Here is a smooth random function on the unit disk,

rng(1), random = randnfundisk(0.1);

and here is a paraboloid on the same domain,

paraboloid = diskfun(@(theta,r) 2-4*r.^2,'polar');

If we plot the sum of the two in zebra mode, we get an interesting picture:

f = random + paraboloid;
plot(f,'zebra'), axis equal off Of course zebra mode isn't the only way to plot a function. Here is a contour plot:

contour(f), colorbar, colormap('default'), axis off And here is a surface plot:

surf(f), zlim([-10 10])
camlight, camlight
view(0,60), axis off The smooth random functions produced by randnfundisk are defined by finite Fourier series with random coefficients; see . As discussed in Section 7 of that paper, random surfaces have been studied since Longuet-Higgins in 1957 , and application areas include oceanography , biology , cosmology [2,6,9], condensed matter physics , and the melting of the Arctic . There is also interest among pure mathematicians  and other theoretical physicists . Chebfun's smooth random functions are examples of Gaussian random fields .

Our choice in this example to show random functions on a disk is arbitrary. Good times can also be had with randnfun, randnfun2, and randnfunsphere.

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