The Nova fractal is a variation of the Newton's method fractal. The iteration formula is:
z_{n+1} = z_n - \frac{z_n^3 - 1}{3z_n^2} + c
where $c$ is a point in the complex plane, and $z_0$ is a fixed starting value (in this case $z_0 = 1$). This formula is derived from Newton's method for finding the roots of the polynomial $p(z) = z^3 - 1$, but with an extra term $c$ added in each step.
This creates a Mandelbrot-like fractal. The set of points $c$ for which the sequence remains bounded forms the Nova fractal. For more information on the general principles, see the descriptions of the Mandelbrot and Newton fractals.
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.