why do imaginary bases make fractals?

explore: https://thegraycuber.com/imaginary_ba... see more of Thomas's work: https://thomaskaldahl.com/ support the channel: https://ko-fi.com/thegraycuber my other projects: https://thegraycuber.com/ we can create fractals by using applying numeral systems to the imaginary numbers! in this video we explore what it means to use an imaginary base in the Gaussian Integers, we see how to apply those same ideas to a set of hexagonal imaginary numbers called the Eisenstein Integers and we find the requirements for such a system to nicely represent all integers uniquely. i had an apple this morning and it was delicious :)