Magnet 2 — Fantastic Fractals

This is another type of magnet fractal. The iteration is defined by:

z_{n + 1} = z_{n} - \frac{( z _{n}^{2} - 1 ) ^{2}}{4 z _{n}^{3} + 4 z _{n}^{2} c}

This variation produces different but equally complex and beautiful patterns compared to Type 1. In this implementation, the point $c$ in the formula is the same as the initial point $z_{0}$ , which is the coordinate of the point on the complex plane being tested.

This type of fractal, where the parameter $c$ is the same as the starting point $z_{0}$ , is sometimes called a "Multibrot" type set.

Parameters

GUI Parameters

Iterations: This integer value determines the maximum number of times the formula is applied for each point.

Complex Parameters

This fractal does not have any complex parameters that can be controlled directly as control points. The complex number $c$ corresponds to each point on the plane being tested.