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:
| Exponent |
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. |
| Root | 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