Random "point by point" generation may be implemented also with the additional constraint that any next point (son cell) is plot in a random nearest position respect to the previous point (mother cell). A similar constraint is typical fo cellular automata and simulates a random process of living cell generation.
So 3D Mandelbrot-Mandelbrot-Mandelbrot, or Julia-Julia-Julia, or Julia-Mandelbrot-Mandelbrot, etc., are generated by cellular automata resembling living like systems. Remarkably chance seems to be oriented towards final ordered structures as attractors as if they were organs in a living body.
Fractals from Quaternions plotted randomly by cellular automata