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.