Does the distribution of galaxies in the universe follow a large-scale fractal pattern?

The existence of galaxies beyond our own was first discovered in 1924, and our catalog has since grown significantly. We now know there are trillions of galaxies throughout the universe, but they are not evenly dispersed.

Using data from nearly 800,000 galaxies from the Smithsonian Astronomical Observatory Telescope Data Center, Wiesław Macek and Dariusz Wójcik conducted a fractal analysis to determine if galaxy clusters point to a large-scale structure of matter distribution within the cosmos.

They found the distribution of the galaxies tested follows a multifractal structure called a weighted Cantor set model. In other words, as space gets divided into smaller and smaller self-similar areas, the probability of a galaxy being present in the area scales accordingly, modified by a weighting parameter that describes the universe’s large-scale voids.

Despite the fact that the physical processes that occur on cosmological scales are fundamentally different from local scales, the multifractal patterns that appear in the universe have similar characteristics. For example, a similar type of weighted Cantor scaling governs the distribution of matter in the heliosphere, the bubble of the Sun’s magnetic influence that protects its planets from interstellar wind.

“In our view, the universality of multifractal patterns in nature remains one of the most intriguing open problems in nonlinear dynamics and fractal theory,” said Macek.

The researchers plan to expand their methods to a larger catalog of galaxies to include those at the edge of our limits of observation, which are moving much more rapidly.

“On the hundredth anniversary of the discovery of the first galaxy beyond the Milky Way, we anticipate that our recent finding on nonlinear multifractal scaling laws of galaxies will represent a major step toward the ultimate explanation of matter distribution in the universe,” said Macek.

Source: “Multifractal spectrum observed in the Universe distribution of galaxies,” by W. M. Macek and D. Wójcik, Chaos (2026). The article can be accessed at https://doi.org/10.1063/5.0289242 .