The Angel's staircase: Cell cycle, and the embryogenesis of vertebrates

I present a simple model of vertebrate embryogenesis, coupling cell division, differentiation, and morphogenesis. The model relies on a gradient of cell cycle period, in a flat shell of tissue. When the cell cycle period varies linearly between two points, a cascade of cell division occurs in the tissue, which generates a staircase of cell sizes (the Angel's staircase). The variation in cell size is associated to a stepwise variation of mechanical properties, which induces a deterministic pattern of folds. The folded shell is recognized as an animal.