30-degree tiling with an infinite set of pieces

The following transform shows how an infinite set of 30-degree pieces can be used to create a design.

The first diagram shows the transformation of triangles. Each triangle is transformed into a design that uses larger triangles. Thus, as the design grows, the triangle gets larger and larger.

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

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

The following shows the diamonds D₀ to D₃ and larger diamonds D2₀ and D2₁.