Bigger and Smaller I - Lemon Tea Variant

Bigger and Smaller I – Lemon Tea Variant

Bigger and Smaller I  

The title refers to Escher’s Smaller and Smaller print. This tiling uses a 5-fold geometry, as is obvious from the pentagonal profile, and is based on the same Kite tile as that used in the Penrose tiling. The tiles emerge and disappear into numerous singularities.

A different colour variant is on display in the Art Science Museum at the Marina Bay Sands in the exhibition:

Journey to Infinity: Escher’s World of Wonder

Richard says:  This fractal is not shown at its limits, although in this arrangement, it will approach a decagonal limit, which has sides in the proportion of the Golden Ratio. However, in order to proceed to the limit, another tile is necessary to resolve an anomaly where the tiles do not tile the plane without gaps or overlaps. This tiling, with over 400,000 tiles, is under construction but has reached a different kind of limit – my computer processing power.  With luck this will be resolved within the next year by Moore’s law.

As in the Penrose tiling, the colouring with minimal number of colours does not relate to the geometry, instead it applies a kind of camouflage distribution, which to a large degree visually masks the rotational symmetry. This combination of symmetry and randomness is very appealing to me.