Wednesday, July 15, 2015

Escher Triangle

The mathematical illusions of M.C. Escher fascinated me as a child, and nothing has changed in the decades since. Woodcuts, lithographs, and mezzotints rather than drawings and paintings, but the medium is ultimately insignificant when compared with the paradoxes, and the proof, if that is what it is, that infinity can be described in other visual forms than just the perfect circle.

He uses many techniques in many different kinds of picture (see the illustrations below, which reflect my other attempts to unravel him), but one technique in particular caught my attention, and you can see it in "Waterfall", in "Ascending and Descending", in "Relativity, in "Belvedere" and many others.

 I spent hundreds of hours trying to work it out, and shall not reveal the secret here, except to say that eventually I did, and the version of the triangle posted here is a simplification of the technique to such a degree that anyone should be able to follow suit and make the same finesse.

Many interesting routes for anyone to follow, if the fascination has turned contagious. 

Paschal's Triangle, for example,  must surely have been one of Escher's sources

My own efforts included this, in my January 2000 diary:

as well as this:

as well as this:

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