How did Escher make his tesselations?

Question for the: Topic Challenge #1 – Famous Designers

I remember as a kid my favourite book in the whole house wasn’t a book of fairy tales or colourful illustrations. It was The complete works of M.C. Escher. I could stare at his works for hours on end. Trying to wrap my head around how those little people could go up and down the stairs forever.

But what intrigued me even more were his Tessellation pieces, where he would divide a plane into interlocking figures, such as here:

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Later, in his Metamorphosis pieces, he would take this a step further and morph one tesselation into another, like so:


Nowadays, it’s pretty trivial to get a computer to calculate an optimal tesselation, but Escher didn’t have any of that. And the metamorphosis works add a whole new level of complexity even a computer would find hard to do. So my question is quite simply: How did Escher make his art? If I wanted to do something similar today, how would I go about it?

Answer

With a pattern.

In this case a 3 axis grid (triangular).
enter image description here

Once you know what to draw on each piece, you need to repeat this.
You can have and use sub-patterns or smaller ones to be more exact.enter image description here

These patterns are pretty easy to draw, and they are used for example in architecture in different cultures. We are used more to a square pattern, but this triangular pattern can produce hexagonal and rhomboidal patterns as well.

enter image description here

And you can play with it to start building ripples, but still, you repeat the internal objects on this now deformed patterns.enter image description here

Look how many patterns you have with this triangular grid.enter image description here

Grab a paper and a ruler, draw some pages and find some more patterns!

This is a typical example of introductory classes at the University. We called it “Little Squares 101” Or “Sticks and Balls II” (That was the second course) and yes, we drew this by hand.

You can also see these patterns in 3D often used in Architecture.


Regarding the comment:

I really see no difficulty to draw this lizard by hand. Look at the second image, it clearly marks the middle of the triangle and where the legs should intersect them. I would probably have a reference drawing but draw those by hand. Especially if the next lizard will turn into a duck… Metamorphosis…

Additionally, comparing two lizards they are not exactly the same.enter image description here

When you are using a pattern, you let the pattern guide you.


Edited some years later. Let us explore how Escher used these grids to develop part of his work.

Here is a screen capture of the website: https://mcescher.com/gallery/symmetry/

where you can see how he used a two-axis grid rotated 45° next to a work using a three-axis grid. The grid even shows in pencil.

enter image description here

The grid is only a starting point. You have some other resources like mirroring, rotating, and scaling. But art is about taking the resources you have as a guideline, not as a limitation.

Here the “deformation” of the grid is extreme, the grid itself has its own new shape:

enter image description here

Source: https://mcescher.com/gallery/mathematical/


Remember that you can create subpatterns (smaller ones) or superpatterns (bigger ones)

Attribution
Source : Link , Question Author : PieBie , Answer Author : Rafael

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