I first learned about figurate numbers, which are exclusive to the natural numbers. I wanted to learn about a method for integers, that is, to include negative numbers, and I learned about James Tanton's method of stacks and sandholes.
Then I wanted more, and I learned about a very similar method, but extended to rational numbers, and this was Conway's tangle theory.
But then I wanted one that would allow me to work with the entire real number line, and that's how I learned about Hackenbush strings.
I've been looking for days for a method that extends to complex numbers, but I haven't been successful in finding one.
The closest thing I've come across are two video games. One is Quantum Odyssey, which uses logic gates involving complex numbers.
The other is a video game made by a developer with a YouTube channel featuring an astronaut who teleports.
But of course, I'm obviously dissatisfied, because they don't feel like an extension of what the previous conceptual models already achieved
Interestingly, something that catches my attention about these models is that you can represent a number through a structure, and through the rules, you can perform operations, regardless of whether it's sand, tangles, or strings