Revealing Dimensions

The Socolar tiling is a non-periodic tiling of the plane — it fills space without gaps or overlaps, but never repeats in a regular way. Discovered by Joshua Socolar, it belongs to the same family of aperiodic tilings as the better-known Penrose tiling, but has its own distinct structure and local matching rules.

The mural was commissioned by the Tulsa Regional STEM Alliance for their headquarters. At 42′×8′, it allows viewers to see the large-scale structure of the tiling — the way local arrangements generate global order without any periodic repetition — at a scale where that order becomes visible.

The image starts as a collection of vertices, reminiscent of the night sky, before gradually adding one dimensional lines connecting the vertices, the two dimensional tiles then make an appearance, each a different colour. The structure is actually a projection from six dimension, bu beyond two dimensions is left to the imagination of the viewer.