Math

18 Splashes.

1. AttractorsIn 1963 the scientist Edward Lorenz made a very simple model of moving air: three short equations.
2. Möbius StripA Möbius strip is a loop with a half twist in it.
3. Klein BottleA Klein bottle is a surface with no inside and no outside.
4. Menger SpongeA Menger sponge is a fractal.
5. 4D ShapesA hypercube, or tesseract, is a cube in four dimensions.
6. Torus KnotA torus knot is a knot that winds around the surface of a donut shape, called a torus.
7. GyroidA gyroid is a curving surface that splits space into two tangled mazes of tunnels that never meet.
8. MandelbulbThe Mandelbulb is a 3D fractal, a cousin of the famous flat Mandelbrot set.
9. Sierpinski TetrixA Sierpinski tetrahedron is a fractal pyramid.
10. Platonic SolidsThe Platonic solids are the only five convex polyhedra whose faces are all the same regular shape, meeting in the same way at every corner: the tetrahedron (4 triangles), the cube (6 squares), the octahedron (8 triangles), the dodecahedron (12 pentagons) and the icosahedron (20 triangles).
11. Seashell SpiralMany seashells grow in a spiral.
12. Graph PlotterA graph turns an equation into a picture.
13. Surface PlotterA surface plot is a graph in 3D.
14. Circle and WavesThe unit circle is a circle with a radius of 1.
15. Fourier CirclesCircles turning on circles can draw almost any closed shape, given enough of them.
16. Pythagoras ProofIn a right triangle, the two short sides a and b and the long side c always fit a rule: a² + b² = c².
17. Splat SelectorA word or picture becomes a tree of splats.
18. Splat EquationEvery splat has a place and a color.