Scientists Uncover the Universal Geometry of Geology (2020)

Columnar basalt formation has been understood for a long time, I really don't understand what this explained that wasn't already known?

Sure, the pieces average 6 faces when materials are relatively homogenous and iostropic (i.e. no preferential direction to break in and no free surface nearby). However, as they note in the article, this isn't always the case. Things like mud flats and other cases with very anisotropic materials and/or free surfaces nearby don't fracture with the same average.

This is a good example of a potential metric that could be used to give some clues about overall material behavior even if all you have are the broken remains.

Fractal dimension is also pretty esoteric. However, it's somewhat widely used in geoscience, even though what we're measuring isn't _actually_ fractal. It's still a very useful comparative metric, though, because it lets us measure how complex an interface or surface is quantitatively and scale-independent.

Gábor Domokos, Douglas J. Jerolmack. Plato’s cube and the natural geometry of fragmentation. PNAS (2020)

https://www.pnas.org/doi/10.1073/pnas.2001037117

Abstract:

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.

Some researchers are just incredible achievers.

I am often surprised to discover different systems that arrive at the same shapes.

You will find it in nature, but also within.

N/A

Organizational charts.

Patterns of traffic.

Ways to Fail.

Despite different inputs and histories they all yield the same outcome.

I use a mental model of sorts.

Local regulations and limits.

Consistent application of weight.

In the end, only a handful of stable shapes endure.

I'm curious now.

Are we overestimating the uniqueness of our systems?

What design patterns to use in your product?

Have you taken note of shapes showing up in different domains time and again? ~