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Playing With Chaos

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Presented at Web Unleashed 2017
More info at www.fitc.ca/webu


Keith Peters
BIT-101
Overview

Get ready for some crazy math, beautiful graphics, and mind twisting concepts. Keith will take a tour through the land of fractals, dynamical systems, chaos, strange attractors, and much more. Even if you don’t understand what’s going on, bring your headphones and some cool music and enjoy the show.

Objective

Learn how to program fractals, chaos and strange attractors in JavaScript

Target Audience

Creative coders, math and fractal nerds.

Assumed Audience Knowledge

Basic JavaScript would be nice, but not totally necessary.

Five Things Audience Members Will Learn

What fractals are
Chaos theory
What attractors are
Different ways to create fractal patterns
Fractals in nature

Published in: Internet
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Playing With Chaos

  1. 1. Playing With Chaos Fractals and Strange Attractors
  2. 2. Recreational Mathematics Puzzles, games, etc.
  3. 3. Algorithmic/Generative Art Don't get too serious about the word “art”
  4. 4. What is a fractal?
  5. 5. A shape
  6. 6. Made from other shapes
  7. 7. Each part a copy of the whole
  8. 8. Theoretically infinite
  9. 9. Sierpinski Gasket
  10. 10. Koch Curve
  11. 11. Koch Curve
  12. 12. Koch Snowflake
  13. 13. Length 4.0 5.3 7.1 +1.3 +1.8
  14. 14. 1 iteration = length 4 20 iterations = length 946
  15. 15. Infinite perimeter. Finite area.
  16. 16. Infinite triangles. Zero area.
  17. 17. Fractal tree
  18. 18. Symmetry and Regularity
  19. 19. Non-symmetry
  20. 20. Irregularity
  21. 21. Pythagorean Fractal A B C
  22. 22. How long is the coast of Britain?
  23. 23. 1 iteration = length 4 20 iterations = length 946
  24. 24. How long is the coast of Britain? It depends on the size of your measuring stick.
  25. 25. The Richardson Effect
  26. 26. Dimensions Line: Square: 1.0 2.0
  27. 27. Fractal Dimensions Line: South Coast of Africa: West Coast of Britain: Koch Curve: Sierpinski Gasket: Square: 1.0 1.02 1.25 1.2619 1.5849 2.0
  28. 28. Chaos Game
  29. 29. Chaos Game
  30. 30. Chaos Game
  31. 31. Chaos Game
  32. 32. Chaos Game
  33. 33. Chaos Game
  34. 34. Barnsley Fern
  35. 35. IFS Tree
  36. 36. Diffuse Limited Aggregation
  37. 37. The Mandelbrot Set
  38. 38. Benoit Mandelbrot
  39. 39. Imaginary Number i = ⎷-2
  40. 40. Complex Numbers Real Number + Imaginary Number 4 + 5i
  41. 41. x -y y -x 4, 2 -2, -1
  42. 42. real -imaginary imaginary -real 4, 2i -2, -i
  43. 43. The Mandelbrot Set z1 = z2 + c z and c are complex numbers z begins as 0+0i c is a point on the complex plane iterate for each point on the plane
  44. 44. ● z goes above a certain value ● color it based on how fast it got there ● z stays in range ● color it black Result of iteration:
  45. 45. -r r i -i
  46. 46. -r r i -i c = -2, -i z = 0, 0i
  47. 47. Strange Attractors
  48. 48. Edward Lorenz
  49. 49. The Lorenz Attractor
  50. 50. Fractals in Nature
  51. 51. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature exhibits not simply a higher degree but an altogether different level of complexity. - Benoit Mandelbrot
  52. 52. Thank You http://www.bit-101.com Twitter: @bit101
  53. 53. http://playingwithchaos.net

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