fractpy.models package¶

Submodules¶

fractpy.models.newton module¶

class fractpy.models.newton.NewtonFractal(func, prec_goal=1e-11, nmax=200)[source]¶

A class for plotting Newton Fractal for a given function.

Newton fractals are fractals created in the plane of complex numbers. An iteration process with Newton’s method (or Newton-Raphson Method) is started at each point on a grid in the complex plane, and a color is assigned to each point according to which of the roots of a given function the iteration converges to. [Sahari, M. and Djellit, I., 2006. Fractal Newton basins. Discrete Dynamics in Nature and Society, 2006, pp.1-16.]

Parameters

func (sympy expression) – The function for which we want to plot fractal (single- variable).
prec_goal (float, optional) – Tolerance for how small the iteration step be relative to the point to break the loop for that point i.e. if relative difference of the iteration step and the point is smaller than this value, it will stop the loop for this point.
nmax (int, optional) – Number of iterations to be run (default is 200). Minimum recommended value is 50, but for some functions may required over 500.

function¶

The function for which the Newton Fractal is being generated.

Type: fractpy.Function

roots_list¶

Roots of the function.

Type: list

Example

To plot Newton Fractal for f(x) = x**4 - 2x**3 + 10 we first make a model, and then plot it in required range and resolution:

>>> model = NewtonFractal("x**4 - 2x**3 + 10")
>>> p = model.plot(-2, 2, -2, 2, (200, 200))

Where p is an object of matplotlib.figure.Figure.

To make a plot which can be zoomed use model.zoom_plot().