Abstract
We present a new computational approach to modelling trajectories on embeddable 2D Riemannian surfaces. By decomposing trajectories into infinitesimal geodesic line segments and rotations, a path through curved space can be represented as a string of basic instructions playing out in curved space. In this way, we can catalog and quantify the fundamental changes a system experiences when expressed in different curvatures. Indeed, we find that curvature can modulate the behaviour of a wide range of trajectories, from discrete and deterministic to continuous and stochastic. Results in constant positive curvature 2-spaces are given for fractals, random walks and diffusion, and we discuss potential applications to biological systems and 4D printing.
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Acknowledgments
J.P. kindly acknowledges the financial support of INRIA for this research.
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Pulwicki, J., Godin, C. (2017). Modelling Curvature Effects Using L-Systems: From Discrete and Deterministic to Continuous and Stochastic. In: MartÃn-Vide, C., Neruda, R., Vega-RodrÃguez, M. (eds) Theory and Practice of Natural Computing. TPNC 2017. Lecture Notes in Computer Science(), vol 10687. Springer, Cham. https://doi.org/10.1007/978-3-319-71069-3_4
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DOI: https://doi.org/10.1007/978-3-319-71069-3_4
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