/sci/ - Science & Math

>>11307062

Glad I can share the love. There's definitely a lot to research concerning fractals, but because it's very complex and messy, you probably won't find much formal help in said research. The guy who "solves" fractals will probably have an extremely diverse and profound understanding of mathematics. That said, even a CS nerd can probably contribute because of that absence of real direction for research, as well. The fact that many fractals seem to pop up in various parts of mathematics is quite intriguing, and the reason why I say this.

If you're the CS+Math+Artsy kind, I suggest you implement your own fractal renderers, either in 2D over complex polynomials (generalize the Julia protocol from z^2+c to any polynomial) or more general classes of complex functions (cos^2(z) + c). Consider various ETF protocols (not just Julia) and some Mariani-Silver algorithm goodness (pic related).

Do note that basically any ring/algebra can have an associated polynomial ring (and many have some definition of exp/cos/sin/etc through Taylor series) and can lead to various spaces and types of fractals. Though for n-dimensional fractals of the kind shown by Lasenby and Wareham, you'll probably have to learn geometric algebra (definitely worth the look, check Alan MacDonald on youtube for a basic gist) and raytracing as well (raytracing on fractals in particular can sometimes use techniques specific to fractal rendering).