Nova fractal

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$A PhonexDoubleNova fractal, rendered using 5 layers in UltraFractal$

A PhonexDoubleNova fractal, rendered using 5 layers in UltraFractal

$A nova fractal with default parameters (this formula is one of the 'standard' formulae that ships with the popular fractal rendering software, UltraFractal )$

A nova fractal with default parameters (this formula is one of the 'standard' formulae that ships with the popular fractal rendering software, UltraFractal )

$A nova fractal with relaxation.real set to 2.0$

A nova fractal with relaxation.real set to 2.0

$A nova fractal with relaxation.real set to 3.0$

A nova fractal with relaxation.real set to 3.0

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

An 129804.49 times magnification at the point (-0.43608549343268, -0.102470623996602) on the novaMandelbrot fractal with start value (9.0, 0.0), exponent (3.0, 0.0) and relaxation (2.9, 0.0).

1 About
2 Formula
3 Nova variants
4 public nova fractal formulae — dmj.ufr
5 References

[edit] About

Nova fractal refers to a family of fractals related to the newton fractal. The formula was named by Paul Derbyshire. Nova is a formula that is implemented in most Fractal Art software.

[edit] Formula

The formula for novaMandelbrot is:

z = z − relax · ( z^power − 1 ) / ( power · z^{power − 1} ) + pixel

[edit] Nova variants

There are a number of related variants of the nova fractal formula, that combine parts of other fractals such as the phoenix fractal and the halley fractal, as well as variants that "double-up" parts of the calculation.

The nova fractal formulae have names like DoubleNova, HalleyNova and PhoenixDoubleNova, each one has a Mandelbrot and a Julia variant.

[edit] public nova fractal formulae — dmj.ufr

The nova formulae that are publicly available,^[1] include a 'relaxation' parameter, which increases the complexity of the resulting image under certain settings.

This formula generates 2-dimensionally dense high-frequency detail when the 'relaxation.real' parameter is increased. This is especially true inside the nova lake.

Because of the high level of detail that Nova Fractal can create it can be a challenge to capture a well antialiased image of it.