Revealing Dimensions — Edmund Harriss

The full mural design as a wide panorama: the Socolar aperiodic tiling, deep blue at the left where only faint vertices show, brightening across to gold at the right where dense blue tiles fill the pattern. — Full design for the wall.

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.

Detail of the mural: white vertices scattered like a night sky across the top, gradually joined by white lines into decagons, pentagons and squares toward the bottom, on a dark grey ground. — Details of the mural, reading left to right: vertices scattered like a night sky, the lines and tiles emerging, and finally the two-dimensional tiles picked out in colour.

Detail where the tiling gains colour: white-and-blue tile outlines on a dark blue ground at the left give way to solid blue tiles on a gold ground at the right. — Details of the mural, reading left to right: vertices scattered like a night sky, the lines and tiles emerging, and finally the two-dimensional tiles picked out in colour.

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.