What fractal patterns reveal about planetary surfaces and possible non-terrestrial artificial structures

In a recent article, I explored how machine learning is and can be used to identify anomalous patterns in planetary datasets. This has applications in planetary exploration and planetary SETI. One of the challenges of characterizing planetary surfaces based on remote sensing data is that each planet is unique. A feature on one planet that is formed by running water might actually be formed by lava or sublimating ice on another planet. There is also a parallel challenge with identifying possible artificial structures on planetary surfaces since it is possible that non-terrestrial technology will take a form that may not be immediately recognized and become mistaken as an natural feature. If we can’t necessarily trust our intuition when it comes to planetary surfaces, one possible solution is to examine fractal patterns on planetary surfaces since different planetary processes will result in fractal geometries which are distinctive to specific processes. This could also be true of technology and is thus also relevant for SETI research.

Planets, like people, are individuals. Each planet is unique, a self-contained system which is shaped by its distinctive mass, atmosphere, composition, and orbital position around its star. For example, on Mars there are gullies that were likely formed by the sliding blocks of subsurface carbon dioxide ice as the ice began to sublimate. These gullies look very similar to channels created by rain water on Earth. This demonstrates how very similar features on two planetary surfaces can be formed by very different underlying processes.

These Martian gullies look like they were formed by water but were actually formed by sliding blocks of carbon dioxide ice. Image credit: NASA-Malin Space Science Systems

For this reason, we cannot assume that a planetary feature, such as a narrow groove that looks like a river, was formed by the same process across planetary bodies. This is the reason why planetary mapping is primarily descriptive rather than diagnostic. In planetary geologic mapping, we talk about “tholi,” “chaos terrain” and “lineae.” instead of just calling them “mountains,” “badlands,” “channels“ since such names are descriptive and imply an underlying process.

Badlands, for example are formed by wind and water erosion, but it is possible that that chaos terrain observed on Mars or Europa was actually formed by a completely different process. This is definitely the case for Europa which lacks an atmosphere to support running liquid water or wind at the surface. For this reason, most planetary geologists withhold diagnostic descriptions until we can get a rover, lander, or even human boots on the ground to confirm what a feature actually is based on close up examination, rather than simply based on orbital imagery data, the most common source of data we have on interpreting geologic features on planetary surfaces.

Notice the similarities in Conamara Chaos terrain on Europa (left), Ister Chaos terrain on Mars (middle), and the Chinle Badlands in Utah, United States (right). Images credit NASA and Wikipedia. They look similar but that doesn't mean the same process formed them.

This is also relevant to the identification of possible artificial structures. Just as we don’t necessarily know the underlying formation mechanism of a feature on a planetary surface without closer examination, we also can’t say for certain what an artificial structure is used for and may not even be able to immediately recognize it as artificial. Just like human cultures do not all build the same structures, a non-terrestrial intelligence may build very different structures from those that we would expect from humans. Consider, for example, beehives and termite mounds, neither of which bear strong resemblance to human-made structures.

If we can’t trust our intuition about what is artificial and what is not when it comes to non-terrestrial artificial structures, how can we detect them? This is where fractals may be useful. Fractals and fractal geometry are the result of the tendency of certain processes to create structures that are scale invariant and self-similar. This means that they look the same regardless of scale so that each component of the structure resembles a small scale image of the whole. Natural coastlines are a common example of this phenomenon as pointed out in 1967 paper by the mathematician Benoit Mandelbrot, How Long is the Coast of Britain? Fractal patterns have already been suggested as a way to investigate planetary processes, since landscapes will vary in how fractal they are based on the process that formed them, for example, glacial erosion versus a tectonic structure created by fault activity.

This principle has actually been proposed as a way to detect artificial versus natural structures for national security reasons since human-made structures tend to be Euclidean, rather than fractal. This means they have a definite shape of lines and polygons that is not scale invariant. Suppose you have a town next to a coastline. If you zoom out from a 1 km scale to a 100 km scale, the general pattern of the coastline will not have changed but the town will appear much smaller with fewer visible details or have disappeared entirely. The pattern of a building or city will not necessarily re-appear on a larger scale. This approach has also been explored in archaeology as a way to infer patterns of human settlement. We know nothing about the architectural and spatial design preferences of non-terrestrial intelligences. Nonetheless, it is possible structures created using technology may all have a fractal signature that can be detected by machine learning even if such a signature is not visibly obvious to a human observer.

This is reflected in the fact that certain architectural forms were independently developed in different cultures across human history. Egyptians and Mayans both independently developed pyramids as a principle part of their architecture. There appears to be something about pyramids that just makes them intuitive for building, possibly because a pyramid is the most mechanically stable form you can make if you want to create something large and you do not have advanced materials that would make it easy to construct, say, a skyscraper. Certain structures built by civilizations may have similar characteristics which can be detected even if it is not a characteristic as obvious as a stone pyramid.

Investigating fractality is a way to investigate what processes shaped planetary surfaces. Fractality could be used to identify whether a landscape is likely to have been formed by known processes, such as glacial erosion or faulting, or anomalous processes. An anomalous process could be a previously unknown natural process, as in the case of Martian “spider” features, or it could be a cognitive process, that is, evidence of technology. The way fractals are already being used in both planetary science and anthropological research makes it a promising route for improving our ability to detect anomalous surface features and understand planetary surface processes.

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