Visually, (F_p)^m can be embedded in R^m trivially, but I suspect you are interested in animations of operations on F^p, which indeed would look different from

Visually, (F_p)^m can be embedded in R^m trivially, but I suspect you are interested in animations of operations on F^p, which indeed would look different from R^m due to modular arithmetic, and so would be beyond the scope of the OP.