We simulate the solution (flow line) of the ODEs z'(t) = e^(i (h(y(t)) + theta)) dt, z(0) = z_0 = 1/2+ 1/2 * i, where theta are angle parameters in [0, 2*pi], and h is a sample of Discrete Gaussian Free Field (DGFF) in [0,1] x [0,1]
sampling_DGFF_into_file.m: this file initializes/samples discrete Gaussian Free Field (DGFF) and put it in a file such that we can use this sample for many purposes instead of sampling again everytime.
DGFF_simulation.m: this file samples DGFF and plots it.
ode_randomwalk.m: solve the ODE with different thetas. Plot the flowlines. Colors depend on the size of theta.