Animating Mathematics
GIFs aren’t just for cat videos
Clayton Shonkwiler
Colorado State University
/icerm
this talk!
GIFs? Really?
Really?
Yes, really
Spiral Light, by Dave Whyte (@beesandbombs)
Unoriented
Reveal
Reinvention
Coalesce
My First GIF
Geodesic
A to Z
Closure
Tiling
...?
Spherical Dodecahedron
a.k.a. pentagonal tiling of the sphere
+ Stereographic Projection
= Stereographic Dodecahedron
Rotation
...of what?
z↦z−1i(z+1)
z \mapsto \frac{i (z+1)}{z-1}
The Hyperbolic Plane!
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}]And much more mathematics...
Schwarz–Christoffel Mapping
Langer & Singer's Trefoil
Brownian Bridges
Lawson Surface
The Klein Quartic
4-D Rotations
Roman Surface
Polytope Cross-Sections
Pentagon Tilings
How?
The Answer for Most People:
Processing
+
ImageMagick / gifsicle
Official @beesandbombs
GIF-making guide
The Answer for Me
- Mathematica
- Online color palette collections
- gifsicle
Example
Backstory
Only certain pentagons tile the plane
But all quadrilaterals tile!
So I decided to build a quadrilateral tiler...
(requires free Wolfram CDF player)
Colors
Also: design-seeds.com, color.adobe.com, swisscolors.net, and many more
Last Step: gifsicle
> gifsicle -O2 -k128 input.gif > output.gif“optimize”
# colors
(≤256)
Download from lcdf.org/gifsicle/ or install from your favorite package manager
Thank you for listening!
Animating Mathematics GIFs aren’t just for cat videos Clayton Shonkwiler Colorado State University http://math.graphics @shonk /icerm this talk!