QuasiG V1.4 is a freeware Penrose tiling program that will show and print full-colour Penrose tiling patterns, and more general quasi-crystal patterns, on any Windows 95/98 or NT/2000/XP PC. At first sight, these tilings may seem esoteric, but they have found practical application in coating non-stick cookware, and making more attractive toilet paper rolls. A subset of quasicrystals (Penrose tiles) have even funded the retirement dreams of the legions of lawyers that prosecuted their use on the toilet rolls...

*Table of Contents*

BackGround | Examples | Animation | Penrose Marking | Storey Hall | Printing this page | Links | Download

## Background

Quasi-crystal tilings are assembled from two rhomb shaped tiles (squashed squares with equal length sides). The smaller angle in one rhomb is half that of the smaller angle in the other rhomb. The angle divides into p (PI) an odd number of times (n). p (PI) is 180 degrees, or half a circle. The number (n) gives the degrees of symmetry that can be observed in the pattern (you can find parts of the pattern which can be rotated n times through the smaller angle and still look the same).

Penrose tilings are a subset of these in which there are 5 degrees of symmetry (n = 5 ), and in which tile edges are matched to satisfy the patterns in Figure 1 at left (see examples in Penrose Marking section below )

Tilings are constructed by finding ways of combining the 2 angles possible with each of two tile orientations so as to add up to 2p (2 x PI) - and thus span a full circle around a vertex. For example, with n = 5, there are 7 different ways to arrange the tiles at a vertex (or 8 ways if you count two star patterns that look the same except for the markings).

Eric Weeks's site provides an explanation for the methods used in an dual grid algorithm based on N.G.deBruijn's dual grid. It can generate penrose tilings ( see quasi.c http://www.physics.emory.edu/~weeks/software/quasic.html. http://www.physics.emory.edu/~weeks/software/quasic.html ) ..

For other sites explaining more about non-periodic tilings, see the links section below.

Eric's quasi.c, on which this is based, does not enforce the strict tile-matching rules that the classic Penrose tilings have. Nor could it draw them. But it's source code can be adapted to produce them. And, the non-penrose patterns can be just as interesting.

## Using QuasiG

Using QuasiG is meant to be simple. It has default input values that will produce a simple image of penrose tiling. Details QuasiG features and its options are described in here.

Example Screenshots images below demonstrate some of the patterns possible with QuasiG.

Click here to download QuasiG.

## QuasiG Examples

The image below is an example of QuasiG's screen output for 5 degrees of symmetry, auto-scaling on, central pattern only, fill on, black edge on, color-doubling on, color gradient off, all 4 quadrants displayed, and 30 generating lines (I used PaintShop Pro's screen capture to get this). The title bar summarises the options selected - in this version Offset Multiplier was 1.