In a simple decision task, the sequence of response times is a monofractal. What constraints does this impose upon possible stochastic mechanisms that might explain the distribution of response times? Could it be a diffusion process, or perhaps a race between independent accumulators?
yes of course, the fractality of a series does not mean that it has a deterministic generator. You have fractional Brownian motions that are stochastic with fractal scaling laws.
Please find attached and linked some helpful literature outlining a variety of the competitive outlooks on fractal series.
Best wishes,
Damian
http://www.ejwagenmakers.com/2009/TorreWagenmakers2009.pdf
fractal set has the MAIN properties of compactness , measurable, and infinite. so you can study these properties for sake of comparison.