PyMandelbrot package

PyMandelbrot.mandelbrot module

This module implements the base class to compute the Mandelbrot dynamics.

class PyMandelbrot.mandelbrot.MandelbrotDynamics(z0: Optional[ndarray] = None, c: Optional[ndarray] = None, clip_value: float = 4.0)

Bases: object

Implementation of the f(z) = z**2 + c function for the Mandelbrot Dynamics.

Examples

One Mandelbrot dynamics iteration:

>>> import numpy as np
>>> from PyMandelbrot.mandelbrot import MandelbrotDynamics
>>> cs = np.linspace(-1,1,5) # offset parameter
>>> cs
array([-1. , -0.5,  0. ,  0.5,  1. ])
>>> z0s = np.zeros_like(cs) # starting point
>>> z0s
array([0., 0., 0., 0., 0.])
>>> dynamics = MandelbrotDynamics(z0s, cs)
>>> z1s = dynamics()
>>> z1s
array([-1. , -0.5,  0. ,  0.5,  1. ])

n = 4 iterations:

>>> z4s = dynamics.n_steps(n=4)
>>> z4s
array([ 0.     , -0.30859,  0.     ,  1.62890, 26.     ])

Divergency speed calculation:

>>> it = dynamics.get_divergency_iter()
>>> it
array([20, 20, 20,  5,  2], dtype=int16)

property c: ndarray

Offset parameter property.

check_params()

Checks parameters are set.

Raises

ValueError – If either starting point z0 or offset parameter c is None.

get_divergency_iter(threshold: float = 4.0, max_iter: float = 20) → ndarray

Computes the number of iteration needed by the dynamics to exceed some threshold.

Given the stored starting point, it computes the number of steps for the dynamics modulusu to exceed a given threshold.

Parameters

• threshold (float) – The threshold above which the dynamics is considered divergent.

• max_iter (int) – The maximum number of steps to be evaluated.

Returns

The iteration number at which the dynamics has diverged.

Return type

np.ndarray

n_steps(n: int)

Computes n steps of the Mandelbrot dynamics for the given starting point.

Parameters

• z0 (np.ndarray) – Starting points of the Mandelbrot dynamic.

• n (int) – Number of steps of the Mandelbrot dynamics.

reset_c()

Resets the offset parameter to None.

reset_z0()

Resets the starting point to None.

property z0: ndarray

Starting point property.