This is a type of magnet fractal, known for its intricate, magnetic-like patterns. It is a Mandelbrot-like fractal, where the set of points $c$ is determined based on whether the sequence remains bounded.

The iteration formula is:

z_{n+1} = \left( \frac{z_n^2 - 1}{2z_n + c} \right)^2
    

with $z_0 = 0$, and $c$ being the point on the complex plane under test.

For more information on the general principles of this type of fractal, see the description of the Mandelbrot 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.