumination there is no
visible work, and presumably the optimum illuminant is white light, as
it contains all the colors in equal proportions to start with. In the subtractive
model, a red pigment absorbs the green and blue energy in a white illuminant,
and reflects the red.
In computer graphics, we start with a dark (optimally, black) surface,
and add in the color energy we desire. Thus a red area is simply
made to emit red light, and the work is visible in complete darkness (and
conversely, may be hard to see clearly in a brightly lit environment).
This convention came about because the standard output device for computer
graphics is a television monitor, as opposed to a canvas or sheet of paper.
The main difference between additive and subtractive color, is that
the primary colors of the two systems are complementary. In subtractive
color (contrary to what you were taught in grade school), the primaries
are magenta, yellow and cyan. In additive color, they are red, green, and
blue. Thus, for instance, in additive color we must learn to think of yellow
as a sum of red and green (not immediately obvious), and brown as a dim
version of a reddish orange.
We also find that images developed on the luminous monitor may not
be nearly so striking when mapped to a subtractive medium. Plate
1 is one of the few examples in my own experience, that looks fairly
good in both media--though there is a magical luminous quality on the monitor,
which is missing in a reflective print.
There is a hard copy solution to this: back-lit transparencies. Unfortunately,
these are quite expensive to produce: The light box alone can cost several
hundred dollars (and be ugly to boot) for good-sized print. Back-lit transparencies
to have one significant advantage over reflective prints, however: The
computer image's inherent lack of surface detail, as in the impasto of
a painting, is obscured as one's attention is simply not naturally drawn
to the physical surface in a luminous display.
4. 2. 4 Archival Reproduction
Color reproduction from digital data is a difficult problem. It seems unlikely
that a television monitor would be accepted as an artwork by collectors
or the art consuming public. Monitors are large, heavy, low resolution,
and, to face facts squarely, they look big TVs and not like something to
hang on your wall. The market is, and will remain for some time to come,
for (thin) two-dimensional images on a surface, like a painting or a print;
not for four inch deep, ungainly light boxes with dangling power cords,
and certainly not for a big, ugly, expensive, high quality video monitors.
Thus we face the problem of making high quality reflective prints of
the artworks, which both the artist and the collector can be happy with.
Achieving the artist's satisfaction may require a large investment of time
and money on the his or her part, to find a printing house to produce such
objects. The artist can expect to spend several thousand dollars on this,
and what is produced is not generally a one-of-kind object, but a series
of prints. This affects the market for the work; it is not like a painting,
but more at a lithograph or photographic print series.
The second criterion, making the collector happy, complicates the reproduction
problem further. Serious collectors require archival artworks--pieces
that can be expected to last 100 years, without significant fading or other
such degradation. This rules out color photographic prints, none of which
are considered archival. (Gloss Cibachrome prints are considered to be
semi-archival, i. e. , they may last about 50 years; no backlit transparency
even comes close, due to the high, UV rich light levels in a light box.
) What this leaves us with, at the time of this writing, is four
color offset printing. Such prints can be made on acid-free paper, or at
very high (400 dot per inch) line screen resolution using carbon pigments
on a polyester substrate. The former is the equivalent of a quality lithographic
print; the latter is superarchival, with a life expectancy of about 500
years, but is very expensive and constrained to modest physical dimensions.
These problems mean, in practice, that color reproduction is largely
an unsolved problem. It is not realistic to expect the artist to be able
to sink several thousand dollars into each finished work, as artists are
notoriously indigent. Thus I for one consider myself to be, so far, an
artist without a product.
4. 2. 5 What is the Product?
Given that there were a product, we face the well known question in computer
art: What exactly
is the "product"? Is it an object, such
as a color print? Is it the metarepresentation, the image data?
Is it the formal system? Or is it the formal system plus its machinery
of interpretation, i. e. , the program, the input, and the computer that
runs it?
Of all of these possibilities, the only reasonable one is the first:
The product is some tangible hard copy object or print. The metarepresentation
is not particularly valuable as it is exactly reproducible, due to the
determinism of the process that creates it, and because it is so difficult
to translate into an art object. The product cannot be the formal system--I
have years invested in the program that creates all of my images; I would
not sell exclusive rights for its use for any price. And even if I did
I am capable, in principle at least, of recreating an exactly equivalent
formal system, and indeed upon a sale of this sort I would immediately
have to do my best to do exactly that, just to be able to get back to work
again. That would no doubt lead to disgruntlement among the collectors
of my work. Finally, it is absurd to propose the last option, that the
work consists of both the program and the computers that run it: Even if
I were to give the software away for free, the hardware cost could reach
into six figures and that hardware would have no special value whatsoever
to the collector, as the computers I use are always off-the-shelf units,
exactly replaceable by the manufacturer. That is, it has absolutely no
uniqueness associated with the image--it would be like including the paints,
paintbrushes and easel in the sale of a painting; they are of no use to
the collector, are generally quite replaceable to the artist, and are of
no direct relevance to the finished piece.
4. 2. 6 What Constitutes the Original Work?
A final image is typically rendered at a very high resolution: perhaps
three hundred dots per inch, at a final print size of two to four feet
on a side. The television monitor on which the images are developed can
display at most about two thousand pixels (dots) on the horizontal axis,
and typically closer to one thousand. Therefore the image that is sent
to the printing device, regardless of what technology or medium that device
is based on, is usually of much higher resolution than can ever be previewed--the
first preview is of what comes off the press, so to speak. Therefore, given
that the
product is the final physical print, that print is also
the
original in a very real and significant sense, as there never
existed any visible, full resolution representation or even metarepresentation
prior to the final print. This may have consequences to the value of the
print, in the eyes of collectors.
5. Discussion
Let us now briefly discuss the implications of this new process.
5. 1. What Role Intent and Understanding?
As I have pointed out, the computer can be quite readily be used as a novel
canvas, paint, and paintbrush, for use as with prior two-dimensional media
for the visual arts. Used that way, the resulting works will be essentially
"of the hand," and thus part of the existing continuum of two dimensional
media.
When the artwork is algorithmic, issuing directly and unmodified
from a formal description, it becomes more interesting. When the algorithm
is deterministic, it becomes more interesting still (after all, artists
such as Sol Lewitt have produced non-deterministic algorithmic artworks
for some time now).
But I maintain that deterministic algorithmic artwork is only truly
significant when the artist is also the author of the formal system, and
can claim to understand it thoroughly and to have intended (modulo serendipity)
to create the result produced. Thus artworks created by someone else using
my software would lack conceptual significance, even if they were more
aesthetically sophisticated. If Picasso had invented a "Picasso engine,"
and others used it to create Picasso-like works, these works would simply
would not be quite the same as an original Picasso, after all--even if
others were able to "improve upon" Picasso.
The artist can only really claim to have accomplished self-expression
through formal logic, when he or she authored, for that specific purpose,
the formal system through which the expression is obtained.
5. 2. What of Turnkey Systems?
What then, of turnkey software for creating computer art? There are
many powerful programs becoming available that unlock the substantial potential
of the digital medium, and there will continue to be ever more, of greater
sophistication, power, and novelty. Programs such as Adobe Illustrator
and Photoshop are revolutionizing the way many artists, and perhaps most
designers, work.
There is, and will always be, a role for such systems. Indeed, the vast
majority of practicing "computer artists" will always use such "canned,"
preexisting software. It would be absurd to propose that all, or even many,
artists pay the substantial dues required to get up to speed in this peculiar
process I am describing. No, this process will always exist and be practiced
on the fringes--there will never be more than a handful of people who are
qualified to use this process, requiring as it does an extensive background
in art, science, mathematics, logic, and computers.
Let me use an analogy: there have been great drivers, for almost as
long as there have been cars. But these drivers are rarely the builders
of the cars they drive. Indeed, no single person can expect to build an
automobile of any sort, much less a race car, without the help of many
others (no more can I expect to build the computers I use, or to have invented
every technique I apply). But a good driver, whose vehicle is largely the
result of their own creative vision, would always be a special competitor,
though they might never turn in the fastest time.
There will always be room for the virtuoso users of tools provided by
others, and such users can always be expected to predominate the field
of performers. The greatest violin maker is not the greatest violinist.
Likewise, there will always arise, here and there, now and again, visionaries
with "the madness of the poet" who will create their own tools and do with
them what might never have occurred to others. And there is, at least,
always some significance to being the first to have done something of interest
and of significant difficulty. This process I describe is probably best
characterized as such an undertaking.
5. 3. The Role of Traditional Media
New as it may be, this process certainly does not stand outside precedence.
As the result is a two-dimensional work, all the rules and discipline of
two-dimensional art apply, most saliently those of visual composition and
color usage. As the modeling is done in three dimensions, rules of form
and lighting also apply. When animation is undertaken, the rules of cinematography
will come into play. When we produce a tangible product, any sort of physical
manifestation, all the rules and practice of the medium in which that product
is executed will apply. We cannot presume to create a new art form in a
vacuum; we will need to borrow and appropriate everything we can use, from
what has come before.
We may, however, need to invent a viable new medium in which to represent
the product. It may be that computer art as a whole will not truly come
into its own, until some essentially new display technology, such as large,
bright, flat panel color displays or laser projectors, comes into common
usage. Immersive VR technology, for instance, holds considerable promise
as the unique, new medium for the apotheosis of computer imagery.
5. 4. Mastering the Process and Medium
As painting has been mastered, so must this new process. Painting, photography
and sculpture did not reach maturity overnight; neither can we expect computer
art to do so. The fact is, the computer artwork has not yet been produced
which could stand a side by side comparison with, say, a great van Gogh
painting. My own best image would pale, stood beside a Bierstadt. The austere
beauty of the underlying formalism denies computer generated imagery access
to the fascinating, continuous behavior of such a medium as oil paint--there
is simply nowhere near the amount of information in a standard digital
image file, as there is in a well executed painting. The range of scales
over which a good painting is interesting is also generally much larger
than that for a computer generated image, fractals notwithstanding. There
are at least two scales at which a good painting is interesting: the large
scale, where visual composition predominates, and the small scale, where
surface texture, impasto, juxtaposition of colors (as with Seraut) in a
stroke, etc. , provide another visual richness. We will need to include
such complexity, or simply find another grounds for legitimacy with as
great an aesthetic significance, before we can call our works truly fine
art.
One interesting and useful distinction was drawn by Ansel Adams, who
posited the analogy of the negative as the score, and the print as the
performance. In this analogy, we currently have the capability in this
new process to produce the negative or the score, almost literally. But
we currently lack the means of translating this score into an impressive
performance. That is the challenge of creating the final artwork.
One wonderful distinction of the process I've presented is its simultaneous
use of both analytic and intuitive thinking. Sitting at the computer creating
an image, one must rapidly switch back and forth between the "right brain"
mental faculties required to assess aesthetic issues and the "left brain"
analytic processes required to deal with the logic-based machinery of production.
This is certainly an unusual way to go about producing a visual artwork;
its closest analogue may be in musical composition.
6. Conclusions
This new process may mark a truly novel event in the history of creative
process in the fine arts. Provided, of course, that the artist intends,
understands, and can in some valid sense take responsibility for, the formalisms
behind the product. I am claiming that a number, along with the appropriate
(and well defined) interpretation machinery can represent artistic self-expression,
that this number can be derived deterministically, and that the method
of this derivation adds conceptual significance to the result.
Be careful to note that I am not claiming that the machine is self-expressing.
A computer has no more aesthetic ability than any inanimate object, and
indeed, it can be more refractory than most. The expression is the human
artist's; the computer is the tool through which the artist makes his or
her statement, it is at best an idiot savant assistant.
Biographically, I wish to add that it is fortunate that landscapes are
my personal predilection for self-expression. In painting and photography,
I have always preferred landscapes. When I entered the field of computer
graphics research, landscape modeling and rendering were in their infancy;
it has been my pleasure to substantially improve the state of the art in
such through the course of my doctoral research [8] at Yale University
under Benoit Mandelbrot, the father of fractal geometry. In a remarkable
bit of serendipity, I appear to have been the right person in the right
place at the right time. There was a narrow temporal opportunity, that
I happened to precisely meet; had I shown up a few months or years earlier
or later, the opportunity would not have existed.
6. 1. Constraints and Opportunities
Let me quickly recap the significant constraints and opportunities of this
new process, as I see them.
6. 1. 1 Working in Three Dimensions
While sculptors and stage designers have worked in three dimensions for
millennia, the peculiar way in which we do so in this new process is significantly
different. We differ at least in scale: we are creating landscapes, entire
planets, and even, potentially, a finite synthetic universe. The challenges
are different, and appropriate practice will therefore undoubtedly be different.
Thus we will need to invent and refine some new methodologies. While landscape
rendering has as rich a precedence as any other area of visual art, prior
landscape artists were not generally responsible for creating their entire
scene, in full three dimensions. Soon, when interactive exploration of
our scenes becomes possible, we may also find ourselves confronted with
responsibility for guiding, through whatever means we find artful, the
explorations of visitors to our worlds.
6. 1. 2 Algebraic Color
While we cannot and should not expect to redefine the rules of color usage,
neither can we manipulate color in the ways which visual artists are accustomed.
First, we work in the unfamiliar additive color space, where heuristics
for mixing colored pigments are either inverted or simply invalidated.
Second, there is no physical system in which color interacts--it is all
simply a model. Nothing happens at all, except for what we explicitly specify.
We may seek to have those specifications mimic as closely as possible the
behavior of the real world (a very hard thing to do, in general) or we
may bend or break such laws in our system. In any case, the specification
and interactions of colors on surfaces is couched in the mathematical language
of algebra--certainly an unfamiliar way of dealing with color for the average
studio artist. Colors are all numbers; they mix by the arithmetic operations
of addition, subtraction, and multiplication, and they are often modulated
by exponential operators (such as
gamma correction).
Color theory for computer graphics is often elegant, and is quite internally
consistent. But it is not something familiar to the average artist.
6. 1. 3 Proceduralism
Proceduralism, the practice of encoding behaviors in formally defined,
deterministic functions, is at the very heart of this process. Strict adherence
to this practice is whence the intellectual significance we claim for the
process emanates. We can gain a wonderful elegance in this approach, as
with the fractal models that can so succinctly describe manifestations
of potentially unbounded visual complexity. It is a significant challenge
to maintain the discipline of using only such relatively simple logical
constructs for visual expression, and it is a significant constraint to
work only with global parametric control.
There can come great benefits from such discipline, though. Imagine
a procedurally defined planet, or array of planets, which possesses a wealth
of detail everywhere, detail that the artist did not explicitly and laborious
specify, but which issues directly and automatically from the functions
from which the model is composed. Plates 2 and 3
illustrate an example of such a model: Plate 2 shows an entire planet and
Plate 3 is a landscape that is actually physically situated on the face
of that planet! The animation "Spirit of Gaea," currently in production,
will serve as a proof of this concept. In this animation, the point of
view will move in from deep space, up to the planet, down through its atmosphere
to its landscape, up very close to the terrain (the equivalent of a few
feet away), then straight back out into deep space. This will all be accomplished
with a single procedural model, and while rendering will be far from real-time,
it is only a matter of engineering to get to where we can move around the
planet (and its universe) interactively, at will. That will be an unprecedented
development.
6. 1. 4 Ambiguities in Logic and Art
Our use of formal logic for self-expression entrains with it the precision
and lack of ambiguity of mathematics and science. Lack of ambiguity is
not familiar, or even desirable, in the arts. But such precision in the
creative process does not in any way preclude the kind of deliberate ambiguity
that lends depth and interest to art. Rather, it stands beneath, as an
unusually solid foundation for artistic creation. Its use allows scientific
models to mapped into creative opportunities--something that I personally
find an exciting undertaking, having always been fascinated with the beauty
of such models in their own right. Finally, our basis in formal logic entrains
with it the intellectual depth of the philosophical discipline of logic
and the mathematical models of the sciences. These are deep conceptual
roots indeed, which we have only begun to tap.
6. 2. Some parting Questions
I will conclude with some questions, questions that do admit to immediate
answer.
How do we obtain self-expression through formal logic?
I claim to have done so, but I can no more tell you how than the average
painter can tell you precisely how they painted a particular painting.
I hope that, with my own artworks, I have shown it to be possible, and
I fervently hope to be surpassed by future practitioners.
How do we know when we have?
If my claim is valid, it should be verifiable. There are only two
ways to do this: Ask the artist, and ask yourselves, the audience. Success
or failure will be found to be a fickle thing.
So what's new here?
I have attempted to illuminate that in this essay, nevertheless
I feel very incomplete about it. My own analysis of this event is preliminary;
I may spend the rest of my days fleshing it out. It seems to me that, as
is typical in new areas of intellectual inquiry, the ideas formulated and
presented to date are perforce preliminary and vague. Certainly my own
arguments could benefit from a deeper foundation in the history of art.
But I hope that the time is ripe to begin to expound them, that they might
be honed or discredited through the dialectic.
Is it important?
Time, of course, will tell, at least in the eyes of our culture.
Obviously,
I think so. But then, I am primarily trained as a scientist
rather than as an artist, and I am certainly not an authority on art history.
Nevertheless, I do know enough to recognize and put my professional reputation
at stake, that something big is going on here. Unfortunately, the requirements
for a full appreciation are backgrounds in mathematical logic, natural
sciences, and computer science, as well as aesthetic training and sensitivity.
Thus the audience who can apprehend, and perhaps be impressed by, these
arguments is necessarily small.
Will it fly?
Again, time will tell. If I continue to suffer occasional visual
inspiration, I may help bring it to maturity as an art form. I am certainly
counting on others to help, and hopefully to soon create works that will
make my own appear crude and preliminary. Fortunately I am not alone in
my views or my efforts. To quote Judson Rosebush [12]:
In practice, proceduralist computer art is among the most contemporary
products of our culture, and will increasingly be appreciated as a major
art movement by this and future generations.
|
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