Nova fractal

A PhonexDoubleNova fractal, rendered using five^{[clarification needed]} layers in UltraFractal.

A nova fractal with default^{[clarification needed]} parameters.

A nova fractal with Re(R) = 2.0.

A nova fractal with Re(R) = 3.0.

A 129804.49 times magnification at the point (-0.43608549343268, -0.102470623996602) on the novaMandelbrot fractal with start value z₀ = (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 novaMandelbrot^{[citation needed]} is a special case of the generalized Newton fractal:

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

where R is said to be a relaxation constant and $p\in\mathbb{C}$. Note that this expression is equivalent to

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

for f = z^p − 1, which is exactly the formula describing Newton fractals for a specific f.

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