# File:Heat smiley.gif

Original file(1,200 × 954 pixels, file size: 4.69 MB, MIME type: image/gif, looped, 50 frames, 5.0 s)

# Structured data

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## Summary

 Description English: Illustration of the Heat equation. Date 16 May 2017 Source Own work Author Nicoguaro
 This GIF graphic was created with Python.

## Python

```"""
Illustration of the heat equation

Solve the heat equation using finite differences and Forward Euler.

Based on: https://commons.wikimedia.org/wiki/File:Heat_eqn.gif
"""

from __future__ import division, print_function
import numpy as np
from mayavi import mlab
import subprocess

path_to_convert = "C:\Program Files\ImageMagick-6.9.3\convert.exe"

def step_function(N, scale, X, Y, shape="crescent"):
"""Function that is 1 on a set and 0 outside of it"""
shapes = ["crescent", "cylinder", "hexagon", "superquadric", "smiley"]

if shape not in shapes:
shape = "crescent"

if shape == "cylinder":
Z = np.ones_like(X)
Z[X**2 + Y**2 < 0.5] = 0
Z[X**2 + Y**2 > 2] = 0

Z = np.ones_like(X)
Z[np.abs(X)**0.5 + np.abs(Y)**0.5 > 1.5] = 0

if shape == "hexagon":
Z = np.ones_like(X)
hexa = 2*np.abs(X) + np.abs(X - Y*np.sqrt(3)) +\
np.abs(X + Y*np.sqrt(3))
Z[hexa > 6] = 0

if shape == "crescent":
c = 2
d = -1
e = 1
f = 0.5
k = 1.2
shift = 10
Z = (c**2 - (X/e - d)**2 - (Y/f)**2)**2 + k*(c + d - X/e)**3 - shift
Z = 1 - np.maximum(np.sign(Z), 0)

if shape == "smiley":
Z = np.ones_like(X)
fac = 1.2
x_eye = 0.5
y_eye = 0.4
bicorn = fac**2*(Y + 0.3)**2*(1 - fac**2*X**2) -\
(fac**2*X**2 - 2*fac*(Y + 0.3) - 1)**2
left_eye = (X + x_eye)**2/0.1 + (Y - y_eye)**2/0.4 - 1
right_eye = (X - x_eye)**2/0.1 + (Y - y_eye)**2/0.4 - 1
Z[X**2 + Y**2 > 2] = 0
Z[bicorn > 0] = 0
Z[left_eye < 0] = 0
Z[right_eye < 0] = 0

Z = scale * Z
return Z

def data_gen(num):
# Solve the heat equation with zero boundary conditions
for cont in range(ntime_anim):
Z[1:N-1, 1:N-1] = Z[1:N-1, 1:N-1] + dt*(Z[2:N, 1:N-1] +
Z[0:N-2, 1:N-1] + Z[1:N-1, 0:N-2] +
Z[1:N-1, 2:N] - 4*Z[1:N-1, 1:N-1])/dx**2

surf = mlab.surf(X, Y, Z, colormap='autumn', warp_scale=1)
# Change the visualization parameters.
surf.actor.property.interpolation = 'phong'
surf.actor.property.specular = 0.3
surf.actor.property.specular_power = 20
surf.module_manager.scalar_lut_manager.reverse_lut = True
surf.module_manager.scalar_lut_manager.data_range = np.array([ 0.,  scale])

return surf

N = 500  # Grid points
L = 2.5  # Box size
X, Y = np.mgrid[-L:L:N*1j, -L:L:N*1j]
scale = 2
Z = step_function(N, scale, X, Y, shape="smiley")
CFL = 0.125
dx = X[1, 0] - X[0, 0]
dy = dx
dt = CFL*dx**2
end_time = 0.05
time = np.arange(0, end_time, dt)
nframes = 50
ntime = time.shape[0]
ntime_anim = int(ntime/nframes)

#%% Plot frames
fname = "heat_smiley"
bgcolor = (1, 1, 1)
fig = mlab.figure(size=(1200, 1000), bgcolor=bgcolor)
fig.scene.camera.azimuth(180)
mlab.get_engine()
engine = mlab.get_engine()
scene = engine.scenes[0]
for cont in range(nframes):
mlab.clf()
surf = data_gen(cont)
scene.scene.camera.position = [-8, -8,  7]
scene.scene.camera.clipping_range = [7, 22]
scene.scene.camera.focal_point = [0, 0, 1]
print(cont)
mlab.savefig("{}_{n:02d}.png".format(fname, n=cont))

#%% Generate video
args = [path_to_convert, "-delay", "10", "-loop" , "0", fname + "_*.png",
fname + ".gif"]
subprocess.call(args, shell=True)
subprocess.call(["del", "/Q", fname + "*.png"], shell=True)
print("Done!")
```

## Licensing

I, the copyright holder of this work, hereby publish it under the following license:

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current03:12, 20 May 20171,200 × 954 (4.69 MB)Nicoguaro (talk | contribs)User created page with UploadWizard
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