z_{n+1} = z_{n}^{1} + z_{o}
This is of course hardly very interesting, nor fractal.

z_{n+1} = z_{n}^{2} + z_{o}
The traditional Mendelbrot, M = 2.

z_{n+1} = z_{n}^{3} + z_{o}

z_{n+1} = z_{n}^{4} + z_{o}
In general there are M1 main lobes which result in M1 degrees of
rotational symmetry.

z_{n+1} = z_{n}^{5} + z_{o}

z_{n+1} = z_{n}^{6} + z_{o}

z_{n+1} = z_{n}^{7} + z_{o}

z_{n+1} = z_{n}^{8} + z_{o}

z_{n+1} = z_{n}^{10} + z_{o}
The shapes get increasingly circular looking, but the detail on zooming
in remains fractal..
