File:Mandelbrot numpy set 1.png

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Computing the Mandelbrot set with NumPy and complex matrices (Part 1)

Summary[edit]

Description
Deutsch: Die Mandelbrot-Menge wird mit NumPy unter Verwendung komplexer Matrizen berechnet. Die verwendeten Färbungen werden von Javier Barrallo, Damien M. Jones und Arnaud Chéritat beschrieben: -Smoothing, Normalized Iteration Count, Exterior Distance Estimation und Boundary Detection.
English: The Mandelbrot set is calculated with NumPy using complex matrices. The colorings used are described by Javier Barrallo, Damien M. Jones and Arnaud Chéritat: -Smoothing, Normalized Iteration Count, Exterior Distance Estimation and Boundary Detection.
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Source Own work
Author Majow
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This plot was created with Matplotlib.
Source code
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Python code

import numpy as np
import matplotlib.pyplot as plt

d, h = 800, 600  # pixel density (= image width) and image height
n, r = 200, 500  # number of iterations and escape radius (r > 2)

x = np.linspace(0, 2, num=d+1)
y = np.linspace(0, 2 * h / d, num=h+1)

A, B = np.meshgrid(x - 1, y - h / d)
C = 2.0 * (A + B * 1j) - 0.5

Z, dZ = np.zeros_like(C), np.zeros_like(C)
D, S, T = np.zeros(C.shape), np.zeros(C.shape), np.zeros(C.shape)

for k in range(n):
    M = abs(Z) < r
    S[M], T[M] = S[M] + np.exp(- abs(Z[M])), T[M] + 1
    Z[M], dZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1

fig = plt.figure(figsize=(12.8, 9.6))
fig.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)

ax1 = fig.add_subplot(2, 2, 1)
ax1.imshow(S ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")

N = abs(Z) >= r  # normalized iteration count
T[N] = T[N] - np.log2(np.log(np.abs(Z[N])) / np.log(r))

ax2 = fig.add_subplot(2, 2, 2)
ax2.imshow(T ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")

N = abs(Z) > 2  # exterior distance estimation
D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])

ax3 = fig.add_subplot(2, 2, 3)
ax3.imshow(D ** 0.1, cmap=plt.cm.twilight_shifted, origin="lower")

N, thickness = D > 0, 0.01  # boundary detection
D[N] = np.maximum(1 - D[N] / thickness, 0)

ax4 = fig.add_subplot(2, 2, 4)
ax4.imshow(D ** 2.0, cmap=plt.cm.binary, origin="lower")

fig.savefig("Mandelbrot_numpy_set_1.png", dpi=200)

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
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current22:35, 24 September 2023Thumbnail for version as of 22:35, 24 September 20232,560 × 1,920 (1.04 MB)Majow (talk | contribs)Uploaded own work with UploadWizard

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