Escher Fractal Exploration
Escher experimented with some simple fractals. If you start with a square, and inscribe successive squares you will get a fractal. I re-created one of his works and shaded in several triangles.
1. Copy the design to the right hand side.
We can go one step further and divide all triangles in two. This can easily be achieved by drawing both diagonal in the large square and the next smaller square. I shaded alternate triangles. (This is also a copy of one of Escher's fractals.)
2. Copy the design to the right hand side.
More interesting fractals were created by repeatedly dividing squares in fourths:
3. Divide the bottom four squares into fourths.
4. Repeat this process on the picture in stage 2. You should get something like this:
5. Copy one of the patterns done by Escher onto the square below. Use shading to make the repeating pattern of the fractal visible. See for instance Visions of Symmetry, Pg. 315