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http://www.geocities.com/rlbagulatftn/Henon2nd_kiss.gif
Here the Henon of the second kind ( rotational)
is scaled to get a kissing fractal.
I got the idea for this from my efforts to get a Weizsäcker-Kuiper
like vortex of circles-ellipses.
The Henon law is based on conservation of the area in the x direction.
The first two are trianguloids like the elliptical signature curve,
but the inner curves are
four cornered.
Mathematica:
Clear[f, dlst, pt, cr, ptlst, x, y]
RandomSeed[];
a0 = 1.5732;
dlst = Table[ Random[Integer, {1, 2}], {n, 250000}];
f[1, {x_, y_}] := N[ {2*x*y/(x^2 + y^2) , (y^2 - x^2)/(y^2 + x^2)}];
f[2, {x_, y_}] := N[{x*Cos[a0] - (y - x^2)*Sin[
a0], x*Sin[a0] + (y - x^2)*Cos[a0]}/(1.55)];
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] |
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