May 1, 2014

Fermat's Spiral with Mathematica

Fermat's Spiral with Mathematica

With their opposing pattern, these two Fermat spirals are surprisingly beautiful.  They look like something you might encounter in nature and yet result from a very basic mathematical formula.

Here's the Mathematica code I used to generate them:

(*Fermat's Spiral*)
width = 0.005;
graphColor = RGBColor[70/255, 137/255, 102/255];
k = GoldenRatio;
g[t_] := k*Sqrt[t]

PolarPlot[{-g[t], g[t]}, {t, 0, 15*Pi},
PlotStyle -> {{graphColor, Thickness[width]}, {graphColor,
Thickness[width]}}, PlotRange -> {{-12, 12}, {-12, 12}}, Axes -> False]