When mud breaks apart on Earth, or ice shatters on Jupiter’s moon Europa, or the surface of an ancient lake on Mars fractures, do these cracks follow some underlying blueprint?
Could parallel patterns elsewhere suggest that water was once present and might have supported life?
For geophysicists, answering such questions would revolutionize our understanding of planetary surfaces and the habitability of celestial bodies throughout the universe.
A recent paper from Douglas Jerolmack at the University of Pennsylvania, and Gábor Domokos at Budapest University of Technology and Economics, tackles this subject from an intriguing angle.
They propose that a planetary body’s way of breaking up is not a mere coincidence, and this conclusion may help identify environments on other worlds that might have been habitable.
“What’s wild is that nature keeps favoring the same patterns across vastly different environments,” remarked Jerolmack, a professor of earth and environmental science.
“We expected some consistency, but the degree to which planetary surfaces organize themselves into predictable crack geometries – whether it’s ice, rock, or mud – was surprising. It suggests these patterns are fundamental, not just quirks of specific planets.”
The team’s conclusions expand on an earlier study in which they verified a statement by the Greek philosopher Plato, who suggested that Earth itself could be made of cubelike components.
Rather surprisingly, if you take the thousands of fragments that are produced and you measure the number, you count the number of faces and corners and edges, and you average the hell out of it, then you end up with six as an average for the faces, eight, as an average number for the vertices, and 12 for the number of edges,” Jerolmack explained.
The group’s new research concentrates on fracture networks in two dimensions.
Rather than investigating the three-dimensional shape of individual fragments, they focus on crack patterns observed on relatively thin outer layers of planetary bodies.
“We wanted to explain patterns on other planets that are here right now, because the problem is, we don’t get to see how they evolved,” Domokos said. “We weren’t there. And we can’t go back in time.”
Domokos noted that only a static snapshot of these fracture networks is available. The forces that caused them are not directly visible, and the cracks may still be developing in ways we cannot observe.
“But what if, from this one snapshot, you could extrapolate the whole plot of the movie?” Domokos asked.
To explore this possibility, Ph.D. student Sophie Silver from Jerolmack’s lab gathered satellite imagery of planetary surfaces around the solar system and compared them with laboratory data and Earth-based geologic features, searching for any pattern preferences.
“I looked at a bunch of satellite images of planetary surfaces, compared them to lab experiments and geological formations on Earth, and tried to figure out the distinct ‘fingerprints’ or the geometric signatures in their crack networks,” Silver said.
Their classification method focuses on how often three types of crack junctions appear: T’s, X’s, and Y’s.
“The T’s take on a sort of brick wall-like formation. They’re the most common, the most boring – we see them all over the place, on Earth and in space – and they’re associated with hierarchical fracture networks formed by repeated breakage,” she explained.
Structures dominated by X’s only occur in ice. “So far, excluding Earth, we’ve only spotted X’s on Europa, the smallest of Jupiter’s four largest moons,” she added.
This geometry reflects crack repair and overprinting, in which a fracture heals (generally by ice refreezing) before a new crack crosses the healed area, producing an X junction.
Meanwhile, Y junctions, reminiscent of honeycomb patterns, form when T junctions undergo cycles of expansion and contraction – such as mud drying and wetting or ice warming and cooling – that gradually shift T’s into Y’s.
Mathematician Krisztina Regős, a doctoral researcher at the Budapest University of Technology and Economics, worked with Domokos and mathematician Péter Bálint to refine the mathematical models behind these evolving crack mosaics.
Their approach connects the physical processes underlying fracturing with the resultant patterns in a way that aligns with ideas from dynamical systems theory.
“If we understand the rules governing how the cracks form and change, we can ‘rewind the tape’ and reconstruct the missing frames of the movie,” Domokos explained.
“If we had actual time-lapse footage of a planetary surface changing over millennia, we could just watch and learn. But since we don’t, we had to create a mathematical model that lets us extract time from space.”
Regős’s framework maps crack patterns onto a symbolic plane – an abstract mathematical domain where the evolution of fracture networks unfolds.
By identifying the average geometric features of each network, specifically the frequency of T, X, and Y junctions, and noting how these values cluster, researchers can hypothesize how the networks emerged in the absence of direct observation.
“We don’t have movies of planetary surfaces cracking and shifting over eons, but this model allows us to create something similar,” Domokos noted.
“By using a dynamical model that incorporates the rules of fracture and change, we can get pretty close to showing the evolution, by predicting how a crack network started and how it may end.”
To confirm their approach, the team matched the model’s projections with known geologic evidence from cracks on Earth, Mars, Venus, and Europa.
The model’s output was consistent with the documented processes that formed these fracture networks, prompting them to describe it as a “jolly good guess.”
“This project started with an absurdly simple geometric categorization of crack networks,” Jerolmack said. “The dynamical systems theory then distilled the different mechanisms for cracking into absurdly simple geometric rules.”
“We created a toy universe of fracture patterns and processes; shockingly, the actual universe seems happy to comply with this model. But we need to test this more.”
Right now, Silver is running experiments that replicate planetary cracking mechanisms under controlled conditions – specifically, simulating Martian mud cracks and the icy fractures of Europa.
Such experiments allow the team to observe in real time how a crack network evolves, giving them a powerful way to assess how accurately the dynamical crack model performs.
“I’m hopeful that presenting these results from the experiments and how well they corroborate the model will influence more people to implement this method on planetary surfaces, on Earth surfaces, and even in laboratory settings,” Silver said.
“I ideally want to see this methodology widely reproduced and used by multiple people in multiple different fields … potentially identifying good places to send a Rover; for example, it’d be cool if someone thought, ‘Oh, this place has lots of hexagons here – maybe that means that it’s been wetted and dried a bunch,’ and thought to launch a probe.”
Though the researchers don’t anticipate obtaining time-lapse footage from actual planetary landscapes in the coming decades, they plan to continue harnessing static images from space missions to build more robust methods for inferring past conditions and potential future evolutions on each planet.
“It was a great opportunity to work on this interplanetary project,” Regős said, “because even if you can’t make these movies yet, I think it will have an impact on how we approach space travel.”
The team looks forward to data from NASA’s Europa Clipper, which is due to arrive on Jupiter in 2030, and ESA’s Jupiter Icy Moons Explorer (Juice), which is already en route and should deliver high-resolution imagery of ice-covered worlds.
Those new data sets may further test their tools and offer additional chances to see whether their model accurately predicts the fractures’ origins and possible evidence of water.
“We’ve built this theoretical structure, but the real test will come when we get fresh, high-resolution images of these planetary surfaces,” said Jerolmack.
“With more detailed data from upcoming missions, we can refine our model, test its predictive power, and even identify places where we should look for evidence of past water activity.”
The study is published in the Proceedings of the National Academy of Sciences.
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