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MathGroup Archive 2004

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Farey Comb Histogram

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49419] Farey Comb Histogram
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Mon, 19 Jul 2004 07:46:09 -0400 (EDT)
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

The function that gives a Farey triangle effect is :
f[a,b]=a/(b-a) if 0<=a/b<=1/2
f[a,b]=(b-a)/a if 1/2<a/b<=1
The distribution histogram is a count of the frequency of the different
values  between zero and one.
It is the same histogram function I use for noise analysis.
This comb result is remarkably like the comb effect I got in my self 
similar integer
sequences.
As a result of this I think that there may be a fractal dimension
associated with rational numbers produced in the Farey manner
even if their measure as a set is zero.
Respectfully, Roger L. Bagula

tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 
619-5610814 :
URL :  http://home.earthlink.net/~tftn
URL :  http://victorian.fortunecity.com/carmelita/435/

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