Tricorn (mathematics)

In mathematics, the tricorn, sometimes called the Mandelbar set, is a fractal defined in a similar way to the Mandelbrot set, but using the mapping ${\displaystyle z\mapsto {\bar {z}}^{2}+c}$ instead of ${\displaystyle z\mapsto z^{2}+c}$ used for the Mandelbrot set. It was introduced by W. D. Crowe, R. Hasson, P. J. Rippon, and P. E. D. Strain-Clark.^[1] John Milnor found tricorn-like sets as a prototypical configuration in the parameter space of real cubic polynomials, and in various other families of rational maps.^[2]

The characteristic three-cornered shape created by this fractal repeats with variations at different scales, showing the same sort of self-similarity as the Mandelbrot set. In addition to smaller tricorns, smaller versions of the Mandelbrot set are also contained within the tricorn fractal.