Even random "point by point" generation allows to combine Mandelbrot or Julia like recurring law according to several different combinations so obtaining e.g. either Mandelbrot-Mandelbrot-Mandelbrot, or Julia-Julia-Julia, or Julia-Mandelbrot-Mandelbrot, etc. structures. Remarkably chance seems to be oriented towards final ordered structures as attractors.
Fractals from Quaternions plotted randomly
Mandelbrot-Mandelbrot-Mandelbrot
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Julia-Julia-Julia (C = -0.7454294)
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Julia-Mandelbrot-Mandelbrot (C = -0.7454294)
