A constructive theory of shape

We formulate a theory of shape valid for objects arbitrary dimension whose contours are path connected. apply this to the design and modeling viable trajectories complex dynamical systems. Infinite families qualitatively similar shapes constructed giving as input finite ordered set characteristic points (landmarks) value continuous parameter κ∈(0,∞). prove that all belonging same family located within convex hull landmarks. The is constructive in sense it provides systematic means build mathematical model any taken from physical world. illustrate with variety examples: (chaotic) time series, plane curves, space filling knots strange attractors.