Creating Escher-like Tessellations Exploration

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Time-45.svg

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.

Translations

1. Use translations 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!

Parallellogram-net.png

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

Square-net.png

Reflections

3. On the following geometric tessellations, modify the top of the square, and propagate that change throughout the tessellation by translation. Next modify one of the sides of the square and reflect your modifiations so you get the changed side PLUS its reflection along that one side. Now use translations to move this symmetric change throughout the tiling. Finally, create a tessellation with a recognizable figure! Be creative. You may need to use several images together to create the tiling.

Square-net.png


Rotations

4. Change one of the sides on the square. For this first try keep the change to the side fairly simple. Use 90 degree (4-fold) rotations to transfer the change over to all the other sides of the squares. After changing all the sides sketch the figures suggested by your shapes. Make sure that the images follow the rotations you used in creating this tessellation. In other words: when you are done your drawwing should show 4 fold rotational symmetry.

Square-net.png

5. A sligthly different way of using rotations when creating a tessellation is to choose a side, find the midpoint of the side and modify one half of your edge. Next rotate the change through 180 degrees so that the whole side has been changed. Do this to a horizontal side and a vertical side. You may use different changes on the horizontal side versus the vertical side.

These changes can be propagated throughout the tessellation by translations. Now create a tessellation by recognizable figures. Your resulting tessellation should have 2 fold rotational symmetry.

Square-net.png


Handin: A sheet with answers to all questions.