File:Mandelbrot numpy set 3.png
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Summary
[edit]DescriptionMandelbrot numpy set 3.png |
Deutsch: Die Mandelbrot-Menge wird mit NumPy unter Verwendung komplexer Matrizen berechnet. Es wird eine von David Madore und Anders Sandberg vorgestellte logarithmische Projektion verwendet. Die so erstellten Bilder werden auch Exponential Maps oder Mercator-Mandelbrot Maps genannt. Durch diese Projektion lässt sich die Berechnung von Zoom-Animationen sehr vereinfachen. English: The Mandelbrot set is calculated with NumPy using complex matrices. A logarithmic projection presented by David Madore and Anders Sandberg is used. The images created in this way are also called Exponential Maps or Mercator-Mandelbrot Maps. This projection makes the calculation of zoom animations much easier |
Date | |
Source | Own work |
Author | Majow |
Other versions |
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PNG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python codeimport numpy as np
import matplotlib.pyplot as plt
d, h = 200, 1000 # pixel density (= image width) and image height
n, r = 800, 5000 # number of iterations and escape radius (r > 2)
a, b = -1.748764520194788535, 3e-13 # https://mathr.co.uk/web/m-location-analysis.html
x = np.linspace(0, 2, num=d+1)
y = np.linspace(0, 2 * h / d, num=h+1)
A, B = np.meshgrid(x * np.pi, y * np.pi)
C = 4.0 * np.exp((A + B * 1j) * 1j) + (a + b * 1j)
Z, dZ = np.zeros_like(C), np.zeros_like(C)
D = np.zeros(C.shape)
for k in range(n):
M = Z.real ** 2 + Z.imag ** 2 < r ** 2
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)
N = abs(Z) > 2 # exterior distance estimation
D[N] = np.log(abs(Z[N])) * abs(Z[N]) / abs(dZ[N])
ax1 = fig.add_subplot(3, 1, 1)
ax1.imshow(D.T ** 0.05, cmap=plt.cm.nipy_spectral, origin="lower")
X, Y = C.real, C.imag # zoom images (adjust circle size 50 and zoom level 8 as needed)
R, c, z = 50 * (2 / d) * np.pi * np.exp(- B), min(d, h) + 1, max(0, h - d) // 8
for i in range(8):
axs = fig.add_subplot(3, 4, 5 + i)
axs.scatter(X[i*z:i*z+c,0:d], Y[i*z:i*z+c,0:d], s=R[0:c,0:d]**2, c=D[i*z:i*z+c,0:d]**.5, cmap=plt.cm.nipy_spectral)
axs.set_xticks([])
axs.set_yticks([])
axs.axis('equal')
fig.savefig("Mandelbrot_numpy_set_3.png", dpi=200)
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[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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current | 22:35, 24 September 2023 | 2,560 × 1,920 (3.03 MB) | Majow (talk | contribs) | Uploaded own work with UploadWizard |
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