       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/Log
(* 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 }
>