Random Fractals and the Stock Market

Unifractal Cartoons - Dimension

Here are the graphs of the unifractal cartoon examples, H = 0.25 on the left, H = 0.75 on the right.

The H = 0.25 graph certainly looks rougher than the H = 0.75 graph.

To emphasize this point, here is a picture of the graphs side by side, and with the same vertical scale.

To give this visual difference some computational support, we note that graphs satisfying dY ≤ k ⋅(dt)H have box-counting dimension db ≤ 2 - H.

Here is a sketch of a proof.

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