How Did M. C. Escher Create His Tessellations?

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M.C. Escher’s art has always been fascinating to look at; his tessellations especially. I was first introduced to him by my psychology teacher when we looked at optical illusions, and then, once again in art class when he was introduced as an amazing artist, rightfully so. Being a fan of his art, I was amazed to find I could translate it in math terms as well; tessellations turn into geometric ratios and formulas. From psychology, to art, to math, M.C. Escher’s art has been widely acclaimed as beautiful, eye catching, and mathematically calculated. But, how exactly does he use math to create his tessellation pieces?
Choosing this piece will help me understand art better, and understand that math really is everywhere. By understanding the tessellations and math behind it, I could possibly try to use math in everyday life when I sit down to create
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The most common tessellations today are ones like, floor tilings that use square or rectangular shapes. However, Escher’s tessellations aren’t so simple. Instead, they are recognizable shapes, such as a type of bird or animal, such as the one below.

However, sometimes he makes up shapes that can fit together like puzzle pieces. The simplest examples of his tessellations is simply taking a typical square grid and drawing just to change the edges ever so slightly, like how the diagram below shows.

As you can see, the vertical lines look the same as every other vertical line, and every horizontal line matches as well.
There are principles of tessellations that set up the basis of the math. “If we shift the whole plane over the distance AB, it will cover the underlying pattern once again. This is a translation of the plane. We can also turn the duplicate through 60 degrees about the point C, and we notice that again it covers the original pattern exactly. This is a rotation. Also if we do a reflection about the line PQ, the pattern remains the same.

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