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

supernova

(* "SuperNova": Evolute of a hypotrochoid with varing parameter h *)
Clear[myDotStyle]
myDotStyle = Table[{PointSize[.015],Hue[i,3.33 (.3-i),1]},{i,0,.3,.3/39}];

Do[
	j = (i 1/(3/7))^3;
	ParaPlot[
		Hypotrochoid[1, 3/7, j][t],
		{t, 0, 18.22, 3 2 Pi/(7 40)},
		PlotEvolute->True, PlotCurve->False,
		DotStyle->myDotStyle,
		PlotRange->{{-1,1},{-1,1}} 1.05 (1+3/7+j),
		AspectRatio->Automatic, Axes-> False
	],
	{i,0,.54,.54/100}
];
Clear[myDotSyle]

kaleido-glass

(* "Kaleidoglass": Pedal of hypotrochoid with varing parameter h *)
Do[
	ParaPlot[
		Hypotrochoid[1, 1/4, i][t],
		{t, 0, 2 Pi, 2 Pi/(4 21)},
		PedalPoint->{0,0},
		PlotDot->False,
		LineStyle->{Hue[.34,1,.8]},
		PlotRange->{{-(1-1/4+i),(1-1/4+i)},{-(1-1/4+i),(1-1/4+i)}} 1.05,
		Axes->False, AspectRatio->1
	],{i,0/4,4/4, 1/100}
]

star fish

(* "star fish*)
(* Secants of hypotrochoid with varing parameter h. *)
Do[
	j = (i 1/(2/5))^3;
	ParaPlot[
		Hypotrochoid[1, 2/5, j][t],
		{t, 0, 3 2 Pi, 2 2 Pi/(5 22)},
		SecantConnection->{5 3,1},
		Axes->False, PlotDot->False,
		AspectRatio->Automatic,
		PlotRange->{{-1,1},{-1,1}} (1-2/5+j) 1.05
	];,
	{i,0,.51,.51/120}
]