# Simulated 2D correlated data

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## Main Question or Discussion Point

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?

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.