| Here we present a variant of the limit set, forbiding all combinations of inversions that are expansions. | |
| Here we use driven IFS to map which combinations of inversions result in expansions when the inverting cirlces overlap. | |
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| First we survey Escher's tilings and other works motivated by his desire to encomapss the infinite in a finite range. |  |
| A tiling or tessellation is a division of the plane into congruent, nonovelapping figures. We review some simple plane tilings. |  |
| A simple way to make more complicated tiles is midpoint displacement. |  |
| How can we tell a fractal tiling from a Euclidean tiling? Here we review the relevant property of fractals. |  |
| Fractals can be distinguished from Euclidean tiles by using the area-perimeter relationship. |  |
| With midpoint displacement we can build some simple fractal tiles. |  |
| Here is one simple method for producing simple fractal tilings. |  |
| Here is another simple method for producing simple fractal tilings. |  |
| Here is a more mathematically demanding method of generating an infinite variety of fractal tiles. |  |
| Here is a practice final, here is another practice final. | |
| Here are the answers for the seventh and eighth homeworks. |