I ran calculations for a model with a single "neutral" DNA base, that can be A or B; so two possibilities instead of the usual four. Neutral means that individuals with base A have an equal chance of survival and reproduction as individuals with base B.
In this model, the population size N is fixed. Each step consists of picking one random individual and copying it, with μ probability of a mutation happening for the copy. At the same time, another random individual dies to keep the population size fixed. N steps count as 1 generation.
The first two graphs show equilibrium distribution for the DNA for different population sizes N, for a "mutation rate" of μ = 10-7.