Python - Math - Drawing Geometric Shapes and Fractals(Drawing the Mandelbrot Set)

Doing Math with Python

開発環境

• OS X El Capitan - Apple (OS)
• Emacs (Text Editor)
• Python 3.5 (プログラミング言語)

Doing Math with Python: Use Programming to Explore Algebra, Statistics, Calculus, and More! (Amit Saha (著)、No Starch Press)のChapter 6.(Drawing Geometric Shapes and Fractals)、Programming Challenges #4: Drawing the Mandelbrot Set, (No. 4122)を取り組んでみる。

Programming Challenges #4: Drawing the Mandelbrot Set, (No. 4122)

コード(Emacs)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import matplotlib.pyplot as plt
import matplotlib.cm as cm
import random

def initialize_image(x_p, y_p):
    image = []
    for _ in range(y_p):
        x_colors = []
        for _ in range(x_p):
            x_colors.append(0)

        image.append(x_colors)
    return image

def color_points():
    MAX_ITERATION = 1000
    x_p = 400
    y_p = 400
    image = initialize_image(x_p, y_p)
    x_p1 = [-2.5 + (1.0 - -2.5) / (x_p - 1) * x for x in range(x_p)]
    y_p1 = [-1.0 + (1.0 - -1.0) / (y_p - 1) * y for y in range(y_p)]
    for i, x in enumerate(x_p1):
        if i % 10 == 0:
            print(i)
        if i % 100 == 0:
            plt.imshow(image, origin='lower', extent=(-2.5, 1.0, -1.0, 1.0),
                       cmap=cm.Greys_r, interpolation='nearest')
            plt.title('Mandelbrot Set_{0}'.format(i))
            plt.savefig('mandelbrot_set_{0}.png'.format(i))
            
        for k, y in enumerate(y_p1):
            z1 = 0 + 0j
            c = complex(x, y)
            iteration = 0
            z1 = z1 ** 2 + c
            iteration += 1
            while abs(z1) < 2 and iteration < MAX_ITERATION:
                z1 = z1 ** 2 + c
                iteration += 1
                image[k][i] = iteration
                
    plt.imshow(image, origin='lower', extent=(-2.5, 1.0, -1.0, 1.0),
               cmap=cm.Greys_r, interpolation='nearest')
    plt.title('Mandelbrot Set')
    plt.savefig('mandelbrot_set.png')
    plt.show()
    
if __name__ == '__main__':
    color_points()

入出力結果(Terminal, IPython)

$ ./sample4.py
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$