# Mathematica Animate function question

1. Oct 16, 2011

### Munin

Hi

Im doing a 2 dimensional heat spreading simulation.
I've created a matrix with 3 indices with the first index being for time step and the two other for element coordinates.

Code (Text):

height = 20;
width = 4;
a = 0.5;
J = Round[height/a];
L = Round[width/a];
h = 0.1;
roomT = 20;
T = 90;
t = 1000;
Dev = Normal[ConstantArray[1, {t, J, L}]];
u = T*Normal[ConstantArray[1, {J, L}]];

J*L

v = Normal[ConstantArray[0, {J*L, 1} ]];
A = Normal[ConstantArray[0, {J*L, J*L}]];

u[[All, 1]] = roomT;
u[[All, L]] = roomT;
u[[1, All]] = roomT;
u[[J, All]] = roomT;

For[j = 1, j <= J, j++,
For[l = 1, l <= L, l++,
index = (j - 1)*L + l;
v[[index, 1]] = u[[j, l]];
];
];

For[i = 1, i <= J*L, i++,

A[[i, i]] = -4;

If[i + L <= J*L, A[[i, i + L]] = 1, A[[i, i]] = A[[i, i]] + 1];

If[i - L >= 1, A[[i, i - L]] = 1, A[[i, i]] = A[[i, i]] + 1];

If[i + 1 <= J*L, A[[i, i + 1]] = 1, A[[i, i]] = A[[i, i]] + 1];

If[i - 1 >= 1, A[[i, i - 1]] = 1, A[[i, i]] = A[[i, i]] + 1];
]
A = A/a^2;

Ett = SparseArray[{i_, i_} -> 1, {J*L, J*L}];
Mtemp = Ett - h*A;
M = Inverse[Mtemp];

For[i = 1, i <= L, i++,
M[[i, All]] = 0;
M[[(J - 1)*L + i, All]] = 0;
M[[i, i]] = 1;
M[[(J - 1)*L + i, (J - 1)*L + i]] = 1;

];
For[i = 1, i <= J, i++,
M[[1 + L*(i - 1), All]] = 0;
M[[1 + L*(i - 1), 1 + L*(i - 1)]] = 1;
M[[L*i, All]] = 0;
M[[L*i, L*i]] = 1;

];
k = 1;

While[k < t + 1,
For[j = 1, j <= J, j++,
For[l = 1, l <= L, l++,
index = (j - 1)*L + l;
u[[j, l]] = v[[index, 1]];
];
];
Dev[[k, All, All]] = u;
If[u[[Round[J/2], Round[L/2]]] < 21,
Break[]
];
v = M.v;
k++;
];
t = k;
Print[t]
The simulation works fine but when I try to run an animate function over the time steps it only plots a density plot in the first time step. Is this the correct way to do an animate funtion for my density plot?

Code (Text):
Animate[ListDensityPlot[Dev[[m, All, All]],
ColorFunction -> (RGBColor[1, 1 - #, 0] &)], {m, 1, t},
AnimationRunning -> False]
As it is now the color in the color function is relative to the highest value for the time step. Is there a way to get the colors relative to the highest value for all steps?

2. Oct 17, 2011

### Munin

Ok, I fixed the animate problem with this.
Code (Text):

Animate[ListDensityPlot[Dev[[m, All, All]],
ColorFunction -> (ColorData["TemperatureMap"]),
ColorFunctionScaling -> True], {m, 1, t, 1},
AnimationRunning -> False]

But I still cant get the colors to scale correctly, any advice on how to do this would be very helpful.

3. Oct 17, 2011

### Bill Simpson

Define a function outside your Animate that is based on your entire dataset that would map any value to the color you desire and then use that inside your animate as an argument to your ColorFunction.

If you are defining your argument to ColorFunction the way you wrote it inside your Animate then it is only dependent on the available data for that frame of the Animate and that was exactly what you observed, the color function changes as the Animate frame changes.