Nova fractal

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A PhonexDoubleNova fractal, rendered using five[clarification needed] 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 zoom at -0.5610029695, -0.78403
Nova Fractal zoom at 0.231565014, 0.514381289 (Mandelbrot Island)

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.


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".