A constructive theory of shape

Vladimir García-Morales

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

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

Keywords: Viable evolutions; Parametric equations; Space-filling curves; Knots; Time series (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007803

DOI: 10.1016/j.chaos.2021.111426

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