Today, a long overdue foray into the realm of VORTEX MATHEMATICS :)

00:00 Intro
04:16 The vortex
08:10 The maths of remainders and digital roots
13:25 Demystifying the vortex
16:30 A matter of base. The 8 fingered Tesla.
19:21 Explanation why the digital root is the remainder on division by 9
24:01 Tristan's challenge
24:44 The magic of modular multiplication maths
25:19 Intuition for multiplier - 1 petals
28:23 Thank You!

Coding competition:
My wish list for the modular times table diagram app:
-Being able to color line segments according to length.
-Indication of the "direction" of multiplication. 1x2 = 2 and so there should really be a little arrow from 1 to 2 not just a simple connection :)
-different loops in different colors.
...
Here is the prize, a copy of my and Marty's new book.
https://bookstore.ams.org/mbk-141/

That early Mathologer video featuring the modular times tables
Times Tables, Mandelbrot and the Heart of Mathematics
https://youtu.be/qhbuKbxJsk8

A really nice article about various ways to generate the cardioid by Dave Richeson
https://divisbyzero.com/2018/04/02/i-heart-cardioids/

Nice debunking/demystifying article about vortex math by "Professor Puzzler"
https://www.theproblemsite.com/vortex/

For a growing pile of implementation of modular times table diagrams see my comment pinned to the top of the comment section of this video.

Simon Plouffe's website
http://plouffe.fr/Simon%20Plouffe.htm
Articles by him relevant to this video can be found in this directory
http://plouffe.fr/Inverseofprimes/
See in particular the files
The shape of b^n mod p.pdf
La forme de bn mod p.pdf

What I am talking about in this video is really just the tip of a bizarre mathematical iceberg that most mathematically minded people are completely unaware of. Have a look at this presentation by Marko Rodin on vortex math (beware serious nutty and at the same time truely beautifully presented numerology ahead :) A LOT more than is usually reported on in popular YouTube videos.
https://sciencetosagemagazine.com/vbm-vortex-based-mathematics-with-marko-rodin/
In turn this iceberg is just another tip of an even bigger iceberg of mainly wishful thinking. Have a look: https://sciencetosagemagazine.com/category/library/

Today's music: Aftershocks by Ardie Son

Enjoy!

Burkard