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Another older one that is a treat : a triangular von Koch type fractal
*To*: mathgroup at smc.vnet.net
*Subject*: [mg65308] Another older one that is a treat : a triangular von Koch type fractal
*From*: Roger Bagula <rlbagulatftn at yahoo.com>
*Date*: Sat, 25 Mar 2006 05:17:44 -0500 (EST)
*References*: <e002hj$pp1$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
My aspect comes out two to one so that when roated 90 degrees it is
distorted, but this picture comes out fine:
(* Cartoon/ von Koch as Peak : Besicovitch - Ursell function*)
f[x_] := 0 /; 0 <= x <= 1/3
f[x_] := -2 + 6*x /; 1/3 < x <= 1/2
f[x_] := 4 - 6*x /; 1/2 < x <= 2/3
f[x_] := 0 /; 2/3 < x <= 1
ff[x_] := f[Mod[Abs[x], 1]]
Plot[f[Mod[Abs[x], 1]], {x, 0, 2}]
s0 = Log[2]/Log[3]
(* Cartoon/ as Sigmoid : Besicovitch - Ursell function*)
g[x_] := 0 /; 0 <= x <= 1/3
g[x_] := (3*x - 1) /; 1/3 < x <= 2/3
g[x_] := 1 /; 2/3 < x <= 1
gg[x_] := g[Mod[Abs[x], 1]]
ParametricPlot[{f[t], gg[t]}, {t, 0, 1}, Axes -> False]
Plot[gg[t], {t, 0, 2}]
hh[x_] = Sum[gg[3^k*x]/3^(s0*k), {k, 0, 20}];
kk[x_] = Sum[ff[3^k*(x)]/3^(s0*k), {k, 0, 20}];
a = Table[{kk[n/30000], hh[n/30000]}, {n, 1, 30000}];
ga = Show[Graphics[{PointSize[0.003], Point /@ a}], Axes -> False]
>
>
> Roger L. Bagula { email: rlbagula at sbcglobal.net or rlbagulatftn at yahoo.com }
>
> 11759 Waterhill Road,
> Lakeside, Ca. 92040 telephone: 619-561-0814
>
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