Abstract We investigate random minimal factorizations of the n -cycle, that is, permutation $(1 \, 2 \cdots n)$ into a product cycles $\tau_1, \ldots, \tau_k$ whose lengths $\ell(\tau_1), \ell(\tau_k)$ satisfy minimality condition $\sum_{i=1}^k(\ell(\tau_i)-1)=n-1$ . By associating to cycle factorization black polygon inscribed in unit disk, and reading one after another, we code by process col...