"Although I am absolutely without training or knowledge, I often seem to have more in common with mathematicians than my fellow artists"

An unusual artist who enjoyed problem solving, and like many artists was interested in creating the impression that a flat surface had depth, and in depicting multiple viewpoints in one image.

The son of an engineer, the artistic young Escher went to the Haarlem School of Architecture and Ornamental Design between 1919-1922. He transferred from architecture to graphic design, where his tutor Jessurun de Mesquita taught him to produce woodcuts, which became his trademark medium.

Repeat themes in his work include Lizards, Fish, Birds, and Landscapes and the use of mirrors or water to show reflection. The objects that appear often change or morph within the piece.

He disowned his own pre-1935 work, which he created in Rome, Italy but realistically these prints were the building blocks for his later work.

In 1935 he moved with his family to Switzerland, then Brussels and finally back to Holland in 1941.He apparently, when away from Italy looked to his own imagination for inspiration, rather than the natural world.

It was in the 50's that he became commercially popular and successful, and he even put his prices up to prohibit too many orders, but it didn't work.

He was knighted in 1955, but became ill during the 60's. He died in March 1972.

The works of M.C. Escher

At first, I thought the works of Escher were just a collection of magnificent drawings that keeps your attention, but there's a line in his works; it can be categorised (he did that as well). Most of the pictures I mention here can be viewed online at http://www.worldofescher.com/gallery/ and http://www.cs.unc.edu/~davemc/Pic/Escher/ which may be helpful to understand the explanations below if you're not familiar with his works.
  • 3D structures
    - Landscapes; mainly created during his life in Italy. Some of these paintings and drawings were used in a later stage (like in the Picture Gallery).
    - penetration of worlds; the Hand with the sphere as a mirror. Noteworthy is, that this implies that he assumed that there's more than one world, or, and more likely when you take his other works into account, one world that can be seen from different perspectives, that it seems to be a different world and that he tried to capture the various points of view all at the same time.
    - abstract mathematical things; like Stars and crystal shapes (his brother was a geologist, and Escher made all illustrations for the book he wrote). All figures are based on the five regular shapes: the tetraeder (4 sides), cubicle (6 sides), octaeder (8), dodecaeder (12) and ikosaeder (20). A picture like Gravity was constructed by placing five-sided pyramids on each side of a dodecaeder.
  • 2D
    - metamorphose; examples is Day and Night (but this may be interpreted as a cyclus too) and the Magic Mirror, but the most famous one is Metamorphose II.
    - cycli; e.g. the reptiles walking out of the paper. The main idea behind this that there's no beginning and no end, like with the metamorphosis there's this transition between stages.
    - infinity; they appear to me like what we call fractals nowadays. In the first stage the infinity of the figures went inside into the picture, but later (with Circle Limit I, II and III) outwards (or ideas about the infinity of the universe maybe?). Those pictures can be generated with a click of a mouse now, he calculated and draw it all by hand!!!
  • The relation between 2D and 3D
    - conflict 2D-3D; see the Dragon, it was constructed by drawing a dragon, cut out, two holes were made in the paper and this construction was drawn again. In other words, he used 3D drawing techniques to emphasize the 2D of the initial object.
    - perspective; Escher used combinations of zeniths, nadirs and vanishing points to create e.g. Relativity and Other World I and II. In Up and Down, the zenith of the lower part of the picture is the nadir of the upper part at the same time. Remarkably, the very same principle has been used for Stair Well with the "wentelteefjes" (the millipede-like creatures).
    - impossible figures; the best know are Belvedere (based on the magicbox from Dr. Cochran), Waterfall (based on the triangle form R. Penrose) and Upstairs Downstairs. Cool thing about the latter is, that the stairs are flat, but you are fooled by the lines of the rest of the building where the architecture is not realistic (ok, ok, it probably is possible to build it with some extra supporting buttresses, but will be extremely uncomfortable to live in). Another one is Concave and Convex: the left side of the picture is convex (with the apparent nadir bottom-left) and the right side concave (with the apparent zenith top-right), whereas the middle is in sort of a transition state.
Chronologically, the above can be divided into 4 distinct periods: 1922-'37 Landscapes, '37-'45 metamorphosis, '46-'56 perspective and '56-'70 to infinity.

Anyway, there are many more pictures than the ones I mentioned that may not seem to be like the ones I picked, nevertheless those ones do have the same mathematical basis (btw, Escher wasn't a mathematician).
There's a very good book that explains how he did it, called "Der Zauberspiegel des M.C. Escher",(translated into the Magic Mirror of M.C. Escher), which outlines his thought processes and shows the working drawings and models for his final works. E.g. the Picture Gallery is "just" based on standard graph paper with some exploded and imploded graph lines...
An example of one of his works, called "Sky and Water I", done in 1938 as a woodcut.



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Doesn't display too well in ASCII art, but the image shows birds at the top, and as you look downward, the birds gradually become background while the spaces between them turn into fish.

Maurits C. Escher (1898-1972) was a Dutch artist, principally famous for his mathematically inspired prints. Because his father had been a civil engineer in Leeuwarden and Arnhem, Escher aspired in his childhood to be an architect and therefore enrolled in the School for Architecture and Decorative Arts in Haarlem. He studied there between 1919 and 1922, during which time he became more interested in drawing and printmaking, something in which he was encouraged by his teacher, Samuel Jessurun de Mesquita. After marrying Jetta Umiker in 1924, EScher moved to Rome where he lived until 1935. At this time, fascist political pressure forced them to move back to Hollandby way of Switzerland and Belgium. Escher lived and worked in Baarn until shortly before his death. During his life he had also been a draftsman, book illustrator, tapestry designer, and muralist.

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