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(click for a larger, unmodified image)
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1. This initial square shape can generate the entire tessellation
through a series of translations. Visualize this for yourself.
Once you have convinced yourself that this square shape can produce
the rest of the tessellation by simple translations, move to step
2. |
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2. We notice much reflective symmetry inside of the initial square
shape. Through a little experimentation, we find that a small
square within the shape can generate the larger square through
the use of two reflections. For example, when the smaller square
is reflected across its lower-right side, a red butterfly. Also,
when the smaller square is reflected across its lower-left side,
a white bird is completed. The smaller square contains exactly
one half of both a red butterfly and a white bird. It is because
of the two reflections that the butterfly and bird are completed. |
The following animation illustrates how to recreate the above
tessellation. The process involves the following steps: reflect the design towards the lower-right, reflect the entire design
towards the lower-left, and translate the entire design to tessellate the plane:
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Print out an example on the hands-on activities page and use the techniques described above to create your own tessellation
based on this example of Escher's artwork. Remember to pick
the activity referencing page 9/12.
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All M. C. Escher works (c) Cordon Art B.V.-Baarn-the Netherlands.
Modifications for demonstration purposes only. Used with permission.
  
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