### Times Table Geometry Simulator

#### (Modular Multiplication on a Circle)

This visual experiment is an interactive recreation of the modular multiplication circle. The circle is based on a simple mathematical pattern wherein the circumference of a circle is subdivided by an arbitrary number of points, and then a multiplication factor is chosen that is used as one of the operands to connect each dot via multiplication. This model was inspired by this video created by Youtube channel Mathologer, which explains the mathematics in detail.

Scroll through the presets and then play around with the controls yourself. By adjusting the modulus (number of points around the circle) as well as the multiplication factor used, many interesting features and patterns appear that are reflected in our natural world, including the golden ratio, sacred geometry and many famous fractal structures. Clicking out of the view window pauses all animation.

Feel free to right-click and save any interesting shapes you find, and share the settings in the comments below! I’m also open to any suggestions for usability improvements of the tool.

See the Pen Times Table Fractal Vortex by Andrew Herman (@hippiefuturist) on CodePen.

Thanks for this tool!

float n = 294.09; // Modulus/Points

float m = 149.548; // Multiplication Factor

I wrote a program based on the video as well. I am using it to generate images for my Redbubble site see:

see: http://www.redbubble.com/people/rupertrussell/works/24454877-modulo-n-294-09-m-149-548?asc=u

You’re welcome, Rupert! That’s a great “zoom-level”.

I browsed your online store a bit. Your work is very fun. It’s great to connect with other artists exploring geometry and mathematics, and the web+programming is a fantastic tool for enabling it. I haven’t used the Processing library yet, but would like to give it a try.

I wonder if there is a way to modify this tool to use powers instead of multiplication factors. That would give some very interesting visualisations of the Euler totient function. (mathematician here)