Why are fractals important

A fractal is a never-ending pattern that repeats, in the same way that a coastline or a snowflake never stops repeating Fractals are very important in art and science

For example, fractals are used in weather forecasting, to help predict a day's weather patterns They are also used in computer graphics, and in the design of highways, bridges, and buildings

Fractals are all around us

There are fractals in art, music, and nature

Mathematics and art are not the only places where fractals appear In nature, there are many things with fractal patterns

the fractal patterns that are found in a pinecones When you look at pinecones from a distance, you only see a pattern of points But when you get closer, you can see that the pattern is made up of smaller patterns, which are made up of smaller patterns, and so on

If you look at a pinecone through a magnifying glass, you will see even smaller patterns

Fractals are also found in the leaves of plants, like the fern

If you look at a fern's leaf through a magnifying glass, you will see that it is made up of smaller fern leaves

Fractals are also found in the clouds in the sky

When you look at clouds from far away, they look smooth and soft

But if you look at a cloud with a magnifying glass, you will see that it is made up of very small droplets of water

Fractals are also found in the behavior of water

A river flows in a constant pattern, over the same path, over and over again It never changes the way that it flows

A river is a fractal It never changes

A river is a perfect example of a fractal that never changes

"WHAT IF OUR UNIVERSE IS A FRACTAL ?"

In the 1960s, a physicist named John Wheeler thought about another way that fractals can be important

Wheeler imagined that everything in our universe could be a fractal

The idea that, if you zoom in far enough, you’ll eventually encounter a structure that repeats the initial pattern you saw on larger scales, is mathematically realized in the concept of a fractal. When similar patterns repeatedly emerge at smaller and smaller scales, we can analyze them mathematically and see if they have the same statistical characteristics as the larger structures; if they do, it’s fractal-like in nature. So, is the Universe itself a fractal?

The answer appears to be almost, but not quite. Here’s the science behind why.

From a mathematical perspective, you can clearly see that if the same rules and conditions apply at all scales, then dependent on what those rules are, you might wind up with a self-similar structure to the Universe, where what appears on large scales also appears on small scales

https://www.forbes.com/sites/startswithabang/2021/01/06/is-the-universe-actually-a-fractal/?sh=1f72efa55415