Escher's Knot

an interactive model in Processing

This multidimensional model of Escher's trefoil knot was modeled, rendered and animated in Processing. The interactive model can be viewed online at (a Java browser plugin is needed to view the model online) or if you prefer, there is a limited version in WebGL at Links to the source code are at the bottom of that page or on GitHub. Getting started with developing in Processing was made possible by an excellent dedicated IDE and online documentation.

Escher's etching of a trefoil knot (printed in 1965 from three woodcut blocks in red, green and brown) was the inspiration for this Processing project (all M.C. Escher works copyright © The M.C. Escher Company B.V. -Baarn-Holland. All rights reserved. The image of the etching below is from the National Gallery of Canada which also has an excellent quotation from George Escher, Maurits' son, on the development of this print. Immersed in the realm of mathematics and working primarily in print media, Escher is to me the essential technical artist.

From Knots (1965), Maurits C. Escher (1898-1972)
From Knots (1965), Maurits C. Escher (1898-1972)

“By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I have made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.” – M.C. Escher

Escher keeping records.

I am also fascinated by math driven art but am very much a novice which is why most of the four months that it took to build this model was spent learning about polynomial curves, knot theory, Frenet frames and matrix translations…good times. Below is the begining of a long list of professors, enthusiasts and developers who's online resources provided invaluable guidance and inspiration. Thanks to you all.