I have a lot of random scripts that I wrote back in January for this project. I got busy and never wrote about them, but I want to put an interesting note here. I might come back to this project when I have time. Basically, you can have a leaper \( (f(n), g(m)) \) for functions \(f\) and \(g\), and you get some interesting results. These can be functions of anything, I guess, but I can't really think of any functions right now that wouldn't be on the number of turns. One really interesting leaper I made was \( L_F = (1, \text{fib}(n)) \), where \( \text{fib}(n) \) is the \(n\)th Fibonacci number and \(n\) is the number of turns. I ran a python script that made this leaper start from one square and go for a while (where this python script is now, I'm not quite sure; it might be worth rewriting some day given how cool the result looks). If I recall correctly, the final result is on a 10000 by 10000 square chessboard. Here is the final image.
There are some interesting questions worth asking, like is any square eventually hit in some finite number of turns? There are some really cool patterns in this image, and I think it's worth zooming in and exploring it. I wanted to upload it here before I forgot it existed.
