I always thought that the next step after Mandelbrot is usually running Doom.
I think it's mandelbrot -> read email -> lisp -> web server -> Doom -> operating system
Operating system would come before Doom, and web server probably the second thing after Mandelbrot set these days.
I wonder if there's some sort of fractal rendering procedure like zooming/rotating/viewing, that could be turing complete with a given fractal. Would be a kind of cool hack.
What does sufficiently Turing-complete mean? I thought a system is, or isn't?
I'm just weaseling out because I don't want to claim that every system that can draw Mandelbrots is Turing complete (not considering pathetic cases like "draw_mandelbrot" keywords/functions/parameters).
I'll leave the proof to interested readers.
Genuinely Turing-complete machines have infinite memory ("tape") and an arbitrarily large number of steps within which to complete an algorithm. I suppose "sufficiently Turing-complete" to mean that you can express an algorithm to the machine such that the algorithm can complete within the resources (RAM and time) that you have to give it.