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(click for a larger, unmodified image)
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1. This initial hexagon shape can generate the entire tessellation
through a series of translations. Visualize this for yourself.
Imagine the pattern within this hexagon being moved in all directions.
The patterns should match exactly. Once you have convinced yourself
that this hexagon shape can produce the rest of the tessellation
by simple translations, move to step 2. |
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2. We notice that the beaks of three black birds meet at the center
of the hexagon. Also, we notice that the wing tips of three white
birds also meet at the center. The hexagon seems to have rotational
symmetry. We find that we can divide the hexagon into a section
which, when rotated around the center of the hexagon, can generate
the other sections. |
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3. There seems to be two birds located mostly inside of this section
of the hexagon. Therefore, we divide it further into two equilateral
triangles, one of which corresponds to a black bird, and the other
of which corresponds to a white bird. Let us focus on the equilateral
triangle containing the black bird. |
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4. We now outline the boundaries located inside of the equilateral
triangle. Comparing these boundaries to those that inside of the
other triangle, we realize that rotating the boundaries of one
triangle will create the boundaries inside the other.
What this means is that the entire tessellation shown at the top
was generated from a pattern inside of a simple equilateral triangle. |
The following animation illustrates how to recreate the above
tessellation. The process involves the following steps: rotate the design around the vertex of the hexagon (60 degrees), rotate the entire design twice around the center of the hexagon (120
degrees each time), and translate 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 5/12.
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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.
  
top of the page
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