Ringkesna

Lisénsi

Karya ini dilepaskan ke domain umum oleh pemiliknya, Loisel di Wikipédia bahasa Inggris. Lisensi ini berlaku di seluruh dunia. Di sejumlah negara, tindakan ini tidak memungkinkan secara sah; bila seperti itu: Loisel memberikan siapa pun hak untuk menggunakan karya ini untuk tujuan apa pun, tanpa persyaratan apa pun, kecuali yang ditetapkan oleh hukum.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')

Log pengunggahan asli

• 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