| To synthesize Brownian motion we took each |
| |dYi| = (dti)1/2, |
| the familiar square root scaling of Brownian motion. |
| We can generalize this some, requiring |
| |dYi| = (dti)H |
| with the same exponent H for each i. |
| Cartoons whose generator satisfies this relation are called unifractal. |
| This H is called the coarse Holder exponent, and is a measure of the roughness of a graph. |
| Computing H is straightforward: take the Log of both sides of the equation above and solve for H. |
| H = Log|dYi|/Log(dti) |
| Applied to experimental data, materials scientists compute the same ratio and call it the roughness exponent. |
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