File:Mandelbrot numpy set 2.png
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Summary[edit]
DescriptionMandelbrot numpy set 2.png |
Deutsch: Die Mandelbrot-Menge wird mit NumPy unter Verwendung komplexer Matrizen berechnet. Die verwendeten Färbungen werden von Arnaud Chéritat und Jussi Härkönen beschrieben: Normal Map Effect und Stripe Average Coloring. English: The Mandelbrot set is calculated with NumPy using complex matrices. The colorings used are described by Arnaud Chéritat and Jussi Härkönen: Normal Map Effect and Stripe Average Coloring. |
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 = 800, 600 # pixel density (= image width) and image height
n, r = 200, 500 # number of iterations and escape radius (r > 2)
direction, height = 45.0, 1.5 # direction and height of the light
density, intensity = 4.0, 0.5 # density and intensity of the stripes
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 = (1.5 + 1.0j) * (A + B * 1j) - 0.5
Z, dZ, ddZ = np.zeros_like(C), 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.sin(density * np.angle(Z[M])), T[M] + 1
Z[M], dZ[M], ddZ[M] = Z[M] ** 2 + C[M], 2 * Z[M] * dZ[M] + 1, 2 * (dZ[M] ** 2 + Z[M] * ddZ[M])
fig = plt.figure(figsize=(12.8, 4.8))
fig.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
N = abs(Z) >= r # basic normal map effect and stripe average coloring (potential function)
P, Q = S[N] / T[N], (S[N] + np.sin(density * np.angle(Z[N]))) / (T[N] + 1)
U, V = Z[N] / dZ[N], 1 + (np.log2(np.log(np.abs(Z[N])) / np.log(r)) * (P - Q) + Q) * intensity
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and light vector
D[N] = np.maximum((U.real * v.real + U.imag * v.imag + V * height) / (1 + height), 0)
ax1 = fig.add_subplot(1, 2, 1)
ax1.imshow(D ** 1.0, cmap=plt.cm.bone, origin="lower")
N = abs(Z) > 2 # advanced normal map effect using higher derivatives (distance estimation)
U = Z[N] * dZ[N] * ((1 + np.log(abs(Z[N]))) * np.conj(dZ[N] ** 2) - np.log(abs(Z[N])) * np.conj(Z[N] * ddZ[N]))
U, v = U / abs(U), np.exp(direction / 180 * np.pi * 1j) # unit normal vectors and light vector
D[N] = np.maximum((U.real * v.real + U.imag * v.imag + height) / (1 + height), 0)
ax2 = fig.add_subplot(1, 2, 2)
ax2.imshow(D ** 1.0, cmap=plt.cm.afmhot, origin="lower")
fig.savefig("Mandelbrot_numpy_set_2.png", dpi=200)
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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 |
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current | 22:35, 24 September 2023 | 2,560 × 960 (927 KB) | Majow (talk | contribs) | Uploaded own work with UploadWizard |
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