09 December, 2009

The Fruits of Asymmetry

A Coxeter Polytype
Coxeter - 'n' dimensional tilings - assuming maximum symmetry

A Penrose Tessellation
A Penrose Tiling - concerned with near symmetry cases

Tessellating Asymmetric Re-entrant polygons Jim Schofield
Tessellation utilising re-entrant polygons
(in this case using a singly re-entrant asymmetric hexagon - or "L tile")

"...What was evident to me was that the essential component in these formal investigations was Symmetry! While my colleagues in Physics were totally wedded to complete maximal Symmetry (and indeed Super Symmetry), I was finding that instead of the limited numbers of tilings and crystal forms that were available to them, I was finding (in 2D at least) a seeming infinite complexity of Forms. With maximally symmetric units, these all funnelled down into a minimal set, but with re-entrant forms (the first deviation from maximal symmetry), and various regular asymmetries, the possibilities were vastly increased.
Indeed, from monolithic tilings (using a single basic unit in a single way) there occurred a wide range of hierarchical forms, which could be different or mathematically similar at each succeeding level."

To read the rest of this paper, click here

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