File:Mandelbrot numpy set 4.png
Size of this preview: 800 × 100 pixels. Other resolutions: 320 × 40 pixels | 2,560 × 320 pixels.
Original file (2,560 × 320 pixels, file size: 201 KB, MIME type: image/png)
This is a file from the Wikimedia Commons. The description on its description page there is shown below. |
Summary
DescriptionMandelbrot numpy set 4.png |
Deutsch: Die Mandelbrot-Menge wird mit NumPy unter Verwendung komplexer Matrizen berechnet. Für die extreme Zoomtiefe der Mercator-Map wird eine von Kevin Martin und Zhuoran vorgestellte Berechnungsmethode verwendet: Perturbation Theory mit Rebasing. English: The Mandelbrot set is calculated with NumPy using complex matrices. For the extreme zoom depth of the Mercator map, a calculation method presented by Kevin Martin and Zhuoran is used: Perturbation Theory with Rebasing. |
Date | |
Source | Own work |
Author | Majow |
Other versions |
|
PNG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python codeimport numpy as np
import matplotlib.pyplot as plt
import decimal as dc # decimal floating point arithmetic with arbitrary precision
dc.getcontext().prec = 80 # set precision to 80 digits (about 256 bits)
d, h = 50, 1000 # pixel density (= image width) and image height
n, r = 80000, 100000 # number of iterations and escape radius (r > 2)
a = dc.Decimal("-1.256827152259138864846434197797294538253477389787308085590211144291")
b = dc.Decimal(".37933802890364143684096784819544060002129071484943239316486643285025")
S = np.zeros(n+1, dtype=np.complex128)
u, v = dc.Decimal(0), dc.Decimal(0)
for k in range(n+1):
S[k] = float(u) + float(v) * 1j
if u ** 2 + v ** 2 < r ** 2:
u, v = u ** 2 - v ** 2 + a, 2 * u * v + b
else:
print("The reference sequence diverges within %s iterations." % k)
break
x = np.linspace(0, 2, num=d+1, dtype=np.float64)
y = np.linspace(0, 2 * h / d, num=h+1, dtype=np.float64)
A, B = np.meshgrid(x * np.pi, y * np.pi)
C = (- 8.0) * np.exp((A + B * 1j) * 1j)
E, Z, dZ = np.zeros_like(C), np.zeros_like(C), np.zeros_like(C)
D, I, J = np.zeros(C.shape), np.zeros(C.shape, dtype=np.int64), np.zeros(C.shape, dtype=np.int64)
for k in range(n):
Z2 = Z.real ** 2 + Z.imag ** 2
M, R = Z2 < r ** 2, Z2 < E.real ** 2 + E.imag ** 2
E[R], I[R] = Z[R], J[R] # rebase when z is closer to zero
E[M], I[M] = (2 * S[I[M]] + E[M]) * E[M] + C[M], I[M] + 1
Z[M], dZ[M] = S[I[M]] + E[M], 2 * Z[M] * dZ[M] + 1
fig = plt.figure(figsize=(12.8, 1.6))
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(1, 1, 1)
ax1.imshow(D.T ** 0.015, cmap=plt.cm.nipy_spectral, origin="lower")
fig.savefig("Mandelbrot_numpy_set_4.png", dpi=200)
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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 |
Items portrayed in this file
depicts
24 September 2023
image/png
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:35, 24 September 2023 | 2,560 × 320 (201 KB) | Majow | Uploaded own work with UploadWizard |
File usage
The following page uses this file:
Global file usage
The following other wikis use this file:
- Usage on de.wikipedia.org
Metadata
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
Software used |
|
---|---|
Horizontal resolution | 78.74 dpc |
Vertical resolution | 78.74 dpc |
Retrieved from "https://en.wikibooks.org/wiki/File:Mandelbrot_numpy_set_4.png"