Sketches for the Art Project Exploration
Objective: Practice several of the techniques that will create an Escher-like tessellation.
Using Translations
We have seen before that we can modify geometric tessellations to create tessellations by recognizable figures. We did several in Escher-Like Tessellations Explorations.
Using Rotations
We can rotate about the center of a side or about a vertex.
1. Create some tessellations with 2-fold, 3-fold and 4-fold rotational symmetry. Which ones are easiest to do? What geometric tessellation(s) should you start with in each case?
Using Reflections
Starting with a tessellation by squares or rectangles we can create tessellations with reflectional symmetry.
2. Create some tessellations with reflectional symmetry.
Using Glide-Reflections
3. Starting with a tessellation by squares or rectangles create tessellations using glide reflections.
Using Other Geometric Tessellations
Semi-Regular Tessellations
Recall the Archimedean tessellations:
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| (3,6,3,6) | (3,4,6,4) | (3,12,12) | (3,3,3,4,4) |
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| (4,8,8) | (3,3,4,3,4) | (4,6,12) | (3,3,3,3,6) |
4. Experiment with these geometric tessellations and create patterns with recognizable figures from them. Think about which symmetries you want. You can just use translation, or maybe rotations and / or reflections.
Polyominoes
5. Start with a tessellation by either a tetromino or a pentomino and create a tessellation by recognizable figures from it. Use a tessellation by an interesting polyomino (i.e. not one of the rectangular ones).
The Art Project
Develop 10 to 15 sketches of tessellations by recognizable figures using several of the above mentioned techniques.
