Aperiodic tiling

by Kirill Demura

Periodic tilings

Have a repeating pattern

Nonperiodic tilings

Tilings that lack a repeating pattern

Wang tiles

Aperiodic tileset

Aperiodic tilings

Non-periodic tiling with the additional property that it does not contain arbitrarily large periodic patches

For example Penrose P3 tiling

Penrose tiling rules


De Bruijn multigrid method

Generating quasiperiodic tilings

Create n axes defined by their unit length

For each axes define normals

Shift normals by some distance

Build grids by shifting normals by unit vector

Multigrid is done

Find intersections of lines

For each intersection find multigrid coordinates of surrounding polygons. They will convert into vertices of tiles

Vertice in tiling is sum of n vectors, where each vector is determined by the angle of axis and its magnitude is coordinate on this axis


Changing shift value

Changing angles of axes

Changing number of grids

Something else can take the place of rhombi. Circles, for example

A few words about angles in V8

Hey, that's not all

How about Game of Life on aperiodic tiling?

Thank you!