Edge Replacement

The Edge Replacement algorithm takes each line in the original pattern and replaces it by the motif

where the tips of the triangles correspond to the ends of the orignal line. When two adjacent lines in the original pattern meet at a point the newly created triangles will share an edge.

When we apply this transformaton to the simple triangle on the left we get the more interesting pattern on the right.

If we apply the transform again we get the next pattern (on the left). The image on the right illustrates the relationship between the two iterations, the black lines being the original pattern and the red ones showing the new one.

The python scripts provided in this section allow the patterns to be initialised with any polygon, with an option to include radial spokes. The triangle above is a three sided polygon without spokes, this pentagon is an example of a starting pattern with spokes.

Applying the transformation three times generates this pattern.

If you would like to try colouring this in there is a higher resolution version on the colouring-in page.