The following diagrams use a different set of pieces than the traditional pattern block pieces. These pieces have the following properties:
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 tesselgon 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 45degree rhombus.
The following diagram shows the diamonds D_{0} to D_{6}.
PDF version (43 KB) 
The following diagram shows the squares S_{0} to S_{6} and S_{7}.
PDF version (56 KB) 

PDF version (142 KB) 
The following diagram shows the stars X_{0} to X_{6}.
PDF version (118 KB) 
The following diagram shows 8 pointed stars S8_{0} to S8_{4} and S8_{5}.
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.
Back to Ideas for other Fractal Designs.
Copyright 19982004 by Jim Millar