File:Fourier heat in a plate.png
Original file (2,960 × 2,960 pixels, file size: 487 KB, MIME type: image/png)
Captions
Summary
editDescriptionFourier heat in a plate.png |
English: Heat distribution in a metal plate, using Fourier's method.
Bahasa Melayu: Pengedaran panas di sebuah plat logam, menggunakan kaedah Fourier.
Sunda: Distribusi panas dina hiji pelat métal, ngagunakeun métoda Fourier. |
Date | 15 February 2008 (original upload date) |
Source | Own work |
Author | Loisel at English Wikipedia |
Licensing
editPublic domainPublic domainfalsefalse |
This work has been released into the public domain by its author, Loisel at English Wikipedia. This applies worldwide. In some countries this may not be legally possible; if so: Loisel grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.Public domainPublic domainfalsefalse |
Creation
editThis file was created with Python
import numpy as np
import matplotlib.pyplot as plt
x = y = np.linspace(0, np.pi, 2**12)
X, Y = np.meshgrid(x, y)
T = 0
N = 200
for n in np.arange(1,N):
term = 2*(-1)**(n+1)/n*np.sinc(n/(N+1))*np.sin(n*X) * np.sinh(n * Y)/np.sinh(n*np.pi)
T += term
fig = plt.figure(dpi=800)
ax = fig.add_subplot(111)
ax.set_aspect('equal')
ax.set_facecolor('none')
plt.axis('off')
plt.pcolormesh(X, Y, T, cmap=black_body)
plt.tight_layout()
plt.savefig("Fourier heat plate.png", bbox_inches='tight', pad_inches=0)
The Black Body color map was obtained here. The sinc function in the code arises in order to eliminate ringing.
A previous version of this file was created with MATLAB
f = @(x,y,n) 2*(((-1).^(2:n+1))./((1:n).*sinh((1:n).*pi))) ...
* (sin((1:n)'*x).*sinh((1:n)'*y));
ys = 0:0.01:pi;
g = [];
for y = ys
n = max(20,min(100,-10*log(pi-y)/(pi-y)));
g = [g; f(ys, repmat(y, 1, length(ys)), n)];
end
g(end, :) = ys';
imagesc(ys,ys,g(end:-1:1,:));
colormap hot
axis square
axis off
print('-dpng', '-r600', 'Fourier heat in a plate')
Original upload log
edit- 2010-01-02 10:24 Fastily 409×410× (20774 bytes) Crop out whitespace
- 2008-02-15 22:32 Loisel 672×504× (12407 bytes) Had to flip MATLAB's silly y coordinates.
- 2008-02-15 22:24 Loisel 875×672× (13817 bytes) {{Information |Description= |Source=self-made |Date= |Location= |Author=~~~ |Permission= |other_versions= }} MATLAB snippet: f=@(x,y,n) 2*(((-1).^(2:n+1))./((1:n).*sinh((1:n).*pi))) ... * (sin((1:n)'*x).*sinh((1:n)'*y)); ys=0:0.01:pi; g=[]; for y=ys
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 00:58, 5 November 2020 | 2,960 × 2,960 (487 KB) | AkanoToE (talk | contribs) | Added more terms for sum and removed Gibbs ringing in upper right corner | |
02:25, 4 November 2020 | 2,960 × 2,960 (446 KB) | AkanoToE (talk | contribs) | Used a similar color map as before, but still perceptually uniform ([https://www.kennethmoreland.com/color-advice/ Black Body]) | ||
22:21, 3 November 2020 | 2,960 × 2,960 (469 KB) | AkanoToE (talk | contribs) | Changed colormap to a perceptually uniform version (https://matplotlib.org/3.1.1/tutorials/colors/colormaps.html inferno) | ||
22:31, 25 April 2016 | 2,932 × 2,752 (56 KB) | Nicoguaro (talk | contribs) | Crop image. | ||
22:28, 25 April 2016 | 4,800 × 3,600 (78 KB) | Nicoguaro (talk | contribs) | Change in colormap and higher resolution | ||
01:51, 15 May 2010 | 409 × 410 (20 KB) | File Upload Bot (Magnus Manske) (talk | contribs) | {{BotMoveToCommons|en.wikipedia|year={{subst:CURRENTYEAR}}|month={{subst:CURRENTMONTHNAME}}|day={{subst:CURRENTDAY}}}} {{Information |Description={{en|MATLAB/Octave snippet: f=@(x,y,n) 2*(((-1).^(2:n+1))./((1:n).*sinh((1:n).*pi))) ... * (sin((1:n)' |
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File usage on Commons
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Horizontal resolution | 314.96 dpc |
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Vertical resolution | 314.96 dpc |
Software used |