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# Playing With Chaos

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Presented at Web Unleashed 2017

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

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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
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