How can I simulate 2D correlated data with continuous-valued variables?

[Goldberry]

Not sure this is the right area to post this.

Let's say I have particles on a lattice, and they all have some property (ie, color) that is correlated at some known correlation length. I want to simulate this! In 1D I could do something like have color be a random walk in the given dimension, but that doesn't work for more dimensions. I'd rather have a continuous-valued variable than not, so spins aren't ideal.

Help?

 

[Stephen Tashi]

they all have some property (ie, color) that is correlated at some known correlation length.

Someone familiar with the physics might known the definition of "correlated at some known correlation length", but if you want advice from the general population of math people, you should define what that means.

As a generality, simulation of correlated random variables can be done by first simulating a set of independent random variables $X_1, X_2,...X_n$ and then defining the correlated random variables as linear combinations of the $X_i$. I don't know whether doing an analogous thing with stochastic processes would satisfy your requirements.