# Difference between revisions of "Escher-Like Tessellations Explorations"

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− | 1. Use translations as described above to create an Escher-like tessellation from this parallelogram tessellation. (Modify the top and left side of one parallelogram, and propagate the modification through the tessellation.) | + | 1. Use translations as described above to create an Escher-like tessellation from this parallelogram tessellation. (Modify the top and left side of one parallelogram, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure! |

[[Image:Parallellogram-net.png]] | [[Image:Parallellogram-net.png]] | ||

− | 2. Use translations as described above to create an Escher-like tessellation from this rhombus tessellation. (Modify the top and left side of one rhombus, and propagate the modification through the tessellation.) | + | 2. Use translations as described above to create an Escher-like tessellation from this rhombus tessellation. (Modify the top and left side of one rhombus, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure! |

[[Image:Diamond-net.png]] | [[Image:Diamond-net.png]] | ||

− | 3. On the following geometric tessellations, modify one side, and propagate that change throughout the tessellation by rotating about a vertex. | + | 3. On the following geometric tessellations, modify one side, and propagate that change throughout the tessellation by rotating about a vertex. Make sure you create a tessellation with a recognizable figure! |

[[Image:Square-net.png]] | [[Image:Square-net.png]] | ||

− | 4. Find the midpoints on one of the following squares, modify half of each of the sides, and propagate this change by 180° rotations through the midpoints. | + | 4. Find the midpoints on one of the following squares, modify half of each of the sides, and propagate this change by 180° rotations through the midpoints. Make sure you create a tessellation with a recognizable figure! |

[[Image:Hexagon-net.png]] | [[Image:Hexagon-net.png]] |

## Revision as of 12:04, 23 July 2007

**Objective:**
Escher developed his tessellations from the more primitive geometric tessellations using isometries. We will practice several of the techniques that will create an Escher-like tessellation.

1. Use translations as described above to create an Escher-like tessellation from this parallelogram tessellation. (Modify the top and left side of one parallelogram, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!

2. Use translations as described above to create an Escher-like tessellation from this rhombus tessellation. (Modify the top and left side of one rhombus, and propagate the modification through the tessellation.) Make sure you create a tessellation with a recognizable figure!

3. On the following geometric tessellations, modify one side, and propagate that change throughout the tessellation by rotating about a vertex. Make sure you create a tessellation with a recognizable figure!

4. Find the midpoints on one of the following squares, modify half of each of the sides, and propagate this change by 180° rotations through the midpoints. Make sure you create a tessellation with a recognizable figure!

**Handin:**
A sheet with answers to all questions.