title: Angular homeostasis: III. The formalism of discrete orbits in ontogeny.
abstract: The formal properties of orbits in a plane are explored by elementary topology. The notions developed from first principles include: convex and polygonal orbits; convexity; orientation, winding number and interior; convex and star-shaped regions. It is shown that an orbit that is convex with respect to each of its interior points bounds a convex region. Also, an orbit that is convex with respect to a fixed point bounds a star-shaped region. Biological considerations that directed interest to these patterns are indicated, and the implications of the prospect of higher orders of star-shapedness mentioned.
authors.forename: K R
authors.initials: KR
authors.lastname: Berger
authors.forename: E A
authors.initials: EA
authors.lastname: Murphy
mesh_terms: D002450:Cell Communication / Q000502:physiology; D004622:Embryo, Mammalian / Q000502:physiology; D004627:Embryonic Induction / Q000502:physiology; D005314:Embryonic and Fetal Development / Q000502:physiology*; D006706:Homeostasis / Q000502:physiology*; D006801:Humans; D016014:Linear Models; D008954:Models, Biological; D009024:Morphogenesis / Q000502:physiology*; D010363:Pattern Recognition, Automated