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

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]