What is the connection between fractals and Brownian motion?

[jimbo007]

hey there,
i'm curious as to why they call it fractional Brownian motion. please don't say its Brownian motion that is fractional

many thanks

 

[berkeman]

I googled "fractional brownian motion" and the first hit seems to explain it pretty well. Sounds fractal...

http://davis.wpi.edu/~matt/courses/fractals/brownian.html

 

[HallsofIvy]

hey there,
i'm curious as to why they call it fractional Brownian motion. please don't say its Brownian motion that is fractional

many thanks

Okay, then, I'll just ask "why do the call what fractional Brownian motion?"!

 

[jimbo007]

why do they call fractional Brownian motion, fractional Brownian motion?

 

[berkeman]

why do they call fractional Brownian motion, fractional Brownian motion?

Here you go -- from the last hit on the first page of the search that I posted:

from http://www.doc.ic.ac.uk/~nd/surprise_95/journal/vol4/ykl/report.html

Mandelbrot proposed the idea of a fractal (short for "fractional dimension") as a way to cope with problems of scale in the real world. He defined a fractal to be any curve or surface that is independent of scale. This property, referred to as self-similarity, means that any portion of the curve, if blown up in scale, would appear identical to the whole curve.

And from the first hit on the search page:
http://davis.wpi.edu/~matt/courses/fractals/brownian.html

The main difference between fBm and regular Brownian motion is that while the increments in Brownian Motion are independent they are dependent in fBm. This dependence means that if there is an increasing pattern in the previous "steps," then it is likely that the current step will be increasing as well.

So it looks like it could be called fractal Bronian motion instead of fractional Brownian motion...