An essential element of
10 PRINT is randomness; the program could not produce its mesmerizing visual
effect without it. This randomness comes by way of
RND, a standard function in BASIC.
been part of the BASIC lexicon since the language’s early days at Dartmouth. What the
function does is easily characterized, yet behind those three letters lie decades, even centuries, of a history bound up in
mathematics, art, and less abstract realms of culture. This chapter
explores randomness in computing and beyond. The role of randomness
in games, literature, and the arts is considered, as are the
origins of random number generation in modern mathematics,
engineering, and computer science. Also discussed is the
significance of “pseudorandomness”—the
production of random-like values that may appear at first to be
some sad, failed attempt at randomness, but which is useful and
even desirable in many cases. The chapter argues that the maze
10 PRINT is entwined with a complex history of aesthetic and utilitarian
coin flips and other calculations of chance.
Since a random occurrence is “hap,” the root of happy, it might seem that “random” would have a happy etymology. But this is not so. In centuries past, before the philosophers and mathematicians in the Age of Enlightenment sought to rationalize chance, randomness was a nightmare. Likely ancestors of the word “random” are found in Anglo-Norman, Old French, and Middle French and include randoun, raundun, raundoun, randon, randun, and rendon—words signifying speed, impulsiveness, and violence. These early forms are found beginning around the twelfth century and probably derive from randir, to run fast or gallop (“random, n., adv., and adj.” 2011). Bumper stickers implore drivers to “practice random acts of kindness,” but only because people in our culture fear random acts of violence so much that this phrase has become ingrained and can be punned upon—and at a deeper level, perhaps, because the speed and violence of other vehicles are to be feared. While in recent days it might be harmless to encounter “a random” sitting in the computer lab exploring a system at random, a “random encounter” centuries ago was more likely to resemble a random encounter in Dungeons & Dragons: a figure hurtling on horseback through a village, delivering death and destruction.
Only recently have the meanings of the word
“random” coalesced around science
and statistics. The history of this word is strewn with obsolete
meanings: the degree of elevation of a gun that maximizes its
range; the direction of a metallic vein in a mine; the sloping
board on the top of a compositor’s frame where newly arranged
pages are stored before printing. These particular randoms kill
opponents, create wealth, or help assemble texts. The
RND command in
10 PRINT selects one of two graphical characters—a kind of
textual composition that recalls the last of these meanings of
10 PRINT’s random is a flip or flop, a symbol like a slash forward or backward
(but fortunately less fearsome than the
horseman’s random slash). The program splays
each random figure across the screen using the
on the Commodore 64 may seem remote from these early meanings of
“random,” there are, beneath the surface, connections to speed, violence, devastation, and even
GAMES OF CHANCE
Life itself is full of randomness and the inexplicable, and it is no small wonder that children and adults alike consciously incorporate chance into their daily lives, as if to tame it. Games of chance are one of the four fundamental categories of games that all humans play, according to the French cultural historian Roger Caillois. Whereas agon are competitive games dependent upon skill, games of mimicry are imaginative, and ilinx are games causing disorder and loss of control, the alea are games of chance. Craps, roulette, the lottery—these are some of the games in this category, ones with unpredictable outcomes. Taken from the Latin name for dice games, alea “negates work, patience, experience, and qualifications” (Caillois 2003, 17) so that everything depends on luck. In Latin, the āleātor is a gambler; in French, aléatoire is the mathematical term for random.
The Appeal of the Random
In his Arcades Project on nineteenth-century Paris, Walter Benjamin devotes an entire section to dice games and gambling, a curious assemblage of notes and excerpts from sources ranging from Casanova to Friedrich Engels. “Gambling,” Anatole France is quoted as saying, “is a hand-tohand encounter with Fate” (Benjamin 1999, 498 [O4A]). Every spin of the roulette wheel is an opportunity to show that fate smiles upon the player.
Fortunes rise and fall in the blink of an eye, the roll of the die, or the cut of the cards. Every gambler knows this, accepts it, and even relishes it.
The allure of gambling—and more generally, the allure of chance in all games—rests on uncertainty. Uncertainty is so compelling that even otherwise skill-based games usually incorporate formal elements of chance, such as the coin toss at the beginning of a football game. As Katie Salen and Eric Zimmerman put it, uncertainty “is a key component of meaningful play” (2004, 174). Once the outcome of a game is known, the game becomes meaningless. Incorporating chance into the game helps delay the moment when the outcome will become obvious.
Consider the case of George Hurstwood in Theodore Dreiser’s Sister Carrie, first published in 1900. Driven by “visions of a big stake,” Hurst-wood visits a poker room:
Hurstwood watched awhile, and then, seeing an interesting game, joined in. As before, it went easy for awhile, he winning a few times and cheering up, losing a few pots and growing more interested and determined on that account. At last the fascinating game took a strong hold on him. He enjoyed its risks and ventured on a trifling hand to bluff the company and secure a fair stake. (Dreiser 1981, 374)
What is intriguing about Dreiser’s account is that it is only when Hurstwood’s good fortune wavers that his interest in the game grows and he begins to enjoy it. Losing a few hands makes a winning streak that much more thrilling. “A series of lucky rolls gives me more pleasure than a man who does not gamble can have over a period of several years,” Edouard Gourdon avers in one sexually charged extract in the The Arcades Project. “These joys,” he continues, “vivid and scorching as lightning, are too rapid-fire to become distasteful, and too diverse to become boring. I live a hundred lives in one” (Benjamin 1999, 498 [O4A]).
Unlike the early, purely malevolent associations of randomness described in the beginning of this chapter, randomness here involves the masochistic interplay between pleasure and pain. There is also a monumental compression of time: a hundred lives in one. Anatole France calls gambling “the art of producing in a second the changes that Destiny ordinarily effects only in the course of many hours or even many years” (Benjamin 1999, 498 [O4A]). Benjamin himself declares that “the greater the component of chance in a game, the more speedily it elapses” (512 [O12A,2]). Waiting, boredom, monotony—these frustrations disappear as “time spills from his [the gambler’s] every pore” (107 [D3,4]).
Forms of Randomness
Perhaps Benjamin describes games of chance with a bit more whimsy than is useful for critical discussion of the role of randomness in culture. Although words like randomness, chance, and uncertainty may be casually interchanged, not all forms of chance are actually the same. To highlight distinctions between various forms of chance, consider the anthropologist Thomas Malaby’s account of gambling in a small Greek city on the island of Crete—an appropriate site of exploration, given alea’s Greek etymology. Malaby’s goal is to use gambling as a “lens through which to explore how social actors confront uncertainty in . . . key areas of their lives” (2003, 7). How do people account for the unaccountable? How do we deal with the unpredictable? And what are the sources of indeterminacy in our lives?
Malaby presents a useful framework for understanding indeterminacy based on four categories. The first category is formal indeterminacy, or what is commonly referred to as chance. This is any form of random allotment, which often can be understood and modeled through statistical methods. Malaby argues that the ascendancy of statistical thinking in the social sciences has so skewed our conception of indeterminacy in gambling (in particular) and in our lives (in general) that formal indeterminacy has become a stand-in for other types of indeterminacies. The second category is social indeterminacy, the impossibility of knowing or understanding someone else’s point of view or intentions. A bluff is a type of social indeterminacy. The third category is performative indeterminacy, that is, the unreliability of one’s own or of another’s actions, say a fumble in football game or misreading the information in plain view on a chessboard. Finally, the fourth category Malaby describes, cosmological indeterminacy, refers to skepticism about the fairness and legitimacy of the rules of the game in the first place at a local, institutional, or cosmological level. Suspicion that a game is rigged, for example, is concern about cosmological indeterminacy (Malaby 2003, 15–17).
Privileging of the stochastic principles of formal determinacy
means that players, scholars, and even programmers dismiss social
and performative indeterminacies altogether. In the case of
thinking about social indeterminacy can reveal several new layers
of randomness, such as the idiosyncratic line numbers in the 1982
and 1984 versions of the program. Likewise, understanding
performative indeterminacies may account for the textual variants
of the program, for example, the version that appeared in the
online publication Commodore Free
that will not actually execute as printed (Lord Ronin
Cosmological indeterminacy is perhaps the most difficult form of
indeterminacy to apply to
10 PRINT. The rise of the scientific method can be seen as one enduring
struggle to impose a more rational view upon the world and to
abolish cosmological indeterminacy. From Aristotle to Galileo to
Newton, classical mechanics defined the universe as an organized
system without random actions. Einstein declared that
“God does not play dice with the universe.” Yet, as a closer examination of randomness
on the Commodore 64 will reveal, there is evidence that randomness
on this computer—and indeed, on any computer—is fundamentally
“rigged” in a way that echoes Malaby’s idea of cosmological indeterminacy.
Randomness and chance operations are so necessary to daily life,
well beyond the realm of games, that randomness itself is framed as
fixed, repeatable, and knowable.
RANDOMNESS BEFORE COMPUTING
Just as the different categories of indeterminacy in games are
often grouped together and called “chance,” so too in the visual arts,
music, and other aesthetic practices is the word
“chance” used instead of “randomness.” In his chapbook
Chance Imagery, the conceptual artist George Brecht (1966) describes two distinct
types of chance operations by which an artist might create a work:
“one where the origin of images is unknown
because it lies in deeper-than-conscious levels of the
mind” and a second “where images
derive from mechanical processes not under the
artist’s control.” The first
definition describes the work of the Surrealists and Abstract
Expressionists, who sought to allow subconscious processes to
dictate their work. The second definition is reminiscent of Dada
and closer to the typical concept of randomness in computing; it
describes the mechanical operations of the artists most directly
10 PRINT. These two senses are worth noting because it is difficult to pull on one of the two senses of
“chance” without the other one—the unconscious, in this
case—at least feeling a tug.
The tension between these two chance operations is captured in William Burroughs’s story about a Surrealist rally in the 1920s. Tristan Tzara suggested writing a poem “on the spot by pulling words out of a hat,” and as Burroughs tells it, “a riot ensued” and “wrecked the theater.” In his version of events, André Breton, the leading Surrealist, expelled Tzara from the group, his purely mechanistic chance operation being an affront to the power and vagaries of the Freudian unconscious (Burroughs 2003). Bur-roughs is most certainly conflating several events, and the break between Surrealism and Dada had as much to do with a personality clash between Breton and Tzara as with their approaches to art (Brandon 1999, 127). Bur-roughs himself clearly preferred the anarchic mode of Tzara and famously described a similarly unpredictable mode of composition, the cut-up method, also proposed by Tzara in his 1920 “To Make a Dadaist Poem.” Burroughs explains that “one way to do it” is to cut a page in four quarters and then rearrange the sections: “you will find that it says something and something quite definite” (90). Tzara suggests pulling words blindly from a bag. The generative possibilities of this cut-up technique resemble the collage in art and the montage in film, and have become far more mainstream today than Tzara might have imagined in 1920. For instance, Thom Yorke, the lead singer for the band Radiohead, wrote the lyrics to “Kid A” in 1999 by pulling fragments of text out of a top hat.
Though Yorke employed a type of cut-up method to address severe writer’s block, artistic experimentation with randomness in the early part of the twentieth century can be seen as a response to the sterile functionality of rationality and empiricism wrought by the Industrial Age and as a deliberate reaction against World War I. Consider Marcel Duchamp’s Three Standard Stoppages (1913–1914). According to his description of the piece, Duchamp dropped three meter-long pieces of string from the height of one meter and let gravity and chance dictate the paths of the twisting string downward. Then he adhered the twisted string onto canvas, the shape and length of which he preserved in 1918 in wooden cutouts, creating three new “stoppages” that parodied the supposed rationality of the meter. When Duchamp described his method in 1914, he observed that the falling thread distorts “itself as it pleases” and the final result becomes “the meter diminished,” subverting both the straightness and the length of what commonly goes unquestioned (Duchamp 1975, 141–142). On his use of randomness, Duchamp said, “Pure chance interested me as a way of going against logical reality” (Cabanne 1971, 46).
Duchamp, like the other Dada artists with whom he associated, saw “logical reality” as a failure, epitomized by the horrors of World War I. Satire, absurdity, and the embrace of indeterminacy seemed to the Dadaists to be the most “reasonable” response to modernity. In the words of the Dada artist Jean (Hans) Arp, “Dada wished to destroy the reasonable frauds of men and recover the natural, unreasonable order. Dada wished to replace the logical nonsense of the men of today with an illogical nonsense.” To Arp, individual authorship was synonymous with authoritarianism and random elements were used to liberate the work (Motherwell 1989, 266).
The major twentieth-century composer to explore randomness was certainly John Cage, who was strongly influenced by Duchamp. From Cage’s point of view, random elements remove individual bias from creation; they may be used to reach beyond the limitations of taste and bias through “chance operations.” Cage influenced generations of artists through his compositions as well as through his writing, lectures, and classes. In his text “Experimental Music,” Cage wrote, “Those involved with the composition of experimental music find ways and means to remove themselves from the activities of the sounds they make. Some employ chance operations, derived from sources as ancient as the Chinese Book of Changes, or as modern as the tables of random numbers used also by physicists in research” (1966, 10).
Cage’s method of random composition was to
create a system of parameters and then leave the results to
circumstance. Cage explained, “This means that
each performance of such a piece of music is unique, as interesting
to its composer as to others listening. It is easy to see again the
parallel with nature, for even with leaves of the same tree, no two
are exactly alike” (1996, 11). Random components are
used to transform a single composition into a space of potential
compositions. Over the decades, Cage used an array of techniques to
insert unexpected elements into his compositions. He defines the
range of techniques he and his contemporaries used in the 1958
lectures “Composition as Process.”
There are generally two methods for using random values in music: to define the work at the
time of composition or to allow for variation when the work is
performed. The most obvious use of randomness in
10 PRINT is in the second category as random decisions are made during the
program’s execution—that is, while the BASIC instructions are performed by the Commodore
Within two-dimensional visual art, artists also explored mechanical
random processes for reasons championed by Cage. The eminent
contemporary painter Gerhard Richter provided a simple answer to
this method’s benefits when he said,
“I’m often astonished to find
how much better chance is than I am.” There are
precedents for chance used within visual works dating back to
collage works by Arp from 1916, but the two early works most
relevant in the
10 PRINT are the Spectrum of Colors Arranged by Chance
collage series (1951) by Ellsworth Kelly and Random Distribution of 40,000 Squares Using the Odd and EvenNumbers of a Telephone Directory
(1961) by François Morellet. These works start with an
even grid and fill the grid carefully with elements based on the
algorithms developed by the artists. Kelly uses squares of colored
paper, placed according to a system he designed. He assigned a
number to each color and plotted the numbers on the grid
systematically (Malone 2009, 133). Morellet employed a stricter
system, reading a series of numbers from the telephone book. He
made a grid of 200 vertical and horizontal lines, painting a square
blue if its assigned number is even, painting it red if it is odd.
In both of these artworks and in
the structure of the grid is what makes it possible to focus on the
variability created through the random operations.
A Million Random Digits
The need for large batches of random numbers is so acute that there are standardized collections of them. In Deborah Bennett’s history of humans’ quest for randomness—which she suggests goes as far back as ancient Babylonia (1998, 17)—she highlights one of the earliest and largest sets of random numbers, A Million Random Digits with 100,000 Normal Deviates (135). This series of numbers (figure 40.1) was generated in 1947 from “random frequency pulses of an electronic roulette wheel” by the RAND Project, a research and development think tank that would eventually become the RAND Corporation. The 1955 publication of the series in book form was an important contribution to any study of probability; the book is still in use today. As the forward to the undated online edition of the table notes:
The tables of random numbers in the book have become a standard reference in engineering and econometrics textbooks and have been widely used in gaming and simulations that employ Monte Carlo trials. Still the largest known source of random digits and normal deviates, the work is routinely used by statisticians, physicists, polltakers, market analysts, lottery administrators, and quality control engineers. (RAND Corporation 1955)
Considering its sophisticated origins and uses, A Million Random Digits proposes a surprisingly unscientific method of using the book: “In any use of the table, one should first find a random starting position. A common procedure for doing this is to open the book to an unselected page of the digit table and blindly choose a five-digit number.” The RAND report goes on to somewhat ominously explain that its one million random numbers were originally “prepared in connection with analyses done for the United States Air Force.” Like so many other advances in computing, randomness, it turns out, is intimately linked to Cold War military strategies. In fact, most of the early work on computer-based random number generation was performed under the auspices of the U.S. Atomic Energy Commission see, for example, Rotenberg’s  work in the late 1950s) or the U.S military (see Green, Smith, and Klem’s  work at MIT, done with joint support of the U.S. Army, Navy, and Air Force).
RANDOMNESS COMES TO COMPUTING
RND command acts as the algorithmic heart of
its flip-flopping beat powering the construction of the maze. The
function is as fully specified as any BASIC keyword, but its output
is, by that definition, unpredictable. Mathematicians and computer
scientists don’t think in terms of predictability, though; rather, the standard mathematical treatment
of randomness defines randomness in terms of probability. A random
process generates a sequence of values selected from a set of
possible values according to a probability distribution. In the case of a discrete
distribution (heads or tails, for instance), the distribution
explains how much weight is on each possible
outcome—how likely that value is to
If, for example, one draws a single card from a thoroughly shuffled deck, the probability distribution from which this draw is done is uniform: it is equally likely that any particular card will be chosen. Similarly, random numbers are typically defined as numbers drawn from a uniform distribution over all possible numbers in some range. A difficulty with this definition is that the randomness of a number is defined in terms of that range. Given a number such as 42, it is impossible to tell how random a selection it was. To determine randomness without knowing the means of generation, one must consider a sequence of numbers; knowing the range in which the numbers are supposed to lie or, more generally, the distribution from which they are supposed to be drawn, is also essential.
Digital computers are deterministic devices—the
next state of the machine is determined entirely by the current
state of the machine. Thus, computer-based random number generators
are more technically described as pseudorandom number generators.
The somewhat dismissive-sounding “pseudo” refers to the fact that a
deterministic process (a computer program) is being used to
generate sequences of numbers that appear to be uniformly
distributed. This works well in practice for sequences that
aren’t astronomically long. But eventually, for
long enough sequences, the deterministic nature of a pseudorandom
number generator will be unmasked, in that eventually statistical
properties of the generated sequence will start diverging from
those of a true random process. In an extremely long sequence, for
example, a true random process will generate the same number many
times in a row. A version of
running using a true random process will eventually generate the
regular image in figure 40.4 (and the image in figure 40.5, and
every other possible pattern), while the pseudorandom number
generator in the Commodore 64 will not. Tests for long runs are one
of the many statistical tests used to judge the quality of
pseudorandom number generators.
Quite simply, the answer to this puzzle is that randomness is necessary for any statistical endeavor, any simulation that involves unknown variables. Practically everything involves unknown variables: the meteorological conditions at a rocket launch site, the flow of air under a bomber’s wings, and the spread of an infectious disease. Additionally, there is the movement and halting of traffic, the cost of bread, and the drip of water from the kitchen faucet. Forecasting any of these phenomena requires reckoning with uncertainty, which in turn requires a pool of random numbers. Furthermore, one or two random numbers are not enough. Large-scale statistical calculations or simulations require large batches of random numbers.
John von Neumann was the first to propose the idea of harnessing a computer to generate random numbers (Knuth 1969, 3). It was around 1946 and von Neumann was fresh off the Manhattan Project and soon to begin his lead work on the hydrogen bomb. Seeking a way to statistically model each stage of the fission process, von Neumann and his colleague Stanislaw Ulam first relied on the Monte Carlo method to generate tables of random numbers. These tables, however, soon grew too large to be stored on computers (Bennett 1998, 138–139). Von Neumann’s solution was to design a computer program to produce random numbers on the fly, using the middle-square method. It worked by squaring an initial number, called the seed, and extracting the middle digits; this number was then squared again, and the middle digits provided a new random number (von Neumann 1961). Because each number is a function of the one before it, the sequence, as Donald Knuth explains, “isn’t random, but it appears to be” (3)—that is, it is “pseudorandom.”
COMPUTATIONAL RANDOMNESS IN THE ARTS
To those interested in randomness and expressive culture, perhaps the most intriguing element of Donald Knuth’s magisterial discussion of random numbers appears in a footnote. Knuth recalls a CBS television documentary in 1960 called “The Thinking Machine” which featured “two Western-style playlets” written by a computer (Knuth 1969, 158–160). In fact, three playlets were acted out on national television that day in October 1960, generated by a TX-0 computer housed at MIT’s Electronics Systems Laboratory. SAGA II, the script-writing program behind the mini Westerns, took programmers Douglas Ross and Harrison Morse two months to develop and consisted of 5,500 instructions (Pfeiffer 1962, 130–138). The key to SAGA II was its thirty “switches,” which made “various alternative or branching paths” possible (136). “Among other things,” Pfeiffer observed, “the robber may go to the window and look out and then go to the table, or he may go to the table directly. You cannot tell in advance which one of these alternatives the program will select, because it does the equivalent of rolling a pair of dice” (136).
Even before the SAGA II playlets, there were other literary experiments with randomness and computers. Noah Wardrip-Fruin identifies the British computer scientist Christopher Strachey as the creator of the first work of electronic literature, a series of “love letters” generated by the Ferranti Mark I computer at Manchester University in 1952 (Wardrip-Fruin 2005). Affectionately known as M.U.C., the Manchester University Computer could produce the evocative love letters at a pace of one per minute, for hours on end, without producing a duplicate. The “trick” is, as Strachey put it, the two model sentences (e.g., “My adjective noun adverb verb your adjective noun” and “You are my adjective noun”) in which the nouns, adjectives, and adverbs are randomly selected from a list of words Strachey had culled from Roget’s Thesaurus. Adverbs and adjectives randomly drop out of the sentence as well, and the computer randomly alternates the two sentences. On the whole, Strachey is dismissive of his foray into the literary use of computers, using the example of the love letters simply to illustrate his point that simple rules can generate diverse and unexpected results (Strachey 1954, 29–30). Nonetheless, a decade before Raymond Queneau’s landmark combinatory work One Hundred Thousand Billion Poems, Strachey had unwittingly laid the foundation for the combinatory method of composition by computer, a use of randomness that would grow more central to literature and the arts in the following decades.
Other significant early works involving random recombination had more visible connection to literary tradition and artistic movements. The 1959 “Stochastic Texts” of Theo Lutz combined texts from Franz Kafka with logical operations to produce “EVERY CASTLE IS FREE. NOT EVERY FARMER IS LARGE” among other statements (Lutz 1959/2005). In the next decade, Fluxus artist Alison Knowles and James Tenney, a programmer who worked in FORTRAN, devised A House of Dust. The program’s output combines a regular stanza form and repetition with random variation in vocabulary, and was printed on a scroll of line printer paper for a 1968 chapbook publication (Pearson 2011, 194–203). More than a decade later, Jackson Mac Low made use of the venerable book A Million Random Digits to devise “Converging Stanzas,” which were randomly populated with words from the 1930 850-word Basic English Word List (Mac Low 2009, 236). This poet’s “Sade Suit” similarly used playing cards and A Million Random Digits to rewrite the work of Marquis de Sade (46).
Early Experiments in Computational Art
The 1960s were a time of radical experimentation with randomness in
the visual arts. Even though computers were available at that point
for the exploration of chance operations, they were used in a very
limited way because it was difficult to gain access to the
machines, and there was a general distrust of computer technology
in the arts. The
program is remarkable because it was created later, when these
barriers were far fewer. The Commodore 64 was relatively
inexpensive and accessible. The public image of the computer was
changing from a machine that supported technocracies to a tool for
self-empowerment and creativity. Before personal computers,
calculating machines could only be found in universities and
research labs and, because of their cost and perceived purpose,
they were typically used exclusively for what seemed more serious
work, not for creating aesthetic images. When artists did gain
access to these machines, it was typically through
artists-in-residence programs at companies such as Bell Labs and
IBM, and through infrastructures such as Experiments in Art and
Technology (E.A.T.) based in New York or the Los Angeles County
Museum of Art’s Art and Technology initiative.
Many of the first aesthetic computer graphics were made not by
artists, but by mathematicians and engineers who were curious about
other uses to which the machines at their labs could be
Within the first years that computer images were made, random processes were explored thoroughly. The first two exhibitions of computer-generated graphics appeared in art galleries in 1965; both shows included pieces that were created using random values. In New York, the works of A. Michael Noll and Bela Julesz, both researchers at Bell Labs, were exhibited at the Howard Wise gallery from April 6–24, 1965, under the title “Computer-Generated Pictures.” In Stuttgart, the works of Georg Nees and Frieder Nake were exhibited at the Wendelin Niedlich Gallery from November 5–26, 1965, under the title “Computer-Grafik Programme.”
In 1962, Noll published a technical memorandum at Bell Labs entitled “Patterns by 7090,” the number referring to the IBM 7090 digital computer. He explained a series of mathematical and programming techniques that use random values to draw “haphazard patterns” to a Carlson 4020 Microfilm Printer. The eight patterns documented in the memo are the basis for his Gaussian Quadratic image that was exhibited in the 1965 exhibition. Noll used existing subroutines of the printer to draw a sequence of lines to connect a series of x- and y-coordinates that he calculated and stored inside an array. The x-coordinates in the array were generated by a custom subroutine he wrote called WNG (White Noise Generator), which produced random values within the range of its parameters, and the y-coordinates were set using a quadratic equation. Through this series of patterns, Noll explored a tension between order and disorder, regularity and random values.
In 1965, Nake created his Fields of Rectangular Cross Hatchings series, which succeeds through pairing ordered patterns with random placement (figure 40.2). Nake explained the way random values are used in the images:
Within a given (arbitrarily chosen) image size, a random number of hatchings were generated. Each one of them was determined by the following random variables: location (x, y), size (a, b), orientation of lines within rectangle (horizontal or vertical), number of lines, pen. So for each rectangle there were seven random numbers determining its details. (Nake 2008)
After the first wave of visual images were created on plotters and microfilm at universities and research labs, a few professional artists independently started to gain access to computers and use them in their practice. The artists with the most success integrating a computer into their work had previously created drawings using formal systems. These artists continue to use computers in their work to this day. Artists who worked seriously with computers in the late 1960s, either individually or with technical collaborators, include Edward Zajec, Lillian Schwartz, Colette Bangert, Stan Vanderbeek, Harold Cohen, Manfred Mohr, and Charles Csuri. All of them employed random numbers in their early works created with software.
Manfred Mohr, for example, started as a jazz musician and later studied art in Paris; he began writing software to create drawings in 1969, at the Meteorological Institute of Paris, during the night after researchers had left for the day. In 1971, Mohr’s work was featured in “Une Esthétique Programmée” at the Musée d’Art Moderne de la Ville de Paris (see figure 40.3), the first solo exhibit of artworks created with a computer at a museum. Random values are used extensively in the creation of the work shown.
Acceptance and Resistance
While the first decade of computer-generated art was well documented in magazines, books, and exhibition catalogues, there are fewer source materials from the 1970s, when public interest veered and the energy needed to publish and exhibit waned. Later in the decade, computer graphics started to make their way into advertising and films. The 1982 film Tron is a landmark in the history of computation and aesthetics that pushed graphics to a new aesthetic level and therefore revealed the limitations of computer imagery at that time. Tron’s images are purely geometric and cold; they lack the organic qualities of our natural world. Ken Perlin, one of the programmers for the graphics in Tron, expressed frustration with the clean look. Later, in 1983, he developed a technique called Perlin Noise to generate organic textures that have a random appearance even though they are fully controllable to allow for careful design. Perlin Noise makes it possible for computer graphics models to have the subtle irregularities of real objects; it is used to create hard surfaces such as rocks and mountains and softer systems like fire and clouds. By the 1990s, it was being used extensively in Hollywood special-effects films and had been incorporated into most off-the-shelf modeling software.
Today the most widely known artists to use random values still do so without computers. For example, 2002 Turner Prize winner Keith Tyson designed sculptures not by using a computer to produce random numbers, but by rolling dice. One reason for this sort of reluctance to use computers, certainly, is the stigma surrounding computers in art. As Manfred Mohr remarked in an interview, “I called my work generative art, or occasionally also algorithmic works. The problem was that no-one understood either of these terms, and I was forced—so to speak—to declare my drawings as art from the computer . . . people accused me of degrading art, because I was employing capitalistic instruments of war—computer was a word non grata!” (Mohr 2007, 35). While Mohr was referring to the situation in the 1970s, the aversion to computers in art remains strong today.
More recently, however, as a new generation of visual artists have started to program their work, computed random numbers are playing an increasing role in the visual landscape. The most prominent programming languages used by visual artists have functions for generating random numbers and noise values, as well as for setting the random seed value to allow for the repetition of sequences. With the perspective of time, it seems that aesthetic computational work and random values are intertwined. Writing in 1970, Noll highlights randomness as an essential feature of the computer in relation to the arts:
The computer is a unique device for the arts since it can function solely as an obedient tool with vast capabilities for controlling complicated and involved processes, but then again, full exploitation of its unique talents for controlled randomness and detailed algorithms could result in an entirely new medium—a creative artistic medium. (Noll 1970, 10)
THE COMMODORE 64 RND FUNCTION
The way that
10 PRINT invokes the randomness provided by the Commodore 64 is of interest
for reasons that will each be explored in turn. First, using
randomness is aesthetically necessary in this program; there is no
other way to achieve a similar effect. Second, the methods used in
Commodore 64 BASIC are historically quite typical of computational
approaches to pseudorandomness since the 1950s. Finally, out of
several common approaches to randomness available on the Commodore
10 PRINT uses a very standard method that is well suited to experimentation,
debugging, and the production of canonical results, although this
method is not without its deficiencies.
10 PRINT produces a wrapping series of diagonal lines that alternate between left and
right unpredictably. This unpredictability is crucial to producing
the impression of a maze. Looking at variations of
10 PRINT that have regular or no alternation demonstrates the significance
of randomness in the program. It’s possible to
write an even simpler program than
10 PRINT to
draw only the left diagonal to the screen in a regular pattern
10 PRINT CHR$(205); : GOTO 10
This program can be extended by writing the other diagonal character to the right to form a chevron that repeats (figure 40.5):
10 PRINT CHR$(205)CHR$(206); : GOTO 10
The next step in this elaboration is the canonical
10 PRINT, which draws either the left or right diagonal to the screen based
on the result of the random number (figure 40.6):
10 PRINT CHR$(205.5+RND(1)); : GOTO 10
10 PRINT,random numbers are provided through
one of ten mathematical functions available in BASIC since the
earliest version of the language. As described the original
Dartmouth BASIC manual (1964),
RND produces a “new and different random
number” between 0 and 1 “each time it is used in a program” (39). These numbers can then
be used to drive unpredictable processes, as in fact they do drive
the coin-toss decision between diagonal lines in
10 PRINT output. A similar process might also determine the direction
changes of ghosts in Ms. Pac-Man
or the way other game elements appear or behave.
RND is, like most computational sources of randomness, a pseudorandom
number generator. While there may be no apparent pattern between
any two numbers, each number is generated based on the previous one
using a deterministic process. When the first number is the same,
the entire sequence will always be the same. In the case of the
Commodore 64, this is particularly important because the same seed,
and thus the same first number, is set at startup. So when
RND(1) is invoked immediately after startup, or before any other
RND, it will always produce the same result: 0.185564016. The next
invocation will also be the same, no matter what Commodore 64 is
used or how long the system has been on. The next
invocation—and all others—will also be the same. Since the sequence
is deterministic, the pattern produced by the
typed in and run as the first program is always the same, on every
computer or well-functioning emulator.
When called on any positive number,
RND(1) is invoked in
RND produces the next number in this sequence.
RND(.333) do exactly the same as
RND, however, has two other modes besides the one used in
10 PRINT. The second is stopwatch-based: when
is called, the clock time since the computer was powered on is used
in generating a new seed, meaning that if
each run of
10 PRINT at a different second should generate a different output. After a
single call to
RND(0), subsequent calls to
will continue generating numbers in that new sequence.
The third mode for RND applies when any negative number is called.
A call to
RND(−17) stores −17 as the seed value for the random
number generator, directly, and produces a new number. This
negative seeding must be followed by positive calls to the
function, such as
RND(1), in order to provide a useful sequence. Because negative calls
simply set the seed, calling
RND(−1) repeatedly will always return 0.544630526. For this reason,
10 PRINT could not be a single-line loop that calls a negative
RND value; that program would output the same diagonal again and again.
A single call to
RND, however, with any negative number, followed by the rest of
10 PRINT program, will generate a unique (and repeatable)
10 PRINT pattern.
Pseudorandomness, however lacking it may sound, is generally acceptable and in many situations desirable. Engineers running a computer simulation, for example, often have many random variables, but every run of the simulation needs those variables to have the same values; otherwise the program cannot be tested or the experiment repeated. Pseudorandom number generators are also highly useful in hashing, since they allow data to be distributed widely but also placed in known locations. Similarly, they are useful in cryptography, where it is vital that sequences be repeatable if (and only if) the initial conditions are known.
The Commodore 64 User’s Guide introduces the concept of randomness using an example that sidesteps the origins of randomness in computing. There is no mention of the hydrogen bomb, computer-generated literature, or prime numbers. Randomness comes into play in the shape of a game when it is necessary to, as the manual puts it, “simulate the throw of dice” (Commodore 1982, 48). This example takes the reader back to preindustrial notions of randomness. Yet, centuries ago, long before Mallarmé provided his assurance that a throw of the dice would not abolish chance, Sir Walter Raleigh wrote of this event as apocalyptic:
Dead bones shall then be tumbled up and down,
In every city and in every town.
Fortune’s wheel and what Paul Auster
called The Music of Chance have long been considered a matter of life and death. As
10 PRINT scrolls its playful, pleasing maze pattern upon the screen, there
may be the faintest echo of the dead bones of the dice and the
random simulation of the hydrogen bomb. And perhaps, as well, there
is the transformation of this grim, military use of randomness into
a thing of beauty.