Fractals. Two important properties of a fractal F F has detail at every level. F is exactly, approximately or statistically self-similar. Koch Fractals (Snowflakes). 1/3. 1/3. 1. 1/3. 1/3. Generator. Iteration 0. Iteration 1. Iteration 2. Iteration 3. Fractal Tree. Generator.
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Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5
Iteration 0 Iteration 1 Iteration 2 Iteration 3
D = log(N)/log(r) N = measure, r = subdivision scale
Hausdorff dimension: noninteger
coastline of Britain
D = log(N)/log(r) D = log(4)/log(3) = 1.26