Sunday, October 12, 2008

Fractal tilings

Fractal shapes can be used as tiles for filling plane. In most cases variations of the Koch snowlake are used. A simple Koch snowflake is represented to the right. To create a set of tiles, which can be used for filling whole plane, we need another variations of the snowlake which exactly match to all convexes and concaves of the first figure.

Two variations of such kind of tilings were represented on Briges 2008 conference, which took place in Leeuwarden (Holland). Both were realized in wood. We see that several kinds of fractal tiles were used in both cases. 

Koch tiling by Edmund Harris

Pentagonal Koch tiling by Chaim Goodman-Strauss

More mathematical issues about fractal tiles you can read in the article about Rauzy fractal.

1 comment:

maxwelldemon said...

I am not sure whether the Conch tiles you show are fairly described as a variation on the Koch tiles. It is true that the edges are made by repeated division of the edge, but this is in a rather non-trivial way by comparison. The Koch curve just has one sort of edge up to rotation, and in this case there are 4. The trick is to find rules where the lines created give tiles that can be combined into larger copies of each other.