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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.

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Presentation on theme: "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."— Presentation transcript:

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

3 Typical Experimental Data Time0 500 x 5 -5

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

5 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

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

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

8 Types of Attractors Fixed Point Limit Cycle TorusStrange Attractor SpiralRadial

9 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

10 Stretching and Folding

11 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

12 Natural Fractals

13 Human Evaluations

14 Aesthetic Evaluation

15 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)

16 “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

17 Symmetric Icons 2 to 9 segments Original Image

18 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

19 Artificial Neural Networks `Neurons’

20 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)

21 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

22 More Gorilla Art

23 Summary n Nature is beautiful n So is chaos

24 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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