Substitution Tessellation Exploration
- Graph paper
- Triangular graph paper
- Two printed pinwheel tessellations
- Using triangular graph paper, make the substitution tessellation for the half-hexagon rep-tile:
- Is the substitution tessellation that you get from the trapezoid a periodic tessellation or a non-periodic tessellation?
- The pinwheel tessellation is not periodic. In fact, the triangular tile is rotated by new and different angles at each stage of the construction.
- On your printed copy of the large pinwheel tessellation, the large triangle is made of five smaller triangles. Find them and highlight their edges. Can you identify the next level of smaller triangles?
- Find rectangles in the pinwheel tessellation. Do you observe any patterns in their size or position? Shade in rectangles to emphasize the pattern (or lack of pattern).