Planetary computation is the concept that a planetary intelligence is emerging out of the complex systems enveloping our planet, including the geosphere (rocks and tectonic plates), the biosphere (living systems), and the technosphere (integrated technological systems such as the internet, satellites, and cities). Very interesting work is being done which could allow for crude maps of the computation level across a planetary surface on an exoplanet using Doppler radar and specular reflection from light curves to identify urban centers at specific latitudes. Since I study solar system bodies not exoplanets, I decided to come up with a way to map planetary computation using an orbiting spacecraft. The idea I came up with is using texture and geometry to identify technosignatures at the landscape level.
It has long been known that natural terrain and artificial structures differ in their fractal index. Buildings tend to be more euclidean whereas natural features tend to have a fractal curve to them. This potentially gives artificial structures a fractal signature which could be used as a proxy for the level of computation on a planetary surface since urban centers are associated with higher levels of computation. To test this, I created an anomaly detection model to identify features of unexpected fractal index, for natural terrain, and tested it on two Earth cities. The results of this preliminary study suggest that high fractal index and high spectral periodicity (how often certain shapes re-occur) may be useful indications of artificiality indicating agricultural or urban terrain as opposed to forest terrain that tends to have low fractal index and low spectral periodicity. Orientation entropy is taken to be an ambiguous signal since it varies considerably across agricultural and urban terrain. This study suggests that the computational complexity of a planetary system could be read off its surface like circuits can be read off a microchip.
Introduction
Nature is fractal. What this means is that nature contains many repeating patterns that appear the same regardless of scale. This is illustrated by a natural coastline. Whether you view a coastline at 100 m/pixel resolution or 10 km/pixel resolution, the natural coastline will look the same in having the same types of gentle curves. Artificial structures often stand out in having sharp regular edges appearing more euclidean. Unlike the fractal nature of the coastlines, these patterns do not always repeat with increasing scale. This is not to say that cities are not fractal, but they have a fractal signature that differs noticeably from natural terrain.
This is important for the search for technosignatures, that is, indications of technology, in the solar system and beyond. It also means that a spacecraft orbiting an planet or exoplanet could in theory detect terrain that is artificial in origin by identifying terrain that is anomalous in its fractal index compared to the expected fractal index of natural terrain. Assuming that more advanced civilizations rework larger areas of their planet’s surface, the fractal index across a planetary surface could also be considered a proxy for how advanced a planetary civilization is and thus the level of planetary computation, that is, how much information is being processed by a planetary system at a given time.
It can be assumed that more advanced civilizations will mean higher levels of computation. For example Ancient Egyptians were just as smart as modern engineers in New York City, but the level of computation being done in modern New York with computers and AI is likely much greater than the computation being done by ancient Egyptians who only had papyrus, brains, and a smaller population.
Methodology
I constructed a variational autoencoder (VAE)-based anomaly detection model trained on natural terrain (forests, hills, etc.), so that it will flag terrain that does not have the geometry and texture of natural terrain as anomalous. For this study, I chose sample two satellite images. One image is of Grand Forks, North Dakota, a city in the North American Great Plains surrounded by farmland. Grand Forks is also the location of the University of North Dakota, where I did my PhD.
The other image is of Manaus, Brazil, a city surrounded by the Amazon rainforest and a large river, the Rio Negro. Grand Forks allows for comparison two types of engineered terrain (urban vs. agriculture). Manaus allows for comparison between engineered terrain and natural terrain (urban v.s. rainforest canopy). For each image, I ran the model to evaluate the fractal index of the urban and agricultural terrain compared to natural terrain (rain forest and rivers).
In addition to fractal index, which deals with texture and how it changes with increasing scale, I included orientation entropy, spectral periodicity, and reconstruction error as model weights.
Orientation entropy is the degree to which edges in an image follow specific directions. A random distribution of edge orientations would result in high entropy whereas a very regular distribution of edge orientations would result in low entropy.
Spectral periodicity involves how often specific patterns occur. Terrain where the same types of shapes occur repeatedly would have high spectral periodicity. Terrain where the shapes vary considerably over space would result in low spectral periodicity.
Finally, reconstruction error is the degree to which terrain differed from what is assumed to be the natural terrain in terms of fractal index, but also orientation entropy and spectral periodicity. These weights were used in calculating the overall anomaly score for terrain, determining how much the terrain differs from what is expected of natural terrain.
Results
For the Grand Forks image, the model revealed that the fractal index (D) was higher for the city (D = 2.55) than the surrounding farmland (D = 2.3-2.4). The surrounding farmland had a lower orientation entropy, suggesting that the country roads are at more predictable orientations (e.g., N-S and E-W) than the city streets. The spectral periodicity was higher for the agricultural land, suggesting that the rectangular plots are more regular than the irregularly shaped buildings and urban lots. Curiously, the anomaly score is higher for the farmland, suggesting that agriculture could also be a strong geometric indicator of artificiality and not just urban centers.
For the Manaus example, the feature with the highest fractal index was the the urban center and the Rio Negro river, suggesting that high fractal index can also indicate specific natural features. The city also showed a high orientation entropy with the lowest orientation entropy being shown by the Rio Negro. In contrast to agricultural land, the natural forest showed low spectral periodicity and low fractal indext, suggesting spectral periodicity and fractal index is may be a reasonable indicator of artificially worked terrain.
Overall, the artificial terrain, the urban centers and the agricultural terrain were characterized by a high fractal index and high spectral periodicity. Orientation entropy is an ambiguous signal since it was high in the urban centers but low in the agricultural centers. These preliminary results provide a guide for principles that could be used to identify artificial terrain on other planets based on texture and geometric patterns.
Current exoplanets are too far away for this kind of analysis and it is unlikely that such analysis is going to reveal evidence of a lost civilization on Mars or the Moon. Nonetheless, analysis of how geometric and texture patterns on planetary surfaces differ between natural and artificial terrain may one day enable probes to identify landscape-scale planetary technosignatures on Earth-like planets.
This is a preliminary study and a follow up study would confirm that the characteristics associated with artificiality would be common across terrain types (for example, would the same principle apply to desert terrain relevant to Mars?). Nonetheless, this preliminary study does suggest the usefulness of this approach. Planetary computation may be written into a landscape the way computation is etched into microchips. We just have to know how to recognize it.
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