Plato’s cube and the natural geometry of fragmentation
| Autor: | János Török, Ferenc Kun, Gábor Domokos, Douglas J. Jerolmack |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
FOS: Physical sciences
Pattern formation Binary number Geometry 02 engineering and technology Condensed Matter - Soft Condensed Matter 01 natural sciences Physics::Geophysics Physics - Geophysics 0103 physical sciences Attractor 010306 general physics Multidisciplinary Cuboid Regular polygon Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks 021001 nanoscience & nanotechnology Breakup Geophysics (physics.geo-ph) Physical Sciences Soft Condensed Matter (cond-mat.soft) Cube 0210 nano-technology Voronoi diagram Geology |
| Zdroj: | Proc Natl Acad Sci U S A |
| ISSN: | 1091-6490 0027-8424 |
| DOI: | 10.1073/pnas.2001037117 |
| Popis: | Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra -- shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural 2D fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons. In 3D the Platonic attractor is dominant: remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato's forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation. main: 6 pages, 6 figures, supplementary: 18 pages, 12 figures |
| Databáze: | OpenAIRE |
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