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Here are some other pictures using the "dual-power" formula explained in the "Summary of 3D Mandelbrot Set Formulas" thread :
x = r^p1 cos(p1*ph) + cx
y = r^p1 cos(th)sin(p1*ph) + 1/3 r^p1 sin(p1*ph)*cos(p2*th) + cy
z = r^ p1 sin(th)cos(p1*ph) + 1/2 r^p1 sin(p1*ph)*sin(p2*th) + cz


p1=3, p2=20


p1=4, p2=20


p1=6, p2=20


The shapes have the look of the 2D Mandelbrot set at power p1 when seen from the side, and the look of the 2D Mandelbrot set at power p2 when seen from the front.