  We study the propagation and diffusion of electric charge fluctuations in the
Bjorken hydrodynamic model with both white and Catteneo noise using purely
numerical methods. We show that a global lattice of noise fluctuations is
required to fully calculate the two-point correlators of charge. We solve the
stochastic differential equations that arise from the charge conservation
equation on the lattice. We explicitly identify the self-correlation term in
the case of Catteneo noise and provide a physical interpretation. We provide a
numerical recipe to remove this contribution from the full two-point
correlators. Finally, we calculate the balance functions for charged hadrons.
By limiting the speed of signal propagation, we observe the expected narrowing
of the balance functions after removing the self-correlations.
