Tricorn (mathematics)

The tricorn, as seen in the fractal zooming program XaoS.

One of infinite Mandelbrot sets contained within the tricorn fractal.

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 $z \mapsto \bar{z}^2 + c$ instead of $z \mapsto z^2 + c$ used for the Mandelbrot set.^[1]

The "tricorn" is generated by multiplying the imaginary number component of the "z" in the Mandelbrot formula by minus one. This complex conjugation is represented by the horizontal line above the z in the previous formula, which is referred to as a "bar", hence the name "Mandelbar".

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.

References

1. ^ Weisstein, Eric W., "Mandelbar Set" from MathWorld.

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