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. |
Return to Unifractal Cartoons.