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Guest
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http://www.geocities.com/rlbagulatftn/3powercycloid.gif
Trying to get something like a standing wave cycloid
in to an IFS I came up with this new parametric which I call a power
cycloid:
Mathematica:
s[x_, y_, n_] := n*2*x*y/(x2 + y2) - (2*x*y/(x2 + y2))^n
c[x_, y_, n_] := n*(x2 - y2)/((y2 + x2)) - ((x2 - y2)/((y2 + x2)))^n
Clear[f, dlst, pt, cr, ptlst, x, y]
dlst = Table[ Random[Integer, {1, 2}], {n, 150000}];
f[1, {x_, y_}] := N[{-x/2 - y/2, x/2 - y/2 + 1/4.4}];
f[2, {x_, y_}] := N[ {s[x, y, 3] , c[x, y, 3]}];
pt = {0.5, 0.75};
cr[n_] := If[n - 1 == 0, RGBColor[0, 0, 1], If[n - 2 == 0, RGBColor[0,
0, 0],
If[n - 3 == 0, RGBColor[1, 0, 0], RGBColor[0, 1, 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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