Is the Universe a Fractal?

For decades cosmologists have wondered if the large-scale structure of the universe is a fractal: if it looks the same no matter the scale. And the answer is: no, not really. But in some ways, yes. Look, it’s complicated.

Our universe is unimaginably vast and contains somewhere around two trillion galaxies. These galaxies aren’t scattered around randomly, but are assembled into a series of ever-larger structures. There are the groups, containing at most a dozen galaxies are so. Then there are the clusters, which are home to a thousand galaxies and more. Above them are the superclusters, which twist and wind for millions of light-years.

Is this the end of the story?

In the mid 20^th century Benoit Mandelbrot brought the concept of fractals into the mainstream. Mandelbrot didn’t invent the concept of fractals – mathematicians had been studying self-similar patterns for ages – but he did coin the word and usher in our modern study of the concept. The basic idea of a fractal is that you can use a single mathematical formula to define a structure at all scales. In other words, you can zoom in and out of a fractal and it still maintains the same shape.

Fractals appear everywhere in nature, from the branches of a tree to the edges of a snowflake. And Mandelbrot himself wondered if the universe is a fractal. If as we zoom out we will see the same kinds of structures appearing again and again.

And in a way, that’s what we see: a hierarchy of structures at ever-larger scales in the universe. But that hierarchy does come to an end. At a certain scale, roughly 300 million lightyears across, the cosmos becomes homogenous, meaning that there are no larger structures and the universe is (at that scale) roughly the same from place to place.

The universe is definitely not a fractal, but parts of the cosmic web still have interesting fractal-like properties. For example, clumps of dark matter called “halos”, which host galaxies and their clusters, form nested structures and sub-structures, with halos holding sub-haloes, and sub-sub-halos inside those.

Conversely, the voids of our universe aren’t entirely empty. They do contain a few, faint dwarf galaxies…and those few galaxies are arranged in a subtle, faint version of the cosmic web. In computer simulations, the sub-voids within that structure contain their own effervescent cosmic webs too.

So while the universe as a whole isn’t a fractal, and Mandelbrot’s idea didn’t hold up, we can still find fractals almost everywhere we look.