Random Fractals and the Stock Market

Unifractal Cartoons

Here we generalize teh last section's Brownian motion cartoons to cartoons with global dependence.

|dY_i| = (dt_i)^H First, we introduce the scaling that characterizes unifractals.

(dt₁)^H - (dt₂)^H + (1 - dt₁ - dt₂)^H = 1 Next, we see that unifractal scaling requires that the generator segments satisfy a condition.

Here is one example of a non-Brownian unifractal cartoon.

Here is another example of a non-Brownian unifractal cartoon.

d_b ≤ 2 - H Finally, here is an observation about the dimensions of unifractal cartoons.

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