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In the present communication we describe the Island-Mainland transition,occurring in a square lattice, when black squares are randomly dropped on awhite background. Initially clusters of black squares are observed on theconnected white background. But as concentration of black sites increases, atsome point the black squares join to form a single continuous black backgroundwith white clusters randomly scattered in it. We show that the minimum in theEuler number, defined as the difference between number of white clusters andnumber of black clusters, reaches a minimum at this point.  This occurs at a concentration higher than the well-known percolation phasetransition and we show that the phenomenon can be related to experimentalobservations in several physical systems.

Identifying 'Island-Mainland' phase transition using the Euler number