Times Tables, Mandelbrot and the Heart of Mathematics
Why Hacker News recommends it
HN recommends it as the clearest explanation of the patterns behind modular multiplication diagrams and times table art.
What it is
Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.
Recommended by 4 HN commenters across 4 different months, 2017 to 2023.
What Hacker News said
Recommends jacobolus · 2017-10 · on “Beauty in Mathematics: Modular Multiplication Tables”
There’s not really a reasonable continuous analog, IMO (unless you just want to see a single solid blob, like in your picture, but that hides all of the interesting part of the structure). But there are moiré-like patterns. Check out [this video] for some insight based on a related type of diagram (related to a single row at a time from the OP’s diagrams).
Recommends espeed · 2019-07 · on “Powers of Two in Lexicographic Order”
How does that work? ... Explanations invited. Hold the 1 fixed. Notice in both sequences the remaining numbers are 3 interleaved ordered sets, in multiples of 2. Then watch this (just happened to post it two hours ago too)... "Times Tables, Mandelbrot and the Heart of Mathematics" [video] [this video] [LINK] NB: And once again we find cycloids hiding underneath it all.
Recommends csbuja · 2020-06 · on “Times Tables Can Make Beautiful Art”
Check out some of the png files to view the art! This YouTube video explains the algo behind what you're seeing. [this video]
Recommends photochemsyn · 2023-04 · on “Number System Invented by Inuit Schoolchildren Makes Its Silicon Valley Debut”
Grasping the concept of number regardless of base system is an interesting exercise (linked to modular arithmetic), see Mathologer on times tables in any number base: [this video]