| In this section we will browse through some of the tessellation
designs created by M. C. Escher. At the same time, we will discuss
the techniques used in hopes of being able to create our own Escher-like
tessellations.
Translation Technique
But first, a very fundamental technique must be discussed, the
translation technique. This technique involves redrawing a side
of a shape and then translating a copy of the new side to every
instance of the original side type. For example, in the following
example, the side AB is redrawn as a curvy line segment and then
copied to the side DC (an instance of the original side type).
When the new side is copied to all instances, a new tessellation
results.
First, side AB is redrawn. Then, a copy (shown in red) of the
new side is translated to side DC. Repeating this change for every
side equivalent to side AB results in the tessellation shown on
the right.
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This animation shows real-time translations.
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Sometimes, the side that is redrawn does not have an instance
on the original polygon. For example, in the following example,
the side AB is not identical to BC nor AC. Similarly, side BC
is not identical to AB nor AC, and side AC is not identical to
AB nor BC. Thus, all three sides can be redrawn.
The sides of equilateral triangle ABC can be completely redrawn
since sides AB, BC, and AC are all distinct types of sides. Notice
that a new type of shape is formed after the sides are translated.
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Another example of a case where the sides to be redrawn are not
next to each other:
The redrawn sides, when translated throughout the tessellation,
are not adjacent to one another.
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Visit the templates page for tessellations on which you can practice this translation
technique.
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