The following transform shows how an infinite set of 45-degree pieces can be used to create a design.

The first diagram shows the transformation of squares. Each square is transformed into a design that uses a larger square. Thus, as the design grows, the squares get larger and larger.

The diagram also shows how the edges of each transform are recursively developed. It is important that the edge of the larger square match with other pieces, including multiple smaller pieces. The transform of the larger square has an edge made of blue diamonds and smaller squares. This edge is created from two edges of the smaller square, plus a larger set of the same diamonds and squares as the smaller square.

The second diagram shows the transformation of the stars and the diamonds. It also shows how the edge of the square is truncated and combined to create the edges of the stars and diamonds.

The following shows the diamonds D_{0} to D_{3} and larger
diamonds D2_{0} and D2_{1}.

PDF version (31 KB) |

The following shows the squares S_{0} to S_{3}, S2_{0}
to S2_{2}, S4_{0} and S4_{2}, and S8_{0} and S8_{1}.
The next is S2_{3}. The last is S_{4}.

PDF version (88 KB) |

PDF version (124 KB) |

PDF version (369 KB) |

The following shows stars St_{0} to St_{2}, St2_{0}
to St2_{2}, and St4_{0} to St4_{1}. The next shows St_{3}.

PDF version (35 KB) |

PDF version (71 KB) |

The next shows how a larger star is created from squares and diamonds. It
shows BSt_{0} to BSt_{2} and BSt_{3}.

PDF version (48 KB) |

PDF version (477 KB) |

Back to ideas for more designs.

*Copyright 1998-2004 by Jim
Millar *