MATLAB: How to use MATLAB to graphically visualize a function of four variables

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I want to use MATLAB to graphically visualize a function of four variables.

Best Answer

To graphically visualize a function of four variables, you can use the x-axis, y-axis, z-axis, and a series of plots (time) to represent the variables. The function value is the fifth dimension, and can then be represented by color.
As an example, consider the following temperature distribtion over time of a shrinking sphere.
% Generate mesh of shrinking sphere over time
tht = linspace(-pi, pi, 40);
phi = linspace(-pi/2, pi/2, 40);
t = linspace(0, 1, 100);
[tht phi t] = meshgrid(tht, phi, t);
r = 1 - t.^2/2;
x = r.*cos(phi).*cos(tht);
y = r.*cos(phi).*sin(tht);
z = r.*sin(phi);
%Determine temperate distribution
c = abs(asin(x-t) + acos(y+t) + asin(y+t).*acos(x-t));
% Generate animation
f = figure('DoubleBuffer', 'on');
while ishandle(f)
      for n = 1:size(x, 3)
          if ~ishandle(f), break,end
          h = surf(x(:,:,n),y(:,:,n),z(:,:,n),c(:,:,n));
          axis([-1 1 -1 1 -1 1])
          title(sprintf('t = %0.3f', t(1,1,n)))
          drawnow
      end
end
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