Nova fractal

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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".

v t e Fractals

Characteristics	Fractal dimension Hausdorff dimension Topological dimension Recursion Self-similarity

Iterated function system	Barnsley fern Cantor set Dragon curve Koch snowflake Menger sponge Sierpinski carpet Sierpinski triangle Space-filling curve T-square

Strange attractor	Multifractal system

L-system	Space-filling curve

Escape-time fractals	Burning Ship fractal Julia set Lyapunov fractal Mandelbrot set Nova fractal

Random fractals	Brownian motion Brownian tree Diffusion-limited aggregation Fractal landscape Lévy flight Percolation theory Self-avoiding walk

People	Georg Cantor Felix Hausdorff Gaston Julia Helge von Koch Paul Lévy Aleksandr Lyapunov Benoit Mandelbrot Lewis Fry Richardson Wacław Sierpiński

Other	"How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension" List of fractals by Hausdorff dimension

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