four parametric projection ifs types

• To: mathgroup at smc.vnet.net
• Subject: [mg101649] four parametric projection ifs types
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Sun, 12 Jul 2009 05:51:47 -0400 (EDT)
• References: <h2fe37\$ppu\$1@smc.vnet.net> <h340hn\$gcn\$1@smc.vnet.net> <h3760n\$f2i\$1@smc.vnet.net>

```http://www.geocities.com/rlbagulatftn/limacon_kiss.gif
So far there are  four working parametric ifs projection types:
circle-ellipse
piriform-drop
lemniscape
limacon

There are two ways to get a kissing Limacon:
inner and outer:
Mathematica:
Clear[f, dlst, pt, cr, ptlst, x, y]
RandomSeed[];
dlst = Table[ Random[Integer, {1, 2}], {n, 250000}];
f[1, {x_,
y_}] := N[ {(1 - 2*(x2 - y2)/(y2 + x2))*2*x*y/(x2 + y2) , (
1 - 2*(x2 - y2)/(y2 + x2))*(x2 - y2)/(y2 + x2)}];
f[2, {x_, y_}] := N[{-x/(1/0.085) - y/((1/0.085)), -1/2 + x/((1/0.085))
- y/(
1/0.085)}];
pt = {0.5, 0.75};
cr[n_] :=
If[n - 2 == 0, RGBColor[0, 0, 1], If[n - 3 == 0, RGBColor[0, 1,
0], If[n - 1 == 0, RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]]
ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]},
{j, Length[dlst]}];
Show[Graphics[Join[{PointSize[.001]}, ptlst]],
AspectRatio -> Automatic, PlotRange -> All]

http://www.geocities.com/rlbagulatftn/limacon_2ndkiss.gif
MATHEMATICA:
Clear[f, dlst, pt, cr, ptlst, x, y]
RandomSeed[];
dlst = Table[ Random[Integer, {1, 2}], {n, 100000}];
f[1, {x_,
y_}] := N[ {(1 - 2*(x2 - y2)/(y2 + x2))*2*x*y/(x2 + y2) , (
1 - 2*(x2 - y2)/(y2 + x2))*(x2 - y2)/(y2 + x2)}];
f[2, {x_, y_}] := N[{-
x/(1/0.255) - y/(1/0.255), -1/2 + x/(1/0.255) - y/(1/0.255)}];
pt = {0.5, 0.75};
cr[n_] := If[
n - 2 == 0, RGBColor[0, 0, 1], If[n - 3 == 0, RGBColor[0, 1, 0],
If[n - 1 == 0, RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]]
ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]},
{j, Length[dlst]}];
Show[Graphics[Join[{PointSize[.001]}, ptlst]],
AspectRatio -> Automatic, PlotRange -> All]

http://www.geocities.com/rlbagulatftn/lemniscape_kiss_iff.gif
A kissing lemniscape fractal ifs:
Mathhematica:
Clear[f, dlst, pt, cr, ptlst, x, y]
RandomSeed[];
dlst = Table[ Random[Integer, {1, 2}], {n, 250000}];
f[1, {x_,
y_}] := N[ {Sqrt[Abs[(((2*x)2 - (2*y)2)/((2*y)2 + (2*x)2))]]*2*x*y/(
x2 + y2) , Sqrt[Abs[(((2*x)2 - (2*y)2)/((2*y)2 + (2*
x)2))]]*(x2 - y2)/(y2 + x2)}];
f[2, {x_, y_}] := N[{-x/(1/0.370) - y/(1/0.370), 1/2 +
x/(1/0.370) - y/(1/0.370)}];
pt = {0.5, 0.75};
cr[n_] := If[
n - 2 == 0,
RGBColor[
0, 0, 1], If[n - 3 == 0, RGBColor[0, 1, 0], If[n - 1 == 0,
RGBColor[1, 0, 0], RGBColor[0, 0, 0]]]]
ptlst = Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]},
{j, Length[dlst]}];
Show[Graphics[Join[{PointSize[.001]}, ptlst]],
AspectRatio -> Automatic, PlotRange -> All]

```

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