File:Mandelbrot numpy set 4.png
Original file (2,560 × 320 pixels, file size: 201 KB, MIME type: image/png)
Captions
Summary
[edit]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 (2013) und Zhuoran Yu (2021) vorgestellte Berechnungsmethode verwendet: Störungsrechnung mit Umbasierung. 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 (2013) and Zhuoran Yu (2021) 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
[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 |
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 (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following 6 pages use this file:
File usage on other wikis
The following other wikis use this file:
- Usage on de.wikipedia.org
- Usage on en.wikibooks.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Software used | |
---|---|
Horizontal resolution | 78.74 dpc |
Vertical resolution | 78.74 dpc |