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Fractals

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Fractals

http://www.ugrad.cs.ubc.ca/~cs314/Vjan2010

- Two important properties of a fractal F
- F has detail at every level.
- F is exactly, approximately or statistically self-similar.

1/3

1/3

1

1/3

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Generator

Iteration 0

Iteration 1

Iteration 2

Iteration 3

Generator

Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5

Generator

Iteration 0 Iteration 1 Iteration 2 Iteration 3

- fractals: not just for “showing math”
- triangle subdivision
- vertex displacement
- recursive until termination condition

http://www.fractal-landscapes.co.uk/images.html

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

- divide in half
- randomly displace
- scale variance by half

http://www.gameprogrammer.com/fractal.html

Demohttp://juliamap.googlelabs.com