\label{fig:configs} Typical configurations of \(1024\)-step walks with specified numbers \(m_t\) of contacts, that have been generated in a simulation at \(\omega=0.5\). The values of \(m_t\) have been chosen such as to cover the whole range of the histogram in Figure \ref{fig:double_peaks}. The configurations illustrate the co-existence of fully dense and swollen parts of the polymer, demonstrating the first-order nature of the transition.