The EN model with periodic boundary conditions, solved with deterministic annealing. (a) OPMs (left) and RMs (right) for N = 103 (upper row), N = 104 (middle row) and N = 105 (lower row) random stimuli and periodic boundary conditions (annealing rate χ = 0.999, see 'Methods' section). β is the continuity parameter in the conventional definition of the EN model (see 'Methods' section, Equation 46) and is scaled, such that a comparable number of columns is emerging in the simulations for each size of the stimulus set. (b) Pinwheel densities of EN solutions for different numbers of stimuli, χ = 0.999. (c) Pinwheel densities of EN solutions for 105 stimuli and different annealing rates. (d) Energies of solutions for 105 stimuli, relative to the energy of a pinwheel-free stripe solution (see 'Methods' section) for different annealing rates. (b-d) Crosses mark individual simulations, red line indicates average values. (e, f) Statistics of nearest neighbor pinwheel distances for pinwheels of (e) arbitrary and (f) opposite and equal charge for 105 random stimuli and periodic boundary conditions, averaged over four simulations (red curves). Black curves represent fits to the experimental data from . (g) Standard deviations (SD) of pinwheel densities estimated from randomly selected regions in the OPM. Black dashed curve indicates SD for a two-dimensional Poisson process of equal density.