Summary: We study mappings obtained as \(s\)-periodic reductions of the lattice Korteweg-de Vries equation. For small \(s\in\mathbb{N}^2\), we establish upper bounds on the growth of the degree of the numerator of their iterates. These upper bounds appear to be exact. Moreover, we conjecture that for any \(s_1,s_2\) that are co-prime, the growth is \(\sim(2s_1 s_2)^{-1}n^2\), except when \(s_1+s_2=4\), where the growth is linear \(\sim n\). Also, we conjecture the degree of the \(n\)th iterate in projective space to be \(\sim(s_1+s_2)(2s_1s_2)^{-1}n^2\).