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Re: Fractal Geometry--> Levy Flights

• To: mathgroup at smc.vnet.net
• Subject: [mg48315] Re: Fractal Geometry--> Levy Flights
• From: "Curt Fischer" <crf3 at po.cwru.edu>
• Date: Sun, 23 May 2004 06:15:41 -0400 (EDT)
• References: <c8muiq$a48$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Roger Bagula wrote:
> Is there a Mathematica Procedure to get Levy Flights?
> http://classes.yale.edu/fractals/RandFrac/Levy/Levy4.html

The pdf mentioned on the above link blows up at an amplitude of 0.  There
may be a fancier way of dealing with this singularity that I don't
understand, but in my analysis here I substitute the exponential
distribution for values of the amplitude of E = 2.71828 or less.

Also, I have used only a one-sided pdf that is zero for all amplitudes less
than zero.  The pictures on the site clearly involved both positive and
negative amplitudes.  Since the joint p.d.f. on the site does not depend on
t, all values of t are equally likely.  I also assumed that we were
interested in the time range between zero and 100.

My notebook isn't annotated very well, but I think you can see the process
of getting to a Levy-flight-like plot.

http://web.mit.edu/curt/www/Levy%20Flights.nb