You could view this as a very complex custom gradient problem; or as an extreme blur problem; or as some kind of color diffusion problem; or in a variety of other ways.
My particular application is prosaic: I have some images that have very irregularly illuminated background. I want to select patches from various areas in the image that I know represent the background color/luminance, then interopolate the intervening areas with guesstimates of the color/luminance to create an approximation of the background.
I can imagine "artistic" uses as well, though. Say I want to simulate the effect of dropping many different colored ink droplets onto various locations in a pan of water and letting them diffuse so as to create a complicated gradient.
I've tried a couple of things: (1) using "Gaussian blur" with an extremely high radius--this works to some degree, but creates Moire patterns, and also the bigger and more intense patches of color tend to "push away" the smaller patches, so the geometry isn't well preserved;
![:-?](./images/smilies/icon_confused.gif)
![:cry:](./images/smilies/icon_cry.gif)