Turing patterns on polymerized membranes: coarse-grained lattice modelling with an internal degree of freedom for polymer direction.

We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in using a surface model for polymerized membranes. The variables used to describe the membranes correspond to two distinct degrees of freedom: an internal degree of freedom for the polymer directions in addition to the positional degree of freedom. This generalised surface model enables us to identify non-trivial interference between the TP system and the membranes.