Nova fractal

A PhonexDoubleNova fractal, rendered using five layers in UltraFractal.

A nova fractal with Re(R) = 1.0, and z0 = c.

A nova fractal with Re(R) = 2.0, and z0 = c.

A nova fractal with Re(R) = 3.0, and z0 = c.

A 129804.49 times magnification at the point (-0.43608549343268, -0.102470623996602) on the novaMandelbrot fractal with start value $z_0=(9.0, 0.0)$, exponent $p=(3.0, 0.0)$ and relaxation $R=(2.9, 0.0)$.

Nova fractal is a family of fractals related to the Newton fractal. Nova is a formula that is implemented in most^{[citation needed]} fractal art software.

Formula

The formula for the Nova fractal^{[citation needed]} is a generalization of a Newton fractal:

$z \mapsto z - R \frac{z^{p}-1}{pz^{p-1}} + c,$

where $R$ is said to be a relaxation constant and $p\in\mathbb{C}$. If c = 0, this expression reduces to the Newton fractal formula:

$z \mapsto z - R \frac{f}{f'}$

for $f=z^p-1$. Usually, $p$ is assigned the value 3, while $R$ is an adjustable parameter, and $c$ is the location variable, for a "Mandelbrot Nova".