Stochastic Painting

Leonardo, Vol. 1, pp. 81-83. Pergamon Press 1968. Printed in Great Britain. STOCHASTIC PAINTING Fred 1 . Whipple* The word stochastic5 derives from the Greek word for target, indicating something random in character . It is now a widely used technical word in mathematics and physics, representing completelyrandom assemblages or processes. Thus, stochastic paintings are those in which shapes and/or colors are structured randomly. The reader immediately asks why? Can there be any creativity or self-expression in random processes ? Can there be any beauty, charm, or interest in a painting that is not planned or organised and does not spring from some internal need for expression or communication on the part of the one who paints it? The answers to these questions may be satisfying only to a minority of those interested in painting, but there are indeed answers. First, a stochasticpainting must be based on a set of rules governing the nature of the randomness. Establishing a set of rules is a creative process and, of course, the actual application of the colors is a type of expression in texture, shading or structuring of the application. Thus, stochastic painting does involve creativity and selfexpression , although not of the classical type. Next, random processes can produce form and pattern, although not repetitive. Most people confuse irregularitywith randomness,which are actually different concepts, although related. Out of any aggregate of random numbers, random colors, or random distributions of colors,there isa high probability of structured patterns, which do not repeat but may be conspicuous. The monkeys with the typewriters willindeed compose poems, eventhough one must look over considerable manuscript to find them. Since random numbers by means of rules can, in fact, produce forms and color distributions, the question of beauty arises next. Here we must define our term. If, to be beautiful, a painting must express feelings, moods or ideas, or communicate them, then stochastic paintings cannot be beautiful. If these traditional assumptions are discarded, as *Director,Astrophysical Observatory, SmithsonianInstitution , 60Garden St., Cambridge, Mass.,02138, U.S.A.§ThedefinitionintheMerriam-Webster's ThirdNew InternationalDictionaryisthe following:'Stochastic,Gk Stochastikos , skillful in aiming, proceeding by guesswork, fr. (assumed)stochastos(verbalof stochazesthaito aimat, guess at, fr, stochos target, aim, guess): random (-processes) (-variables).' 7 they are in certain forms of modern painting, then stochastic painting may be 'charming, interesting, beautiful, and ugly according to diverse viewers.' If the purpose of a painting is only to produce an emotional response in the viewer, then stochastic paintings qualify along with many other modern efforts. An important point concerns the painter himself. Stochasticpainting can be fun because the outcome of a specificset of rules is sounpredictable. Until the painting is completed, one cannot really visualise how it will look, and cannot make the last difficult decision: which side should be up? The vagaries of randomness have a charm of their own. Most viewers find their own interpretation or objective representations in these paintings. Finally, a philosophical overtone: is nature, is a planet, or is man himself anything more than the consequenceof a set of physical rules carried out by random processes in the physical universe? And now for the rules. Here, of course, one findsa googol of possibilities. My first effort was to develop closed areas on a surfacefrompairs ofrandom numbers, selectedfrom a random-number tableg and utilised according to the following rules: 1. The first pair give x and y on a canvas coordinate system for the starting point. 2. The first of the second pair, taken as a decimal of 360",givesa direction from the startingpoint; the second, multiplied by a unit distance, say a centimeter or half an inch, measures a distance in this direction. 3. From the end of the first line the first number of the next pair measures a distance; the second, multiplied by 15",measures an angleturned counterclockwisefrom the tip of the previous line. 4. Successive lines are developed by successive number pairs from the ends of the previous lines or from the outer sidesof closed areas. 5. We now must have a rule for closingthe areas. I first tried a rule that produces areas that are all triangles or polygons with no internal anglesgreater than 180". I chose...