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Composing the Score for Visual Art by Roman Verostko
Written in 1994 with edits in 1996 & 1998.

Note on the algorists: This "Algorithmic Art" page  existed  before we  established the use of the term algorist for artists who practiced algorithmic art. After the term "algorist"  was introduced I inserted a brief account of the algorists on this page. (see below) Several years later I mounted an algorist web site. But I have maintained most of the information on this page as originally posted including the 1995 algorist addition. There have been  some corrections and several footnotes.

  Algorithmic design, Hispano-Moorish tile, 14th C, Nasrid Palace, Granada, Spain   Photo RV   

   algorithm & algorism

Algorithm is a variant of the earlier term algorism.  Early usage in the English language appears variously as augrime, augryme, algorisme, algorism and variations with Latinizing influence as in algorismus. In English the term algorism appears in late 17th Century writing as algorithm which is commonly used today. The transformation to algorithm may have been influenced by classical learning since the Greek term for number is arithmós (’αριθμός) the root for our English term arithmetic. 

Origin. The term algorism most probably descended from the name of an Arabian mathematician active in Bagdad around 820 AD. This mathematician, Abu Ja'far Mohammed Ben Musa, a native of Khwarasm, surnamed al-Khowarazmi, wrote treatises on Hindu arithmetic and algebra.  The title of one of his works, al-jabrawa al-maqàbala, is taken as the source for the term algebra. It is also believed that his name, al-Khowarazmi is the source for the term algorism.

What is an algorithm?  An algorithm or algorism may be viewed simply as a detailed recipe for carrying out a task. The term has its origin in mathematics as the step by step procedure for solving a problem. The  commonplace procedures we use for multiplying and dividing numbers are algorithms. With precise details for each step the procedures yield the same result whether executed by a computer or by a human. This is why robots are able to handle many tasks that were once done only by humans.  Example:  See note 1.

Many view an "algorithmic procedure" as a strictly mathematical operation. Today we are inclined to view any well defined procedure as an algorithm. A recipe for baking bread is an algorithm. Follow the recipe faithfully and you will duplicate the kind of bread made by the person who wrote the recipe.

Applications. Machines can also be programmed to follow recipes. The programmed circuitry in  bread-making machine directs the machine's mechanism on precisely how to mix ingredients, knead the dough,  and bake the bread.  In theory it should succeed every time but there are also factors of  mechanical and human error. The quality and measure of ingredients may contribute to unwanted results.

Within the past quarter century operational instructions have been imbedded in the design of many industrial and household  utilities.  They implement our daily use of  telephones, automobiles, cameras, TV's, and radios. Our hospitals, factories, banks, and shopping centers all depend on the algorithms that control inventories, transactions, communications and security.  They are ubiquitous and our mass culture would collapse without them.  

Algorithmic procedures are also imbedded in  the digital tools used in the arts. Use of these tools influences form in  the practice of film, architecture, photography, music, printmaking, and all types of electronic sound and image. The drudgery of executing algorithms that would require immense time, or even be impossible to execute without computing power, has been  handed over to the machine leaving humans more free to focus on the creative part of their work. For the artist this means improving and improvising the art-making  procedure.  For the algorist, work on the algorithm is work on the procedure. 

History & breadth.   Although the term derives from the name for a 9th century mathematician, the use of algorithms dates from prehistoric times. Study of the stone circles at Stonehenge (c. 2000 BC) reveals an  algorithmic arrangement based on phases of the moon and the annual movement of the sun. While we cannot know the meanings these builders attached to the structure we are able to discern something of the "rules" for stone positions. Their  alignment relates to the annual movement of the sun and the moon. 

Larger image (18 kb) Stonehenge, c. 2000 BC, ff.
Algorithmic arrangement
Salisbury plain, England. ca. 24 ft high

photo RV

Clearly early civilizations developed procedures for counting and measuring. They also created procedures for weaving, grinding, making fire and cooking. Any of these procedures, when well defined, could be viewed as an algorithm. Indeed  weaving technology played an important role in the history of computers.  If we can spell out the procedure for any given task then, given all the necessary materials and skills, we should be able to carry out the task. 

Architectural plans, musical scores and dance notations ( Note 2) bear one feature in common - they are all recipes for carrying out a task. From this perspective a broad range of  notational systems can be viewed and studied as algorithmic procedure.  From this perspective algorithmic procedures for generating artistic forms enjoy a rich and varied tradition  even though we have used other terms to describe them. 

Algorithms and art.  

Gregorian Chant,  Missal, c.1200. Detail from the Sursum Corda.
Musical scores, viewed as instructions, are algorithms for performing music.

In Art History.  A history of algorithms in the visual arts would be voluminous touching many phases in every culture at every turn - the Egyptian canons for drawing the human figure,  the infinite geometric play in Islamic art and the role of both linear perspective and proportion in Renaissance art.   In China we would find the Mustard Seed Manual and in Byzantium the conventions for icon painting.  In Europe, by the  Seventeenth Century we would find extremely sophisticated algorithms for plotting the dizzying perspectives  imaging the passage from earth to heaven.

Even so, notational systems for the visual arts played a limited role when compared to notational systems for music.  A gifted composer could compose  a score for a profoundly moving musical passage that could be played hundreds of years later by a skilled virtuoso. Not so for the painter. While Leonardo could easily employ an algorithm for creating the perspective space in the Last Supper, he could not, at that time, compose an algorithm for rendering the face of Judas. 

The 20th Century.  A 20th Century  history  would find some interesting pre-algorist examples in the 1960's and 1970's.  Fluxus, minimalist and conceptual artists employed various methods of procedural specification challenging traditional conceptions of art.  For example, George Brecht's  early  works were primarily very lean instructions printed on cards; the cards, with the instructions were  the art works.  Occasionally he  mailed an instruction to me and he came to be  associated with "Mail Art" that preceded Fax Art.   His cards could be a very lean,  one or two word event  such as "House Number".   Conceptual art in  its many forms preceded so called "computer art". It was not until artists gained access to computing power that they were able to compose form-generators for the investigation of form. 


George Brecht, 1961, Two Vehicle Events, Detail of a 3.5 " by 4.5. card.  One of many similar kinds of instructions that were given to participants.
Right: Vehicles, drivers & interested students gather before sunset for a performance of George Brecht's "Vehicle Sundown Event".
Location: St Vincent College, Latrobe, PA., parking area behind Sportsman's Hall, 1963

Steve Joy took me to meet  George Brecht in his studio when I was in residence at St Michael's in Manhattan (c.1962). We became friends and GB mailed instruction cards to me.  I brought Steve Joy to St Vincent College when I returned to the monastery from Paris in 1963. GB agreed to provide instructions for an event at St Vincent. For his  "Vehicle Sundown Event", GB published a set of about 50 cards to be given to  participants who participated in the event with their vehicles. Each card held an instruction to be performed with a vehicle. Drivers  were instructed to assemble at sundown in a parking lot and randomly park their vehicles.  Then each driver, with a shuffled deck of instructions, would begin performing at the sound of a signal. Participants  performed about 50 events such as "turn on lights", "start engine", "stop engine", "open window". This work was performed at St Vincent College under the direction of Stephen Joy with Roman Verostko assisting. c. 1963  ( I can confirm that Fr Melvin Ruprecht participated. I believe it was before I went to Washington as NCE editor, rv0


 As computers became more accessible to artists in the 1970's and 1980's some artists began to experiment with algorithmic procedure.  The new technology offered them methods of working algorithmically that were unavailable before the advent of computers. By  the 1980's a number of us were working with the pen plotter,  a machine with a "drawing arm".  Seeing other's work at various venues we came to know each other and share ideas.  Algorists like Harold Cohen, Manfred Mohr, Jean Pierre Hebert and this author had achieved mature work but we had no common identity.  Each in their own way had invented algorithmic procedures for generating their art. By doing so each created their own distinctive style.  Clearly style and algorithm were linked in a very important way (Note 8).

One of the concerns for educators in  the early 1980's was whether we should be teaching programming in our art schools or rather wait for advances in computing power, software programs, and printing technologies.  With the growth of PC computing power, refinement of raster printing technologies, and  professional software for the visual artists more and more artists took up what was generally called "computer art". The unique features and form-generating capabilities for algorithmic procedure in the hands of the artist was easily lost in the widening world of "computer art".  It was in this milieu that a small group of artists, including this author, introduced panels for addressing the role of "algorithms & the artist". Following one such panel at the 1995 SIGGRAPH conference it was Jean Pierre Hebert, Ken Musgrave and myself who agreed to work towards a common identity for those who practiced algorithmic art. 

Within a short time we introduced our identity as "algorists" and Jean Pierre Hebert wrote an algorithm defining an "algorist" as applied to artists  (for this algorithm see note 3). Within a decade this usage led us to a better understanding of the role of algorithmic procedure in shaping world culture at the turn of the Century.

For a detailed & illustrated account of the algorists see: "Who are the algorists?"

Briefing on my algorithmic art 

Larger Image 38KB A Sun Canticle, I. 1995 (38KB)
**Click here for central character detail (48KB)
Example of algorithmically generated art. Pen plot with center brush strokes  illuminated with gold leaf.  The central character-like strokes were algorithmically generated and executed with a brush mounted on the plotter's drawing arm and the gold leaf was applied by hand later. The brush strokes are algorithmic gestures reminiscent  of the painterly automatism I  practiced in the 1960's.  


For the past 40 years I have worked with pure visual form ranging from controlled constructions with highly studied color behavior to spontaneous brush strokes and inventive non-representational drawing. Such art has been labeled variously as "concrete", "abstract", "non-objective", and "non-representational". In its purest form such art does not re-present other reality. Rather "it is" the reality. One contemplates a pure form similar to the way one might contemplate a fine vase or a sea shell.  Early 20th Century pioneers of this art include artists like Piet Mondrian, Frantisek Kupka and the brothers Naum Gabo and Antoine Pevsner. 

In the last quarter of the 20th Century a radically new form-generating procedure became available. By joining algorithmic procedure and computing power some artists began generating forms with surprising visual qualities.  A vast uncharted frontier of form waited to be conceptualized  and concretized. By the 1980's I was composing detailed procedures for generating forms that were accessible only through extensive computing. On-going work concentrates on developing this program of form generators.  By joining these procedures with fine arts practice I create two dimensional art objects to be contemplated much as we contemplate the  forms of nature .

Form generation as epigenesis. The greater part of this creative work in the past 15 years has been developing art form generators.  These are original detailed procedures, for initiating and improvising form ideas. Such form generators may be likened to biological genotypes since they contain the code for generating forms. The procedure for executing the code, somewhat analogous to biological epigenesis, grows the form  (Note 6) . The creation and control of these instructions provides an awesome means for an artist to employ form-growing concepts as an integral part of the creative process. Such routines provide access to countless visual structures that constitute a new frontier of visual forms for the artist.

The first algorithmic brush strokes executed with an oriental brush mounted on a pen plotter were achieved in 1987 with an HI DMP52 pen plotter and my first version of Hodos. 

Above. One of a series attempting to achieve spontaneity and expressive energy as found in Chinese Shufa. These were features that were also found in the work of New York abstract expressionists like Robert Motherwell and Franz Kline. Influenced by the New York School  I had  experimented with spontaneous brush strokes long before my experience in China and my work with code.  As an algorist in the 1980's  I wanted to achieve strokes with spontaneity and expressive energy via coded procedure.

The Work. Works are executed with a multi-pen plotter coupled to a PC driven by the software. The plotter, choosing from an array of pens loaded with pigmented inks draws each individual line. Most works require thousands of lines with  software controlled pen changes. (Note 7)  An optional brush routine allows  occasional substitution of a brush for a pen. Brush strokes are plotted using Chinese brushes adapted to the machine's drawing arm. The Diamond Lake Apocalypse series of illuminated digital scripts is reminiscent of medieval manuscripts. Many of these works are enhanced with a touch of gold or silver leaf applied by hand. However, the design elements illuminated with gold are always code generated and machine plotted.

  Diamond Lake Apocalypse, 24" by 18", 1991, (c) RJV
  pen & ink drawing on paper


Content and Meaning . Over the years the software has evolved by stages yielding a series of works for each stage - Pathway, Gaia, Glyph, Scarab, Apocalypse and Ezekiel. Each of these series has distinctive formal qualities associated with its form generators. None of the works are made with intentional representations in mind. Rather, each work presents one more adventure into a world of forms that have never been seen before. This art does not re-present some sort of subject or object. Just as a botanist might label a newly discovered flower so also I label this or that newly found form or series of forms. Titles are therefore arbitrary and often derived from evocative qualities associated with the work.

Ezekiel Series, The Vision III, 40" by 24", 1993, (c) RJV

 Silver leaf enhancement, lower left, click here.

The art works are visual manifestations of the dynamic procedures by which they grew. They may be viewed as visual celebrations of the information processing procedures embedded in today's culture. The finished works invite us to savor the mystery of their coded procedures whose stark logic yields a surprising grace and beauty. These procedures provide a window on those unseen processes from which they are grown. By doing so they serve as icons illuminating the mysterious nature of our evolving selves.

Click larger image, 35kb Pathway Series, (62kb),
Pen & brush plotted work, 36" by 24", 1978, (c) RJV

Note 1. Terminology briefing

Algorithm – a precisely detailed procedure for carrying out a task.

Here is a drawing task:

(1) Identify two random points on a 100 unit square plane.
(2) Draw a line connecting these two points.

Here is an algorithm for this task written in the elementary BASIC language that could be executed by my first PC:

         window (0,100)-(0,100)
       for n=1 to 4
       next n

Although the algorithm above can be executed by my first PC the BASIC language is actually a "high level" language. Each term in the algorithm has to be interpreted and translated into a lower level code in binary before it can be processed. All of this work is done by the "Operating System" that is also "software". In the end the BASIC algorithm ends up being translated into a series of "on" and "off" instructions that guide the hardware operations.

Software - The algorithm above is software. "Software" identifies instructions written in a language compatible with a given computer. The instructions are "soft" as they can be changed and make it possible to change or modify tasks without changing the "hardware". 

Program - The term program usually refers to software with algorithms integrated to carry out one or more tasks as with a "word processor", or a "spreadsheet".

Pen Plotter Designed primarily for engineering and architectural drawing, a pen plotter draws on paper with ink pens. These machines receive their instructions from software programs designed for architects & engineers. First generation plotter artists created their own software.

Note 2. The Greek origin of the term choreography, to write down (graphein) the dance (choreia), reveals its algorithmic nature.

Note 3.  The classic JPH algorithm, as quoted here, dates from correspondence in September 1995:

if (creation && object of art && algorithm && one's own algorithm) {
include * an algorist *
} elseif (!creation || !object of art || !algorithm || !one's own algorithm) {
exclude * not an algorist *

In the course of our work, with or without computers, we all employ algorithms by our predecessors and colleagues. The use of algorithms in and of itself does not constitute algorist work. As defined in the JPH algorithm, it is the inclusion of one's own algorithms that makes the difference. 

Note 4. First generation pioneers included Piet Mondrian, Wassily Kandinsky, Kasimer Malevich, and the brothers Naum Gabo and Antoine Pevsner.

Note 5. Those drawn to view culture with neo-Darwinian spectacles will relish the evolution of this art. See Daniel Dennett's Darwin's Dangerous Idea (NY 1996) for an engaging discussion of the hyperspace of all possible books (Library of Babel, p 107 ff) and that of all possible genomes (Library of Mendel, p 111 ff). Writing on the new biology of machines Kevin Kelly identified The Library of Form, a frontier hyperspace of form being pioneered by Karl Simms (Chapter 14, Out of Control, 1994). I propose to identify the parameters for a Gallery of D'Arcy Thompson to embrace computable abstract art that is rigorously non-representational, i.e. non-objective, concrete, pure abstract art. Unveiling art within the hyperspace of forms with these parameters was certainly the dream of artists like Frantisek Kupka.

Note 6. The term epigenesis, borrowed from biology, refers to the process whereby a mature plant (phenotype) is grown from a seed or genotype (DNA). By analogy, the art work (phenotype) is grown from the software (genotype). The procedures for growing the work may be viewed as epigenetic. The code (genotype) for each series of works is capable of generating a family of forms with each being one of a kind. This procedure was employed in the limited edition of Boole's Derivation of the Laws. My 1988 Utrecht  paper,  Epigenetic painting: software as genotype outlines procedures developed up to that time.

Note 7. See my essay Art and Algorithm on my early 1990's perspectives on  procedures and issues related to an artist's use of algorithms.

Note 8. For example, Harold Cohen's early algorist work displayed form qualities similar to his pre-algorist work as a painter. The link between form and procedure remains one of the most important links to be explored in algorithmic art.  For notes on algorists whose work exemplifies this relationship see: "Who are the algorists?" 

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