Tuesday, June 19, 2007


Here is a quick little pattern with the triangular grid only partially expanded. The diamond shapes are two triangles that did not have a spacer inserted. These last week have all been variations on a theme. I'm sure I'll switch themes soon. Perhaps I'll start introducing a few of my concrete constructions....

Hour glasses and Pythagoras

There's lot's to see in this pattern. The idea was to elaborate a square grid using triangles. By using larger triangles, the pattern creates a number of interesting features to focus on.

The first features are white hour glasses made with the two white 120 degree isosceles triangles. They have two orientations that alternate. These are the holes that come from the vertices of the original square grid. The size of the orange triangles was selected to have the triangles share a vertex. A smaller size of triangle would leave a gap which could be seen as the white isosceles triangles overlapping.

The second features are large squares that are defined by a purple square and it's four neighbouring equilateral triangles. This square that also be identified as a propeller can be chunked together with similar squares of the same orientations to create a tiling that is a Pythagorean tiling. What is interesting is either orientation of a purple square can be the basis for big squares and that each produce a Pythagorean tiling. It really is just a mater of switching your point of view and chunking different polygons together.

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