M.C. Escher: Art and Science

by H.S.M. Coxeter (Editor), M. Emmer (Editor), R. Penrose (Editor)

The work of Dutch artist Maurits Cornelis Escher (1898-1972) continues to attract wide interest. Mathematicians, physicists, crystallographers, chemists, biologists, psychologists, psychiatrists, art historians, and specialists in computer graphics and visual communications attended this congress. The papers presented here in this illustrated volume confirm that Escher's works are not only good examples of the visualization of scientific problems but also stimulate real scientific research.

Genres: Mathematics

416 pages, Hardcover

First published December 1, 1986

About the author

Harold Scott MacDonald "Donald" Coxeter (1907-2003), CC, FRS, FRSC was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.

Reviews

[Mundy Reimer · Rating 5 out of 5]

*Following my trend as of late to briefly capture the essence of charmingly old or neglected books*

To get into the mood for World Tessellation Day tomorrow ❄️🎉, here we have a work edited by the famous geometers, Donald Coxeter ("the man who saved geometry"), Roger Penrose, and Michele Emmer. This book is basically composed of various papers from invited speakers from around the world to a 1985 interdisciplinary conference devoted to the Dutch artist Maurits Cornelius Escher. The participants included mathematicians, physicists, crystallographers, chemists, biologists, psychologists, psychiatrists, art historians, computer graphics people, etc, and goes to show how broadly applicable Escher's artwork and influence has been across a wide variety of disciplines.

My motivation comes mainly from the mathematical and biophysics areas, but many of the other fields mentioned in here also captivated me (plus, my all-time favorite book is Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter, so I can't help but be an Escher geek as well 🤷‍♀️)

Below are a few pictures breaking down the contents of the book:







Again, this book features papers that are really old, but I'd caution to not let that deter you from discovering each paper's value. Here's one which discusses the mathematics of the 6-fold symmetries of colored butterfly tilings:



One paper even tries to capture how Escher systematically and methodically tried to group his tiling patterns that he experimented with. This is a picture of a picture of a set pictures from Escher's own notebook (very Escher of me, huh? 😉):



A few of my favorite diagrams show how the combinatorial structure of Escher's work plays into topological transformations and lattice ordering. Really neat, especially if you start thinking about formal grammars, cellular automata, and generally rewrite systems as types of transformations on an underlying pseudo-tessellation pattern (feel free to check out my blog series here if those ideas seem interesting to you!)





I just wanted to include this next image to show a charming example of the font used in one academic's paper. Academia, let's bring back some creativity like this!!!



This diagram was especially interesting to me as it shows the intersection of Escher's work with theoretical modeling of biological phenomena. Here we see models of co-operative conformational equilibria of oligomeric proteins (essentially, how can we find the canonical shapes these proteins find themselves in):



Here's another biology one, this time applying Escher's study of lattices to the geodesic structures of the "heads" or protein capsules of viruses. This is an intriguing area for geometers as the shapes of these affect the underlying dynamics of viral transmission!



And finally, here's a diagram of Escher's work discovering new tiling patterns. Note his very mathematical and systematic way of going about this, despite him lacking any training in mathematics!



Hope you enjoyed that brief history + art + math lesson :)