Art with p5.js — Painting unorientable surfaces // Part0

A funky intro to topology and Processing.

Projection of RP2, Image by Author
Reproduction of Pixar’s Carl Fredricksen in UP as a surface, image by artist Mohannad Hussan

The cast of characters — into to topology.

We’re going to take a topological view, i.e. two surfaces are the same if one can be stretched into the other. Surprisingly enough, the surface of a donut and that of a mug are then the exact same, which is commonly called the Torus.

Mug turning into donut, image by
Lucas Vieira
Figure 3: Non-intersecting closed surfaces in R3 are examples of 2D manifolds such as a sphere, torus, double torus (source: Wolfram).
Torus from a band of fabric, image by Kevin Binz
David Benbennick, CC BY-SA 3.0, via Wikimedia Commons

They start running, change hands so they can pass the baton properly but when they get there, they yell at you that you’re sticking the wrong hand out.

The magic of the Mobius strip is that after one lap your right hand became your left and you actually don’t need to swap hands.

Photo by Austrian National Library on Unsplash
A summary of 2D surfaces, image by image by Kevin Binz
Nicholas Longo, CC BY-SA 2.5 <https://creativecommons.org/licenses/by-sa/2.5>, via Wikimedia Commons
Torus shadow showing fishtails, image by Author

Sources

Fantastic blog article by Kevin Binz: An Introduction to Topology

Low frequency high quality writing on data tech.

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