Random Fractals and the Stock Market

Unifractal Cartoons

Here we generalize 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.

Return to Random Fractal Cartoons.

\|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.