The Universe, with its billions of galaxies, presents a complex structure that has intrigued scientists for decades. The question of whether this structure is fractal, meaning similar at all scales, remains relevant.
The Universe hosts approximately 2 trillion galaxies, organized into groups, clusters, and superclusters. These structures span millions of light-years, forming a complex cosmic web. However, this hierarchy of structures does not repeat indefinitely.
A model of the cosmic web, showing luminous galaxies clustering where gas filaments meet.
Image: ESA / Springel et al., Virgo Consortium
Benoit Mandelbrot popularized the concept of fractals in the mid-20th century. A fractal is a structure defined by a unique mathematical formula, maintaining its shape at all scales. Mandelbrot wondered if the Universe could be a fractal.
Fractals are ubiquitous in nature, from tree branches to the contours of a snowflake. Mandelbrot explored whether the Universe, when zoomed out, revealed repetitive structures. Indeed, we observe a hierarchy of structures at different scales.
However, this hierarchy has a limit. At a scale of about 300 million light-years, the Universe becomes homogeneous, with no larger structures. Thus, the Universe is not a fractal, although certain parts of the cosmic web exhibit fractal properties.
Dark matter halos, hosting galaxies and their clusters, form nested structures, with sub-halos and sub-sub-halos. Similarly, the voids of the Universe are not entirely empty, containing a few dwarf galaxies arranged in a subtle version of the cosmic web.
Thus, although the Universe as a whole is not a fractal, fractal properties are ubiquitous in its complex structures. Computer simulations reveal sub-voids containing their own cosmic webs, showing the richness and complexity of the Universe.
What is a fractal?
A fractal is a geometric figure or natural set with a complex and detailed structure at all scales. The concept was popularized by Benoit Mandelbrot, who showed how these shapes appear in nature, from coastlines to plant structures.
Fractals are defined by mathematical formulas that generate repetitive patterns. These patterns are self-similar, meaning they retain their appearance regardless of the scale at which they are observed.
In a cosmological context, fractals have been considered as a possible model for the structure of the Universe. However, observations show that the Universe becomes homogeneous on a large scale, which limits the applicability of the fractal model to the entire cosmos.
And what about dark matter?
Dark matter plays a crucial role in the formation and evolution of cosmic structures. Invisible and non-radiating, it exerts a gravitational attraction that shapes the distribution of galaxies and galaxy clusters.
Dark matter halos, vast clouds of this still mysterious substance, surround galaxies and their clusters. These halos contain substructures, such as sub-halos, which host smaller galaxies.
Computer simulations show that dark matter forms a complex cosmic web, with filaments and voids. This web influences the distribution of visible matter, such as stars and galaxies, and plays a key role in the large-scale structure of the Universe.