The probability for a move to the right during a time step $\Delta t$ is $n_l/N$. The algorithm for simulating this problem may then look like this

• Choose the number of particles $N$.

b* Make a loop over time, where the maximum time (or maximum number of steps) should be larger than the number of particles $N$.

• For every time step $\Delta t$ there is a probability $n_l/N$ for a move to the right. Compare this probability with a random number $x$.
• If $ x \le n_l/N$, decrease the number of particles in the left half by one, i.e., $n_l=n_l-1$. Else, move a particle from the right half to the left, i.e., $n_l=n_l+1$.
• Increase the time by one unit (the external loop).