Recently a series of dips has been observed in the plot of E/M (the ratio of excimer to monomer fluorescence intensity) vs the mole fraction of 1-palmitoyl-2-(10-pyrenyl)decanoyl-sn-glycero-3-phosphocholine (Pyr-PC) in Pyr-PC/DMPC binary mixtures in the liquid crystalline phase at 30 degrees C (Tang and Chong Biophys. J. 1992, 63, 903-910). In order to reveal connections between the E/M dips and the lateral distribution of the components, the membrane is simulated by means of Monte Carlo methods. The simulations confirm the assumption that pyrene-labeled acyl chains tend to distribute regularly in the membrane at mole fractions where E/M dips are detected. The simulations also show that through the assumption of long-range repulsive interaction between the pyrene-labeled acyl chains (a) the area of regular arrangements have maxima at the critical concentrations if the repulsion is strong enough, (b) in the case of weak repulsion the area of regular arrangements is a monotone increasing function of the concentration of the labeled chains, (c) when an E/M dip is measured at critical concentration X(i), then a cluster of type i regular arrangement of labeled chains is always percolated throughout the membrane, (d) when an E/M kink is measured at X(i), a cluster of type i is rarely percolated, (e) between one critical concentration X(i) and the next one X(i+1), an (order of type i) --> (disorder) and then a (disorder) --> (order of type i+1) phase transition takes place.