Transitioning to the random context, a random polyomino chain (RP C n = RP C(n, p)) can be generated as follows: Figures 2 illustrate RP C n for n = 1 and n = 2. When n ≥ 3, a new square can be added in two ways, leading to RP C 1 n and RP C 2 n with probabilities p and 1 -p, respectively (see Figure ), where 0 < p < 1. Hence, a topological index of a random polyomino chain at time n becomes a random variable.