Octagonal-based set of pieces

The following diagrams use a different set of pieces than the traditional pattern block pieces. These pieces have the following properties:

The sides are all the same length
The angles are multiples of 45 degrees

A substitution tiling using these pieces is shown below, used to create the following diagrams.

The square is in the set of pattern block pieces. The star is available in the set of tessel-gon stars from www.tessellations.com and is the same size as the square from the pattern block set. However, neither the set of pattern blocks nor the products at www.tessellations.com have a 45-degree rhombus.

The following diagram shows the diamonds D₀ to D₆.

PDF version (43 KB)

The following diagram shows the squares S₀ to S₆ and S₇.

	PDF version (56 KB)
	PDF version (142 KB)

The following diagram shows the stars X₀ to X₆.

PDF version (118 KB)

The following diagram shows 8 pointed stars S8₀ to S8₄ and S8₅.

	PDF version (70 KB)
	PDF version (153 KB)

The 8 pointed star is interesting because each star is contained in the center of the higher order stars. In fact, as all the designs grow, the designs contain the 8 pointed star at every vertex.

Here is a generalization to other values of n.

Back to Ideas for other Fractal Designs.