# Animating Mathematics

### GIFs aren’t just for cat videos

Clayton Shonkwiler

/icerm

this talk!

### Yes, really

Spiral Light, by Dave Whyte (@beesandbombs)

...?

### Spherical Dodecahedron

a.k.a. pentagonal tiling of the sphere

### Rotation

...of what?

z \mapsto \frac{i (z+1)}{z-1}

### Source Code

inv[z_] := I (z + 1)/(z - 1);
circleinversion[z_] := z/Norm[z]^2;

HRot = ParallelTable[
ParametricPlot[
Flatten[{{10 (t - π), 0},
{ToReal[inv[E^(I t) + #]],
ToReal[inv[
circleinversion[E^(I t) + #]]]} & /@ (E^(I θ)*
DeleteCases[
Flatten[Table[a + I b, {a, -4, 4, 2}, {b, -4, 4, 2}]],
0 + 0 I])}], {t, 0, 2 π}, PlotRange -> 4,
Axes -> False,
PlotStyle ->
Directive[Thickness[.003], RGBColor[{227, 156, 188}/255]],
ImageSize -> {540, 540},
Background -> GrayLevel[.2]],
{θ, 0., π/2 - #, #}] &[π/400];

Export[NotebookDirectory[] <> "HRot.gif", HRot,
"DisplayDurations" -> {1/36}]

processing.org

### Backstory

Only certain pentagons tile the plane

### So I decided to build a quadrilateral tiler...

(requires free Wolfram CDF player)

### Last Step: gifsicle

> gifsicle -O2 -k128 input.gif > output.gif

“optimize”

# colors

(≤256)