Times Table Animation Inspired by #Mathologer (4K @ 60 FPS for best quality)

I created this animation of times tables inspired by Mathologer's video, "Times Tables, Mandelbrot and the Heart of Mathematics" (https://youtu.be/qhbuKbxJsk8). I recommend checking out his video for a good explanation of the mathematics that generates these patterns.

I used Python and PyCairo to generate each frame. Here is the open-source code: 💻 https://github.com/elliotwaite/times-table-animation

How the animation was generated: First, you pick a number for how many lines you want to display on each frame. I picked 512 because I thought it looked nice. Given that I picked 512, you then make a circle with 512 equally spaced points around it, which represent the values 0 to 511. You then multiply each of those values (0 - 511) by a number (for example 2) to get the place where that number maps to (1 maps to 2, 2 maps to 4, 3 maps to 6, and so on). If you then connect those dots on the circle with a line (connecting point 1 to point 2, and point 2 to point 4, and so on), you get one of the patterns shown in the animation. If a value is mapped to a number greater than or equal to 512, that value is divided by 512 and the remainder value is used instead (this is also called applying a modulo of 512). The multiple values can also be non-integers, for example, if the multiple was 1.5, then the point at position 3 would get connected to the point at position 4.5, which would just be the point on the circle in between 4 and 5. Each frame is for a different multiple, starting with a multiple of 1 and increasing it by a small amount (for example 0.01) until the multiple is 513, which ends up producing the same pattern as 1 does due to the fact that 513 mod 512 equals 1. I also extend the line connecting the points beyond the edge of the circle to the edge of the screen, so if a point would map back to itself (for example the 0 point always maps back to itself, or when the multiple is 1, all points get mapped back themselves), then the line is just tangent to the circle. I also colored the lines according to where the initial point is on the circle, just using the sequence of fully saturated RGB colors that cycle through the hues.

If you have any questions, let me know if the comments.

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