Can a Monkey with a Computer Create Art

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

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

Typical Experimental Data 5 x -5 0 Time 500

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

Example (2 -D Quadratic Iterated Map) xn+1 = a 1 + a 2 xn + a 3 xn 2 + a 4 xnyn + a 5 yn + a 6 yn 2 yn+1 = a 7 + a 8 xn + a 9 xn 2 + a 10 xnyn + a 11 yn + a 12 yn 2

Solutions Are Seldom Chaotic 20 Chaotic Data Chaoticequations) Data (Lorenz equations) x Solution of model equations -20 0 Time 200

Probability of chaotic solutions 100% Iterated maps 10% Continuous flows (ODEs) 1% 0. 1% 1 Dimension 10

Types of Attractors Fixed Point Spiral Limit Cycle Radial Torus Strange Attractor

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

Stretching and Folding

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

Natural Fractals

Human Evaluations

Aesthetic Evaluation

A Simple 4 -D Example xn+1 = a 1 xn + a 2 xn 2 + a 3 yn + a 4 yn 2 + a 5 zn + a 6 zn 2 + a 7 cn + a 8 cn 2 (horizontal) yn+1 = xn (vertical) zn+1 = yn (depth) cn+1 = zn (color)

“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 268 = 2 x 1011 different codes n ~0. 01% are visually interesting n Would take 1 year to see interesting ones at a rate of 1 per second

Symmetric Icons Original Image 2 to 9 segments

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

Artificial Neural Networks `Neurons’

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 n Gives ~85% accuracy on training set (200 cases) Gives ~64% accuracy on out-ofsample data (different 200 cases)

Gorilla Art http: //www. koko. org/world/art. html “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

More Gorilla Art

Summary n Nature is beautiful n So is chaos

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