2.8M views · Nov 6, 2015 · 13:37 · 4 HN recommenders · 4 mentions · discussed 2017–2023
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.
Why Hacker News points people here: HN recommends it as the clearest explanation of the patterns behind modular multiplication diagrams and times table art.
“This YouTube video explains the algo behind what you're seeing.”HN comment, 2020
“Check out for some insight based on a related type of diagram”
Gives insight into moire-like patterns in related diagrams.
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).
“Then watch this”
Explains the patterns behind modular multiplication sequences.
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.
“This YouTube video explains the algo behind what you're seeing.”
Explains the algorithm behind the 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
“see Mathologer on times tables in any number base”
Times tables in any number base.
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
