Thread: Python implementation of the mandelbrot fractal set

  1. #1
    Registered User
    Join Date
    Dec 2016

    Python implementation of the mandelbrot fractal set

    Hi guys,

    I appreciate your help in the past, it was valuable this time I need a little help in order to understand this mandelbrot fractal set.

    To begin with what is a fractal? Since English is not my native language, I have a hard time translating this.

    This is my code, I want to know how to generate the image and how to calculate this fractal. I got to how many iterations are needed for (Z on) 2) + Z + C, iterations of what?

    #A mandelbrot set uses a decart coordinate system in order to represent an image and its color based on the
    #iterations needed in order to
    #From pillow(PIL) include the classes Image and ImageDraw
    from PIL import Image, ImageDraw
    #Import libraries os, json, yaml, math
    import os, json, yaml, math
    #Import library pandas named pd for short
    import pandas as pd
    #Import library numbpy named np for short
    import numpy as np
    #Import library matplotlib . pylot named plt for short
    import matplotlib .pyplot as plt
    #Variables block
    image_width = 100
    image_height = 100
    cxmin = 100
    cxmax = 100
    cymin = 100
    cymax = 100
    iterations = 100
    color = 'Green'
    output_image_path = 'target/04_mandelbrot.png'
    #Function declarations block
    #mandelbrot set function
    def render_mandelbrot(image_width, image_height, cxmin, cxmax, cymin, cymax, iterations, color, output_image_path):
        #create an image of type RGBA, size in width and height, color
        img ='RGBA', (image_width, image_height), color)
        #new_pixel_map = img.load()
        #Mandelbrot calculations(scaling)
        for i in range (image_height):
            y = 2*i/image_height - 1.0
            for j in range (image_width):
                x = 2*j/image_width - 1.0
                #compute the mandelbrot set iteself
                g = compute_mandelbrot_value(x, y, iterations=200)
                #color = (g, g, g)
                #new_pixel_map[j, i] = color
        #return the image at the end of the funtion    
        return img
    def compute_mandelbrot_value(x, y, iterations=200):
        g = int(255 * ((x + y)+ 2)/4)
        return g
        img ='RGB', (image_width, image_height), color) function does not save the file
    #Function calling block
    render_mandelbrot(image_width, image_height, cxmin, cxmax, cymin, cymax, iterations, color, output_image_path)
    Last edited by ArakelTheDragon; 06-01-2021 at 09:07 AM.

  2. #2
    Registered User
    Join Date
    Dec 2016
    Latest code for anyone who needs it, its not perfect and there might be mistakes in the comments:
    # Description:
    # To iterate (z on the power of 2) + c we begin with a seed for the iteration. This is a real or complex number
    # which we denote by z0. Applying the function (z on the power of 2) + c on z0, gives the new number.
    # Now we iterate using the result of the previous computation as the input for the next.
    # z0 = 0(this is the seed)
    # z1 = (z0 on the power of 2) + c
    # z2 = (z1 on the power of 2) + c
    # and so on.
    # if we take 0 for the seed, z0 = 0
    # z1 = (0 on the power of 2) + 1 = 1
    # z2 = (1 on the power of 2) + 1 = 2
    # and so on
    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib .pyplot import imshow
    from numpy import newaxis
    import cmath # importing cmat for complex number operations
    def compute_mandelbrot(N_max, some_threshold, nx, ny):      # N_max = max iterations
                                                                # some threshold = threshold for z after which to stop
                                                                # nx = image height
                                                                # ny = image width
                                                                # A grid of c-values
        x = np.linspace(-2, 1, nx)                              # numpy linspace returns evenly placed numbers over a
                                                                # specified interval
        y = np.linspace(-1.5, 1.5, ny)                          # y = np.linspace(interval start, interval end, points)
                                                                # y equals an array of numbers between -1.5 and 1.5,
                                                                # with ny points, in this case 401, the numbers are
                                                                # evenly placed
        c = x[:,newaxis] + 1j*y[newaxis,:]                      # All values of c, these are the points on the image
                                                                # Mandelbrot iteration
        z = c                                                   
                                                                # The code below overflows in many regions of the x-y grid, suppress
                                                                # warnings temporarily
        with np.warnings.catch_warnings():                      # We start the iterations by the formula
            np.warnings.simplefilter("ignore")                  # z(p) = (z(p-1) on the power of 2) + C
            for j in range(N_max):
                z = z**2 + c                                    # The mandelbrot set is the formula z(1) = (z0 on the power of 2) + c
            mandelbrot_set = (abs(z) < some_threshold)          # After we calculate z, we get the absolute value
                                                                # If we give abs() a complex number, then the function
                                                                # returns the magnitude of that number
            print (z)                                           # Prints nan + nan
            print (mandelbrot_set)                              # Prints false
        return mandelbrot_set
    mandelbrot_set = compute_mandelbrot(50, 50., 601, 401)     # Max iterations, threshold, image height, image width
    plt.imshow(mandelbrot_set.T, extent=[-2, 1, -1.5, 1.5])    # The image has dimensions nx and ny, but we scale it to -2, 1 for x and -1.5, 1.5 for y
    plt.gray()                                                 # We assign the right color to our mandelbrot set                                                 # We show the image

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