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# Aperiodic Tilings of 2D and 3D

A fairly recent branch of recreational mathematics, non-periodic/aperiodic tiling
took off as a serious branch of materials science when Danny Schectman discovered
metal alloys displaying a flagrant 5-fold symmetry in their X-ray diffraction
patterns.

Roger Penrose discovered several versions of a particular 2D tiling that came to
be know as Penrose tiles, and Ammann and others furthered our understanding of the
nature of such irrational "tesselations". Schectmannites (the aforementioned alloys)
are basically in a structure that is a 3D extension of the Penrose tiling structure.

There are strong fractal properties of many of these tilings, in that a tiling can be
transformed into a denser tiling by simple substitution rules, and this repeated
indefinitely - a processes termed deflation and inflation.

Most of these links go to the wonderful University of Minnesota's Geometry Centre
pages - a well nice net resource.

## Tiling Images

## Tiling Links

## Tiling Software on the Net

Last updated by *markt@chaos.org.uk*
Mon 18 January 1999