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/ (*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. 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