摘要

授權條款

此作品已由其作者，英文維基百科的Loisel，釋出至公有領域。此授權條款在全世界均適用。 這可能在某些國家不合法，如果是的話： Loisel授予任何人有權利使用此作品於任何用途，除受法律約束外，不受任何限制。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')

原始上傳日誌

• 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