I am trying to run a markov process. I came across this webpage https://martin-thoma.com/python-markov-chain-packages/, which details a simple case of markov process in R and python. While all the details are clear to me including 1) genotype of the children from given diploid parental cross 2) presentation of this parent-child genotype as matrix 3) preparation of this relation as a matrix.
But, **I am not following on what is being plotted on the graph**. **I am mainly confused by this statement that the author makes,"For example, we want to know the probabilities for the current state for the next 20 steps when you started in S3."** Are the parents producing two children and these children are producing another two children for 20 steps??

I know this might be a very comprehensive explanation, but can someone explain in more detail. And how the plot is related to this statement?

Thanks,