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Can a Monkey with a Computer Create Art? J. C. Sprott Department of Physics University of Wisconsin - Madison Presented to the Society for Chaos Theory in Psychology & Life Sciences in Madison, Wisconsin on August 4, 2001

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Outline n How this project came about n Properties of strange attractors n Search techniques n Aesthetic evaluation n The computer art critic n Samples

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Typical Experimental Data Time0 500 x 5 -5

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Determinism x n+ 1 = f (x n, x n- 1, x n- 2, …) where f is some model equation with adjustable parameters

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Example (2-D Quadratic Iterated Map) x n+1 = a 1 + a 2 x n + a 3 x n 2 + a 4 x n y n + a 5 y n + a 6 y n 2 y n+1 = a 7 + a 8 x n + a 9 x n 2 + a 10 x n y n + a 11 y n + a 12 y n 2

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Solutions Are Seldom Chaotic Chaotic Data (Lorenz equations) Solution of model equations Chaotic Data (Lorenz equations) Solution of model equations Time0200 x

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Probability of chaotic solutions Iterated maps Continuous flows (ODEs) 100% 10% 1% 0.1% 110 Dimension

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Types of Attractors Fixed Point Limit Cycle TorusStrange Attractor SpiralRadial

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Strange Attractors n Limit set as t n Set of measure zero n Basin of attraction n Fractal structure u non-integer dimension u self-similarity u infinite detail n Chaotic dynamics u sensitivity to initial conditions u topological transitivity u dense periodic orbits n Aesthetic appeal

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Stretching and Folding

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n Geometrical objects generally with non-integer dimension n Self-similarity (contains infinite copies of itself) n Structure on all scales (detail persists when zoomed arbitrarily) Fractals

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Natural Fractals

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Human Evaluations

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Aesthetic Evaluation

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A Simple 4-D Example x n+1 = a 1 x n + a 2 x n 2 + a 3 y n + a 4 y n 2 + a 5 z n + a 6 z n 2 + a 7 c n + a 8 c n 2 (horizontal) y n+1 = x n (vertical) z n+1 = y n (depth) c n+1 = z n (color)

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“Infinite” Variety n 8 adjustable coefficients n Like settings on combination lock n 26 values of each coefficient n 8-character name: KKGEOLMM n Compact coding! DOS filename n 26 8 = 2 x different codes n ~0.01% are visually interesting n Would take 1 year to see interesting ones at a rate of 1 per second

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Symmetric Icons 2 to 9 segments Original Image

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Selection Criteria n Must be bounded (|x| < 100) n Must be chaotic (positive LE) n 1.2 < fractal dimension < 1.9 n More than 10% of pixels on n Less than 50% of pixels on

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Artificial Neural Networks `Neurons’

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Computer Art Critique n Network trained on 100 “good” images and 100 “bad” images n Inputs are first 8000 bytes of gif file n Network has 16 neurons n A single output (can be + or -) n Gives ~85% accuracy on training set (200 cases) n Gives ~64% accuracy on out-of- sample data (different 200 cases)

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Gorilla Art “It is part of ape nature to paint. Apes like to use crayons, pencils and finger paints. Of course, they also like to eat them.” -- Roger Fouts

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More Gorilla Art

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Summary n Nature is beautiful n So is chaos

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References n lectures/monkey/ (This talk) lectures/monkey/ n fractals.htm (Fractal gallery) fractals.htm n Strange Attractors: Creating Patterns in Chaos (M&T Books, 1993) Strange Attractors: Creating Patterns in Chaos n Chaos Demonstrations software Chaos Demonstrations n

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