Transcript Fractals

Fractals
http://www.ugrad.cs.ubc.ca/~cs314/Vjan2010
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Two important properties of a fractal F
• F has detail at every level.
• F is exactly, approximately or statistically self-similar.
Koch Fractals
(Snowflakes)
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Generator
Iteration 0
Iteration 1
Iteration 2
Iteration 3
Fractal Tree
Generator
Iteration 1
Iteration 2
Iteration 3
Iteration 4
Iteration 5
Fractal Fern
Generator
Iteration 0
Iteration 1
Iteration 2
Iteration 3
Fractal Landscapes
• fractals: not just for “showing math”
- triangle subdivision
- vertex displacement
- recursive until termination condition
http://www.fractal-landscapes.co.uk/images.html
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Fractal Dimension
• D = log(N)/log(r)
N = measure, r = subdivision scale
- Hausdorff dimension: noninteger
Koch snowflake
coastline of Britain
D = log(N)/log(r) D = log(4)/log(3) = 1.26
http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html
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1D: Midpoint Displacement
• divide in half
• randomly displace
• scale variance by half
http://www.gameprogrammer.com/fractal.html
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Mandelbrot set
Demo
http://juliamap.googlelabs.com
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