Many organisms can regenerate their bodies, but it is currently unclear how they accomplish this feat. In this paper, we introduce a cell-to-cell communication mechanism that allows a 3D arrangement of cells to discover its structure and maintain it in the light of random cell death, even at very high death rates. We report results from simulations of an agent-based model that demonstrate the effectiveness of the proposed approach for Planarian worm-like shapes, but the proposed model is general and applies to any shape.