I discovered an interesting plot of composite numbers that I haven't seen before
I got the idea to plot unique composite numbers on a multiplication table in a particular way, and the result turned out more interesting than I expected.
Construction
Each pixel corresponds to a grid point (x,y) with origin (1,1) in the top left, x increasing to the right, and y increasing downwards.
For each pixel where 1 <= x <= y, color the pixel if and only if no other factorization of x*y has a smaller value of y-x.
This ensures that each result of x*y is colored only once on this multiplication table.
Interesting things I noticed
- For every y that's prime, there is an uninterrupted horizontal line
- There are vertical lines in the upper half of this triangle, but none below
- The triangle is divided into different segments bounded by what seems like straight diagonal lines
- There is a region bounded by the main diagonal and a non-linear curve, where every pixel is always colored
- Zooming into the noisy parts of the plot reveals interesting details and cells, some of which resemble shapes I'd playfully describe as "alien hieroglyphics"
Conclusion
This visualization hides a lot of interesting patterns, for most of which I'd expect there to be an obvious explanation. I'd love to read about these if anyone is willing to explain some of them.
I'd also like to know if this particular visualization has been seen before (and if so, what it might be called), or if I stumbled upon something new. In case it doesn't have a name yet, I'd be happy to call it "Tom's triangle". :)