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thrash · 11-26-2020, 12:37 PM

Scientists Uncover the Universal Geometry of Geology

This article describes a recent paper in PNAS (Domokos et al., Plato’s cube and the natural geometry of fragmentation) that makes some predictions about fragmentation using pure math and then confirms them in real world. (Spoiler: it's cubes pretty much all the way down.)

The interesting part for world-building comes about two-thirds of the way down, where the article talks about exceptions to the cubic result. It appears that tectonic plates (on Earth, anyway) follow other types of expansion fractures in forming Voronoi polygons rather than squares or rectangles.

This suggests a relatively simple algorithm for creating random planetary surfaces on Earth-like worlds, where there are oceans and tectonic activity:

Select a number of random points on the surface. Each point is the center of a tectonic plate.
Use a Voronoi algorithm to map the plate boundaries (more challenging on a sphere, but doable).
Assuming that you've already chosen your land-sea surface ratio, assign plates to either oceanic or continental crust to make up the correct proportions.
Give each plate a random velocity vector, based on how active your geology is.
Examine each plate boundary and classify it as spreading, slipping, subducting, or colliding, based on the relative motion of the plates.
Use this information to inform your map-making.

Variations on this process have been suggested before. The innovation here, as I see it, is that the first two steps arrive at a pattern of tectonic plates that is realistic ("real-like") without requiring artistic talent. One feature of Voronoi polygons is that it's easy to add plates by adding points, without disrupting the rest of the map. Having the array of center points up front also makes the fourth step much easier than starting with a pattern and having to derive the centers.

If someone with programming kung fu takes a stab at this, please post a link to your results here. Likewise, if there is a world-building software package that does this already, please let us know.

Finally, I'm not sure whether to be impressed or disappointed that the author made it through the entire article without mentioning Minecraft.

11-26-2020, 12:37 PM	#1
thrash Join Date: Aug 2004 Location: traveller	Simulating plate tectonics using Voronoi polygons Scientists Uncover the Universal Geometry of Geology This article describes a recent paper in PNAS (Domokos et al., Plato’s cube and the natural geometry of fragmentation) that makes some predictions about fragmentation using pure math and then confirms them in real world. (Spoiler: it's cubes pretty much all the way down.) The interesting part for world-building comes about two-thirds of the way down, where the article talks about exceptions to the cubic result. It appears that tectonic plates (on Earth, anyway) follow other types of expansion fractures in forming Voronoi polygons rather than squares or rectangles. This suggests a relatively simple algorithm for creating random planetary surfaces on Earth-like worlds, where there are oceans and tectonic activity: Select a number of random points on the surface. Each point is the center of a tectonic plate. Use a Voronoi algorithm to map the plate boundaries (more challenging on a sphere, but doable). Assuming that you've already chosen your land-sea surface ratio, assign plates to either oceanic or continental crust to make up the correct proportions. Give each plate a random velocity vector, based on how active your geology is. Examine each plate boundary and classify it as spreading, slipping, subducting, or colliding, based on the relative motion of the plates. Use this information to inform your map-making. Variations on this process have been suggested before. The innovation here, as I see it, is that the first two steps arrive at a pattern of tectonic plates that is realistic ("real-like") without requiring artistic talent. One feature of Voronoi polygons is that it's easy to add plates by adding points, without disrupting the rest of the map. Having the array of center points up front also makes the fourth step much easier than starting with a pattern and having to derive the centers. If someone with programming kung fu takes a stab at this, please post a link to your results here. Likewise, if there is a world-building software package that does this already, please let us know. Finally, I'm not sure whether to be impressed or disappointed that the author made it through the entire article without mentioning Minecraft.