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Superfractals - rapid computation of good approximations to random (and "fully" random) process

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Last Edited: May 29, 2009, 11:09 pm

Reading this book currently (ref. 1) , eyeing application in the lottery (possibly) as the (ref. 3) points out:

"Areas of potential applications include computer graphics and rapid simulation of trajectories of stochastic processes The forward algorithm also enables rapid computation of good approximations to random (including “fully” random) processes, where previously there was no available efficient algorithm. "

In a similar venue of Monte Carlo methods, Superfractals promise to venture into areas where deterministic algorithms can not.

This book (ideas therein) is by far one of the most advanced on the topic. Fractals themselves emerge from set of deterministic rules (at least initially) but are supplemented by set of indeterministic cooefficients that set initial random trajectories and by the means of IFS (IFS - Iterated Function System) for the evolution to eventually emerge in some global symmetrical patterns.

Superfractals are new families of random fractals which are intermediate between the notions of deterministic and of standard random fractals and as such allow new type of sampling of the IFS evolution.

If it all sounds sophisticated, it is, ideas set forward in this book are already reverbarating cross multi-disciplinary sciences starting from bio-physics/ cosmology (ie. galaxy formations) / financial modeling / to number and game  theory.

It is my intention to eventually engage this theory (not just in lottery actually) to study random systems in general. 

References:

1. Superfractals - book by Michael Fielding Barnsley

http://www.amazon.com/SuperFractals-Michael-Fielding-Barnsley/dp/0521844932

2. Superfractals - website

http://www.superfractals.com/

3. Superfractals - more detailed technical information - A FRACTAL VALUE RANDOM ITERATION ALGORITHM AND FRACTAL HIERARCHY - MICHAEL BARNSLEY, JOHN HUTCHINSON, AND ÖRJAN STENFLO

http://www.superfractals.com/Superfractals/V-Variables.pdf

Entry #6

Comments

1.
Rick GComment by Rick G - May 30, 2009, 11:09 am
Very interesting, edge. Keep us posted. I think you're heading in the right direction.
2.
Comment by GASMETERGUY - May 30, 2009, 8:47 pm
I have bought and read (three times each book) information about fractals. I can see no use for this mathematical theory. That should not be taken as a negative. My IQ is lower than the value of a dollar and where I have failed, you may suceed.
On second thought, I will not post this.

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