Can a Monkey with a Computer Create Art?

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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

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

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Typical Experimental Data
5
x
-5
500
Time
0
4
Determinism

• xn1 f (xn, xn-1, xn-2, )
• where f is some model equation with adjustable
  parameters

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Example (2-D Quadratic Iterated Map)

• xn1 a1 a2xn a3xn2 a4xnyn a5yn a6yn2
• yn1 a7 a8xn a9xn2 a10xnyn a11yn
  a12yn2

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Solutions Are Seldom Chaotic
20
Chaotic Data (Lorenz equations)
Chaotic Data (Lorenz equations)
x
Solution of model equations
Solution of model equations
-20
Time
0
200
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Probability of chaotic solutions
100
Iterated maps
10
Continuous flows (ODEs)
1
0.1
Dimension
1
10
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Types of Attractors
Limit Cycle
Fixed Point
Spiral
Radial
Torus
Strange Attractor
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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

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Stretching and Folding
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Fractals

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

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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

• xn1 a1xn a2xn2 a3yn a4yn2 a5zn a6zn2
  a7cn a8cn2 (horizontal)
• yn1 xn (vertical)
• zn1 yn (depth)
• cn1 zn (color)

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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

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Symmetric Icons
Original Image
2 to 9 segments
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Selection Criteria

• Must be bounded (x lt 100)
• Must be chaotic (positive LE)
• 1.2 lt fractal dimension lt 1.9
• More than 10 of pixels on
• Less than 50 of pixels on

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Artificial Neural Networks
Neurons
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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)

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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
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More Gorilla Art
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Summary

• Nature is beautiful
• So is chaos

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References

• http//sprott.physics.wisc.edu/ lectures/monkey/
  (This talk)
• http//sprott.physics.wisc.edu/ fractals.htm
  (Fractal gallery)
• Strange Attractors Creating Patterns in Chaos
  (MT Books, 1993)
• Chaos Demonstrations software
• sprott_at_juno.physics.wisc.edu