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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 this hexagon shape being moved to the left and to the
right. The pattern should coincide exactly. Then imagine this
hexagon shape being moved in a diagonal direction (just as a regular
tessellation of hexagons would). The pattern should also coincide
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 three black creatures inside of this hexagon
seem to be symmetric about the center of the hexagon. Upon further
inspection, we realize that the hexagon can be divided into three
sections, each of which is a rotated copy of the other. So, let
us outline one of these three sections. |
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3. We immediately notice that the diamond section can be divided
in half. Each half is a mirror image of the other. So, let us
outline one of the mirror halves, which turns out to be an equilateral
triangle. |
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4. To better understand how the pattern inside of this equilateral
triangle was created, let us draw outlines over the important
boundary lines of the creatures. After doing so, we recognize
the rotational symmetry inside of this equilateral triangle.
What this means is that the entire tessellation shown at the top
was generated from a simple line that started at a vertex of an
equilateral triangle and ended at the center of the triangle. |
The following animation illustrates how to recreate the above
tessellation. The process involves the following steps: rotate the line design twice around the center of the equilateral triangle
(120 degrees each time), reflect entire design across the side of the equilateral triangle, rotate entire design around the center of the hexagon, 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 2/12.
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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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