Twelve repeating patterns: checkerboard, dots, grid, stripes, hexagons, rings, radial lines, spiral, triangles, hearts, waves, and zigzag.
They share one piece of setup, which is why the controls behave the same across all of them. Before any pattern is drawn, the coordinates are centred, rotated by rotation, leaned over by skew, and scaled. Each pattern then works in that prepared space without knowing anything has happened to it, so rotating stripes and rotating hexagons are the same operation.
The patterns themselves are mostly built from one idea: chop the plane into repeating cells, then ask each pixel where it sits inside its own cell. Close to the middle of the cell, or close to an edge, or on one side of a diagonal. That question answers itself differently for each shape and gives you dots, grids, or checks. Hexagons need a small trick, two square grids offset from each other with each pixel taking whichever centre is nearer, which produces a hex lattice without any hexagon maths at all.