Non periodic Tiling (Pinwheel Tiling)

Non periodic tiling are fascinating structures. One of the most famous is by Conway and Radin. The following is the base structure for creating a pin wheel tiling. Its a right triangle of side . Unlike a normal triangle which gives 4 congruent triangle when all the mid points are joined. This is created by dividing the triangle into 5 congruent triangles. The way these 4 triangles are oriented prevents any translational or rotational symmetry.

Notice how to obtain four congruent triangles.