Ultra Fractal newton Newton

The Newton fractal is generated by Newton’s method for solving polynomial equations. Different equations are available by changing the parameters. It is available as a fractal formula in Standard.ufm and as a fractal formula plug-in in Standard.ulb.

This is a simple and attractive fractal type. Newton fractals are strictly self-similar, so they are not very interesting zooming subjects. Instead, try a few different coloring algorithms to decorate them in various ways.

The formula provides the following parameters:


Specifies the exponent of the equation to be solved. The default value is (3, 0), resulting in the equation:

z3 + Root

Try (4, 0), (5, 0) and so on to increase the symmetry order. Non-integer values for the real part of the exponent will interpolate between these. If the imaginary part is not zero, the fractal will be further distorted.


Specifies the root of the equation. This tends to rotate and magnify the fractal.

Bailout value Specifies the minimum difference between subsequent z values at which the formula will stop iterating. Smaller values give more accurate results at the expense of calculation time.

See Also
Nova (Julia)
Standard formulas