Can a Monkey with a Computer Create Art?

1. 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

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

3. Typical Experimental Data 5 x -5 500 0 Time

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

5. Example (2-D Quadratic Iterated Map) xn+1 = a1 + a2xn + a3xn2 + a4xnyn + a5yn + a6yn2 yn+1 = a7 + a8xn + a9xn2 + a10xnyn + a11yn + a12yn2

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

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

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

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

10. Stretching and Folding

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

12. Natural Fractals

13. Human Evaluations

14. Aesthetic Evaluation

15. A Simple 4-D Example xn+1 = a1xn + a2xn2 + a3yn + a4yn2 +a5zn + a6zn2 + a7cn + a8cn2 (horizontal) yn+1 = xn (vertical) zn+1 = yn(depth) cn+1 = zn (color)

16. “Infinite” Variety • 8 adjustable coefficients • Like settings on combination lock • 26 values of each coefficient • 8-character name: KKGEOLMM • Compact coding! DOS filename • 268 = 2 x 1011 different codes • ~0.01% are visually interesting • Would take 1 year to see interesting ones at a rate of 1 per second

17. Symmetric Icons Original Image 2 to 9 segments

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

19. Artificial Neural Networks `Neurons’

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

21. 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

22. More Gorilla Art

23. Summary • Nature is beautiful • So is chaos

24. 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) Chaos Demonstrations software sprott@juno.physics.wisc.edu References