fractals.mandelbrot

The Mandelbrot set is the set of complex numbers “c” for which the series “z_(n+1) = z_n * z_n + c” does not diverge, i.e. remains bounded. Thus, a complex number “c” is a member of the Mandelbrot set if, when starting with “z_0 = 0” and applying the iteration repeatedly, the absolute value of “z_n” remains bounded for all “n > 0”. Complex numbers can be written as “a + b*i”: “a” is the real component, usually drawn on the x-axis, and “b*i” is the imaginary component, usually drawn on the y-axis. Most visualizations of the Mandelbrot set use a color-coding to indicate after how many steps in the series the numbers outside the set diverge. Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications, making the boundary of the Mandelbrot set a fractal curve. (description adapted from https://en.wikipedia.org/wiki/Mandelbrot_set ) (see also https://en.wikipedia.org/wiki/Plotting_algorithms_for_the_Mandelbrot_set )

Attributes

img

Functions

get_black_and_white_rgb(→ tuple)

Black&white color-coding that ignores the relative distance. The Mandelbrot

get_color_coded_rgb(→ tuple)

Color-coding taking the relative distance into account. The Mandelbrot set

get_distance(→ float)

Return the relative distance (= step/max_step) after which the complex number

get_image(→ PIL.Image.Image)

Function to generate the image of the Mandelbrot set. Two types of coordinates

Module Contents

fractals.mandelbrot.get_black_and_white_rgb(distance: float) → tuple

Black&white color-coding that ignores the relative distance. The Mandelbrot set is black, everything else is white.

>>> get_black_and_white_rgb(0)
(255, 255, 255)
>>> get_black_and_white_rgb(0.5)
(255, 255, 255)
>>> get_black_and_white_rgb(1)
(0, 0, 0)
fractals.mandelbrot.get_color_coded_rgb(distance: float) → tuple

Color-coding taking the relative distance into account. The Mandelbrot set is black.

>>> get_color_coded_rgb(0)
(255, 0, 0)
>>> get_color_coded_rgb(0.5)
(0, 255, 255)
>>> get_color_coded_rgb(1)
(0, 0, 0)
fractals.mandelbrot.get_distance(x: float, y: float, max_step: int) → float

Return the relative distance (= step/max_step) after which the complex number constituted by this x-y-pair diverges. Members of the Mandelbrot set do not diverge so their distance is 1.

>>> get_distance(0, 0, 50)
1.0
>>> get_distance(0.5, 0.5, 50)
0.061224489795918366
>>> get_distance(2, 0, 50)
0.0
fractals.mandelbrot.get_image(image_width: int = 800, image_height: int = 600, figure_center_x: float = -0.6, figure_center_y: float = 0, figure_width: float = 3.2, max_step: int = 50, use_distance_color_coding: bool = True) → PIL.Image.Image

Function to generate the image of the Mandelbrot set. Two types of coordinates are used: image-coordinates that refer to the pixels and figure-coordinates that refer to the complex numbers inside and outside the Mandelbrot set. The figure-coordinates in the arguments of this function determine which section of the Mandelbrot set is viewed. The main area of the Mandelbrot set is roughly between “-1.5 < x < 0.5” and “-1 < y < 1” in the figure-coordinates.

Commenting out tests that slow down pytest… # 13.35s call fractals/mandelbrot.py::mandelbrot.get_image # >>> get_image().load()[0,0] (255, 0, 0) # >>> get_image(use_distance_color_coding = False).load()[0,0] (255, 255, 255)

fractals.mandelbrot.img