Mathematical morphology encompasses methods for characterizing land-cover patterns in ecological research and biodiversity assessments. This paper reports a neutral model analysis of patterns in the absence of a structuring ecological process, to help set standards for comparing and interpreting patterns identified by mathematical morphology on real land-cover maps. We considered six structural classes (core, perforated, edge, connector, branch, and patch) on randomly generated binary (forest, non-forest) maps in which the percent occupancy (P) of forest varied from 1% to 99%. The maps were dominated by the patch class for low P, by the branch and connector classes for intermediate P, and by the edge, perforated, and core classes for high P. Two types of pattern phase changes were signaled by abrupt transitions among the six structural classes, at critical P thresholds that were indicated by increased variance among maps for the same P. A phase change from maps dominated by the patch class to maps dominated by the branch and connector classes was related to the existence of a percolating cluster of forest, and the P threshold varied depending on the co-existence of the core class. A second phase change from the edge class to the perforated class was related to the existence of a percolating cluster of non-core (including non-forest) and represents a change of context from exterior to interior. Our results appear to be the first demonstration of multiple phase changes controlling different aspects of landscape pattern on random neutral maps. Potential applications of the results are illustrated by an analysis of ten real forest maps.