curved von Koch
- To: mathgroup at smc.vnet.net
- Subject: [mg49605] curved von Koch
- From: "Roger L. Bagula" <rlbtftn at netscape.net>
- Date: Sat, 24 Jul 2004 03:47:48 -0400 (EDT)
- Reply-to: tftn at earthlink.net
- Sender: owner-wri-mathgroup at wolfram.com
I added a zero segment at the beginning and end and scaled the x as 3*x-1
to get a von Koch like function.
x'=3*x-1-->segment (1/3 , 2/3) goes to (0,1)
So that the curved Farey section behaves as von Koch tent type region.
I also found a Fourier type von Koch function that actually works:
f(x) =0 if 0<=x<=1/3
f(x)=1-(1/2+(4/Pi2)*Sum[Cos[2*(2*n-1)*Pi*(3*x-1)],{n,1, Infinity}]) if
1/3<x<=2/3
f(x)=0 if 2/3<x<=1
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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/