Is the Universe a Fractal?

We find examples of fractals everywhere in nature. Branches, snowflakes, river deltas, cloud formations and more. So it stands to reason to ask the ultimate question: is the entire universe one giant fractal? The answer is … no, but kind of yes.

Benoit Mandelbrot, who almost everyone agrees, introduced the modern concept of fractals into the world (and even coined the term), was the first to wonder whether our universe could be in the form of a fractal. At that time, astronomers had just begun compiling extensive catalogs of galaxies in space and were just beginning to piece together the large-scale structure of the universe.

Since fractals are everywhere, maybe there is fractal everywhere. If you zoom out and see a particular pattern of galaxies, maybe you can zoom out even further and repeat the same pattern. And so on and so on to infinity.

Unfortunately, extensive galaxy studies would show that our universe is not best described as a fractal. There is a limit known as the homogeneity scale, at which one spot in the universe is pretty much like every other spot on the same scale. This scale is about 100 megaparsecs. Zoom out further and you will just see a number of the same patches side by side with no larger pattern.

In addition, there is no simple fractal description of the pattern of galaxies on the way to the homogeneity scale. While Mandelbrot’s idea was really cool, it just didn’t stand up to observation.

But wait, there’s more.

On the largest scales, the galaxies in our universe are arranged in a giant web-like pattern known as (appropriately) the cosmic web. There are long thin filaments of galaxies, dense clusters, wide walls, and huge, empty regions called voids.

However, the cavities are not 100% empty. Careful observations and detailed simulations have shown that the cosmic cavities contain a faint, thin version of the cosmic web. These bubbling filaments are gloomy, dwarf galaxies. And in the void-in-the-void sits an even weaker version of the cosmic web. The repetition doesn’t go on forever: once you hit the scale of individual galaxies, everything collapses, and once you get larger than a single cosmic void, you reach the homogeneity scale.

But between these extremes, between about 5 and 100 megaparsecs, the large-scale structure of the universe exhibits some fractal-like properties. There is still no simple fractal description of the voids, but it is fascinating that while Mandelbrot’s idea did not apply to everything in the universe, it applied to the regions with the most … nothing.

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