Mandelbrot Set - Other Non-analytic Mappings

Other Non-analytic Mappings

Of particular interest is the tricorn fractal, the connectedness locus of the anti-holomorphic family

The tricorn (also sometimes called the Mandelbar set) was encountered by Milnor in his study of parameter slices of real cubic polynomials. It is not locally connected. This property is inherited by the connectedness locus of real cubic polynomials.

Another non-analytic generalization is the Burning Ship fractal which is obtained by iterating the mapping

The Multibrot set is obtained by varying the value of the exponent d. The article has a video that shows the development from d = 0 to 7 at which point there are 6 i.e. (d - 1) lobes around the perimeter. A similar development with negative exponents results in (1 - d) clefts on the inside of a ring.