Write an algorithm that simulates the random motion of $10$ molecules in $1$D$.$

Initially, all molecules are in position $0$ of the $1$D domain. At each iteration of the algorithm, each particle moves of one step of size $1,$ in either positive or negative direction, with equal probabilities.

Demonstrate that after $100$ iterations, the molecules have moved from the initial region of high concentration to regions of low concentration.

Is this system in steady state?