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John Carlos Baez

From 2013 to 2017 I ran a blog called Visual Insight, which was a place to share striking images that help explain topics in mathematics.  Last week I gave a talk about it at the Illustrating Math Seminar. Now you can see the video here:

youtube.com/watch?v=6G611RbO3G

It was fun explaining some great images created by @RefurioAnachro, @gregeganSF, @roice3, @GerardWestendorp and other folks. For more info on the images I talked about, go here:

• math.ucr.edu/home/baez/visual_ 2015 - 01 - 15 — Hammersley Sofa
• math.ucr.edu/home/baez/visual_ 2015 - 12 - 01 — Golay Code
• math.ucr.edu/home/baez/visual_ 2014 - 07 - 15 — {7,3} Tiling
• math.ucr.edu/home/baez/visual_ 2014 - 03 - 15 — {6,3,3} Honeycomb
• math.ucr.edu/home/baez/visual_ 2013 - 09 - 15 — {6,3,3} Honeycomb in Upper Half Space
• math.ucr.edu/home/baez/visual_ 2015 - 12 - 15 — Kaleidocycle
• math.ucr.edu/home/baez/visual_ 2016 - 02 - 15 — 27 Lines on a Cubic Surface
• math.ucr.edu/home/baez/visual_ 2015 - 04 - 15 — Sphere in Mirrored Spheroid
• math.ucr.edu/home/baez/visual_ 2015 - 10 - 01 — Balaban 10-Cage
• math.ucr.edu/home/baez/visual_ 2015 - 09 - 15 — McGee Graph

You can see the whole blog at the AMS website:

blogs.ams.org/visualinsight/au website

or on my own website in a more stripped-down format:

math.ucr.edu/home/baez/visual_ website. But you can also check out individual articles here.... (Yes, read on....)

(1/n)

YouTubeVisual InsightsBy Illustrating Math Seminar
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John Carlos Baez

Here are the articles from 2013. Which one am I featuring here?

• math.ucr.edu/home/baez/visual_ 2013 - 08 - 15 — Tübingen Tiling
• math.ucr.edu/home/baez/visual_ 2013 - 09 - 01 — Algebraic Numbers
• math.ucr.edu/home/baez/visual_ 2013 - 09 - 15 — {6,3,3} Honeycomb in Upper Half Space
• math.ucr.edu/home/baez/visual_ 2013 - 10 - 01 — Catacaustic of a Cardioid
• math.ucr.edu/home/baez/visual_ 2013 - 10 - 15 — Atomic Singular Inner Function
• math.ucr.edu/home/baez/visual_ 2013 - 11 - 01 — Enneper Surface
• math.ucr.edu/home/baez/visual_ 2013 - 11 - 15 — Astroid as Catacaustic of Deltoid
• math.ucr.edu/home/baez/visual_ 2013 - 12 - 01 — Deltoid Rolling Inside Astroid
• math.ucr.edu/home/baez/visual_ 2013 - 12 - 15 — Truncated Hypercube

(2/n)

Atomic singular inner function by Elias Wegert: http://math.ucr.edu/home/baez/visual_insight/20131015%20-%20Atomic%20Singular%20Inner%20Function.html
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John Carlos Baez

Here are the pictures from 2014:

• math.ucr.edu/home/baez/visual_ 2014 - 01 - 01 — Pentagon-Hexagon-Decagon Identity
• math.ucr.edu/home/baez/visual_ 2014 - 01 - 15 — Weierstrass Elliptic Function
• math.ucr.edu/home/baez/visual_ 2014 - 02 - 01 — {5,3,5} Honeycomb
• math.ucr.edu/home/baez/visual_ 2014 - 02 - 15 — Cantor’s Cube
• math.ucr.edu/home/baez/visual_ 2014 - 03 - 01 — Menger Sponge
• math.ucr.edu/home/baez/visual_ 2014 - 03 - 15 — {6,3,3} Honeycomb
• math.ucr.edu/home/baez/visual_ 2014 - 04 - 01 — {6,3,4} Honeycomb
• math.ucr.edu/home/baez/visual_ 2014 - 04 - 15 — {6,3,5} Honeycomb
• math.ucr.edu/home/baez/visual_ 2014 - 05 - 15 — Pattern-Equivariant Homology of a Penrose Tiling
• math.ucr.edu/home/baez/visual_ 2014 - 06 - 01 — Grace–Danielsson Inequality
• math.ucr.edu/home/baez/visual_ 2014 - 06 - 15 — Origami Dodecahedra
• math.ucr.edu/home/baez/visual_ 2014 - 07 - 01 — Sierpinski Carpet
• math.ucr.edu/home/baez/visual_ 2014 - 07 - 15 — {7,3} Tiling
• math.ucr.edu/home/baez/visual_ 2014 - 08 - 01 — {7,3,3} Honeycomb
• math.ucr.edu/home/baez/visual_ 2014 - 08 - 15 — {7,3,3} Honeycomb Meets Plane at Infinity
• math.ucr.edu/home/baez/visual_ 2014 - 09 - 01 — {3,3,7} Honeycomb Meets Plane at Infinity
• math.ucr.edu/home/baez/visual_ 2014 - 09 - 15 — Prüfer 2-Group
• math.ucr.edu/home/baez/visual_ 2014 - 10 - 01 — 2-adic Integers
• math.ucr.edu/home/baez/visual_ 2014 - 10 - 15 — Packing Regular Octagons
• math.ucr.edu/home/baez/visual_ 2014 - 11 - 01 — Packing Smoothed Octagons
• math.ucr.edu/home/baez/visual_ 2014 - 11 - 15 — Packing Regular Heptagons
• math.ucr.edu/home/baez/visual_ 2014 - 12 - 01 — Packing Regular Pentagons

(3/n)

{6,3,5} honeycomb by Roice Nelson: https://math.ucr.edu/home/baez/visual_insight/20140415%20-%20%7b6,3,5%7d%20Honeycomb.html
John Carlos Baez

Here are the pictures from 2015:

• math.ucr.edu/home/baez/visual_ 2015 - 01 - 01 — Icosidodecahedron from D6
• math.ucr.edu/home/baez/visual_ 2015 - 01 - 15 — Hammersley Sofa
• math.ucr.edu/home/baez/visual_ 2015 - 02 - 01 — Pentagon-Decagon Packing
• math.ucr.edu/home/baez/visual_ 2015 - 02 - 15 — Pentagon-Decagon Branched Covering
• math.ucr.edu/home/baez/visual_ 2015 - 03 - 01 — Schmidt Arrangement
• math.ucr.edu/home/baez/visual_ 2015 - 03 - 15 — Small Cubicuboctahedron
• math.ucr.edu/home/baez/visual_ 2015 - 04 - 01 — Branched Cover from (4 4 3/2) Schwarz Triangle
• math.ucr.edu/home/baez/visual_ 2015 - 04 - 15 — Sphere in Mirrored Spheroid
• math.ucr.edu/home/baez/visual_ 2015 - 05 - 01 — Twin Dodecahedra
• math.ucr.edu/home/baez/visual_ 2015 - 05 - 15 — Dodecahedron With 5 Tetrahedra
• math.ucr.edu/home/baez/visual_ 2015 - 06 - 01 — Harmonic Orbit
• math.ucr.edu/home/baez/visual_ 2015 - 06 - 15 — Lattice of Partitions
• math.ucr.edu/home/baez/visual_ 2015 - 07 - 01 — Petersen Graph
• math.ucr.edu/home/baez/visual_ 2015 - 07 - 15 — Dyck Words
• math.ucr.edu/home/baez/visual_ 2015 - 08 - 01 — Heawood Graph
• math.ucr.edu/home/baez/visual_ 2015 - 08 - 15 — Tutte–Coxeter Graph
• math.ucr.edu/home/baez/visual_ 2015 - 09 - 01 — Hypercube of Duads
• math.ucr.edu/home/baez/visual_ 2015 - 09 - 15 — McGee Graph
• math.ucr.edu/home/baez/visual_ 2015 - 10 - 01 — Balaban 10-Cage
• math.ucr.edu/home/baez/visual_ 2015 - 10 - 15 — Harries Graph
• math.ucr.edu/home/baez/visual_ 2015 - 11 - 01 — Balaban 11-Cage
• math.ucr.edu/home/baez/visual_ 2015 - 11 - 15 — Newton’s Apsidal Precession Theorem
• math.ucr.edu/home/baez/visual_ 2015 - 12 - 01 — Golay Code
• math.ucr.edu/home/baez/visual_ 2015 - 12 - 15 — Kaleidocycle

GIF
Mar 20, 2025, 04:55 AM·Public
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John Carlos Baez

Here are the pictures from 2016, and one from 2017.

• math.ucr.edu/home/baez/visual_ 2016 - 01 - 01 — Free Modular Lattice on 3 Generators
• math.ucr.edu/home/baez/visual_ 2016 - 01 - 15 — Cairo Tiling
• math.ucr.edu/home/baez/visual_ 2016 - 02 - 01 — Hoffman–Singleton Graph
• math.ucr.edu/home/baez/visual_ 2016 - 02 - 15 — 27 Lines on a Cubic Surface
• math.ucr.edu/home/baez/visual_ 2016 - 03 - 01 — Clebsch Surface
• math.ucr.edu/home/baez/visual_ 2016 - 03 - 15 — Zamolodchikov Tetrahedron Equation
• math.ucr.edu/home/baez/visual_ 2016 - 04 - 01 — Rectified Truncated Icosahedron
• math.ucr.edu/home/baez/visual_ 2016 - 04 - 15 — Barth Sextic
• math.ucr.edu/home/baez/visual_ 2016 - 05 - 01 — Involutes of a Cubical Parabola
• math.ucr.edu/home/baez/visual_ 2016 - 05 - 15 — Discriminant of the Icosahedral Group
• math.ucr.edu/home/baez/visual_ 2016 - 06 - 01 — Discriminant of Restricted Quintic
• math.ucr.edu/home/baez/visual_ 2016 - 06 - 15 — Small Stellated Dodecahedron
• math.ucr.edu/home/baez/visual_ 2016 - 07 - 01 — Barth Decic
• math.ucr.edu/home/baez/visual_ 2016 - 07 - 15 — Labs Septic
• math.ucr.edu/home/baez/visual_ 2016 - 08 - 01 — Endrass Octic
• math.ucr.edu/home/baez/visual_ 2016 - 08 - 15 — Cayley’s Nodal Cubic Surface
• math.ucr.edu/home/baez/visual_ 2016 - 09 - 01 — Kummer Quartic
• math.ucr.edu/home/baez/visual_ 2016 - 09 - 15 — Togliatti Quintic
• math.ucr.edu/home/baez/visual_ 2016 - 10 - 01 — Diamond Cubic
• math.ucr.edu/home/baez/visual_ 2016 - 10 - 15 — Laves Graph
• math.ucr.edu/home/baez/visual_ 2016 - 11 - 01 — Escudero Nonic
• math.ucr.edu/home/baez/visual_ 2016 - 11 - 15 — Bunimovich Stadium
• math.ucr.edu/home/baez/visual_ 2016 - 12 - 01 — Truncated {6,3,3} Honeycomb
• math.ucr.edu/home/baez/visual_ 2016 - 12 - 15 — Romik’s Ambidextrous Sofa
• math.ucr.edu/home/baez/visual_ 2017 - 01 - 01 — Chmutov Octic

(5/n, n = 5)

Endrass Octic by Abdelaziz Nait Merzouk: http://math.ucr.edu/home/baez/visual_insight/20160801%20-%20Endrass%20Octic.html
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Refurio Anachro

Abdelaziz Nait Merzouk made gorgeous renderings! They are really something to aspire to. I would really like to make similar ones in shadertoy. First get a Newton root finder implemented and then see what I can do with that. Another inspiration is to try and get something like @KangarooPhysics's Seifert-like surfaces for knots.

Yet another project idea is to write a relativistic raymarcher, to render black holes and some other, more weird 4d stuff.

I'm kind of obliged to something along these lines, because I promised some guys to show off with them at the next Evoke demo party in Cologne. That means I have about half a year to get it done, which should be plenty. Should...

@johncarlosbaez

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