We study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling with.

Multicellular organisms develop on a predictable schedule that depends on both cell‐intrinsic timers and sequential cell‐cell interactions mediated by extracellular signals. The interplay between intracellular timers and extracellular signals is well illustrated by the development of oligodendrocytes, the cells that make the myelin in the vertebrate central nervous system. An intrinsic timing mechanism operates in each oligodendrocyte precursor cell to limit the length of time the cell divides before terminally differentiating. This mechanism consists of two components, a timing component, which (...) depends on the mitogen platelet‐derived growth factor (PDGF) and measures elapsed time, and an effector component, which depends on thyroid hormone and stops cell division and initiates differentiation at the appropriate time. The cell‐cycle inhibitor p27/Kip1 accumulates in the precursor cells as they proliferate and is part of both components of the timer. It seems likely that similar timing mechanisms operate in other cell lineages. BioEssays 22:64–71, 2000. ©2000 John Wiley & Sons, Inc. (shrink)