Breaking rocks made easy. Blending stress control concepts to advance geomorphology

Voigtländer, Anne; Krautblatter, Michael

doi:10.1002/esp.4506

Cited by 4 publications

(2 citation statements)

References 79 publications

(103 reference statements)

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“…Whether in rock, ice, or soil, the fracture mosaics cut into stressed landscapes (Fig. 3) form pathways for focused fluid flow, dissolution, and erosion that further disintegrate these materials (33,34) and reorganize landscape patterns (35,36). Moreover, fracture patterns in rock determine the initial grain size of sediment supplied to rivers (36,37).…”

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confidence: 99%

Plato’s cube and the natural geometry of fragmentation

Domokos

Jerolmack

Kun

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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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 two-dimensional (2D) fragments, from mud cracks to Earth’s tectonic plates, has two attractors: “Platonic” quadrangles and “Voronoi” hexagons. In three dimensions (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.

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mentioning

confidence: 99%

Plato’s cube and the natural geometry of fragmentation

Domokos

Jerolmack

Kun

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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“…Whether in rock, ice or soil, the fracture mosaics cut into stressed landscapes (Fig. 3), form pathways for focused fluid flow, dissolution and erosion that further disintegrate these materials 33 .…”

Section: Introductionmentioning

confidence: 99%

Plato's cube and the natural geometry of fragmentation

Domokos,

Jerolmack,

Kun

et al. 2019

Preprint

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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.

show abstract