Times Table Visualisation

For this I used Unity3d v2018.2.x

This effect is produced by distributing X number of points evenly around a circle. Each point is numbered starting with 0. Then for each point you multiply that point's index number by a factor F and use the Modulo operation to wrap the result. Drawing a line from X to the result of X*F. You do this for each point around the circle.

Modulo Times Tables

The Modulo Times table is fundamental to this technique. By allowing the values to wrap, it enables the formulation of the amazing visuals.

What Is Modulo?

3 % 2 = 1

The Modulo ( % ) Operation find the remainder after the division of one integer number by another.

Here are some examples of a zero index modulo times table. You should be able to see from the colouring how there is an area that repeats the same number of times as the multiplication, or scale factor.

Times 0

Times 1

Times 2

Times 3

Shape Repetition

From the left, the Factors are 2, 3, 4. Each frame is a differing number of points. The frames number of points are 4, 8, 16, 32, 64, 125, 256 and back. In essence, the shape stays the same its only the resolution that changes.

What did I learn from this?

How to work with Unity's Graphics

To get the desired result without melting my computer. I learned how to construct simple meshes through code. And how expensive it is to recalculate, then draw 40,000 rectangles per frame. But by using Unity's Graphics interface to draw directly to the screen instead of needing to generate GameObjects is actually something super helpful that I was not expecting to need to learn to produce this.

Patience

To get this working to require a lot of patience, as the road was paved with dangerous problems of the "I don't know what I don't know" variety. But I feel more confident now in my ability to find solutions to such problems.