Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2000 by Xah Lee. (http://xahlee.org/)

Packages and Initializations

Needs["ParaPlot`"]
(*MathSource Item:0207-986*)

Needs["PlaneCurveFormulas`"](*0208-482*)

Needs["PlaneCurveGenerator`"](*0208-314*)

Needs["Graphics`ImplicitPlot`"]
(*MathSource Item:0200-529*)

$HistoryLength = 5;

Epitrochoid, hypotrochoid animation gallary

snow flake

(* "Snow Flake": catacaustic of a hypotrochoid with varing parameter h *)
Do[
	ParaPlot[
		Epitrochoid[1, 1/6, i][t],
		{t, 0, 2 Pi, 2 Pi/(6 9)},
		CausticLineLength->20,
		Axes->False,PlotDot->False, PlotCurve->False,
		CausticLineStyle->{Hue[0,0,1]},
		Background->Hue[0,0,0],
		PlotRange->{{-6,6},{-6,6}}, AspectRatio->Automatic
	], {i,0, 1.5, 1.5/40}
];

snow flake 2

(* "Snow Flake": catacaustic of a hypotrochoid with varing parameter h *)
Do[
	ParaPlot[
		Epitrochoid[1, 1/6, i][t],
		{t, 0, 2 Pi, 2 Pi/(6 9)},
		CausticLineLength->20,
		Axes->False,PlotDot->False, PlotCurve->False,
		CausticLineStyle->{Hue[0,0,1]},
		Background->Hue[0,0,0],
		PlotRange->{{-2,2},{-2,2}}, AspectRatio->Automatic
	], {i,0, 1.5, 1.5/40}
];

flashing diamond

(*"Flashing Diamond". Evolute of a hypotrochoid with varing parameter h *)
Do[
	ParaPlot[
		Hypotrochoid[1, 1/4, i][t],
		{t, 0, 2 Pi, 2 Pi/(4 15)},
		PlotEvolute->True,
		Axes->False, PlotDot->False, PlotCurve->True,
		DotStyle->{{Hue[.6,1,.9],PointSize[.01]}},
		LineStyle->{Hue[0,.9,.9]}, AspectRatio->Automatic,
		PlotRange->{{-(1-1/4+i),1-1/4+i},{-(1-1/4+i),1-1/4+i}} 1.4
	], {i, 0, 1/4, (1/4)/100}
];