We study the self-organization of binary cell mixtures in finite cubic lattices. Depending on the relative attractions between cell types, the binary mixture model generates four distinct cellular associations: complete sorting, shell-core sorting, partial mixing, and complete mixing of heterotypic cells. At the boundaries between these four phases, the cellular associations show large variations, representing phase transitions. We find that the partial mixing phase is highly tolerant to thermal fluctuations. Interestingly, human pancreatic islets, the micro-organs for glucose homeostasis, adapt the partial mixing phase consisting of alpha and beta cells.