Summary

Licensing

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

This 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

• 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