I recently did a poll asking if people knew what a fractal is and the results surprised me!

Of course, not all polls are completely accurate, but over half of the participants didn’t know what a fractal is. So, if you don’t know what a fractal is, don’t feel bad!

Disclaimer: I’m not a mathematician, but I’ve been fascinated and exploring fractals for about 20 years.

Why should you care about fractals?

The subject is very complex, but I’ll try to explain it as short and simple as possible.

The foundation of fractals began to take shape as early as the 17th century. They became more popular in the 1970s when technology became better and mathematician Benoit Mandelbrot coined the term “fractal”. Probably one of the most popular fractals is the Mandlebrot set which was named after him.

Mandlebrot fractal set
Mandlebrot fractal set – (Wikimedia Commons)

Mandelbrot himself summarized it as, “beautiful, damn hard, increasingly useful. That’s fractals.”


So, it just looks like trippy psychedelic art, right?

Probably the most common perception of fractals these days is associated with psychedelia and recreational drugs. But, fractal formulas are complex mathematical equations currently used in research and technology!

Big deal. They’re cool looking math equations. Well, here’s where it gets more interesting…

When you zoom in, fractals exhibit similar self-replicating patterns depending on the formula. This complex geometry literally goes on forever.

This example video is pretty long, but it gives you an idea of what a fractal zoom is.

Mandelbrot Fractal Zoom

Maybe you’re thinking you should have taken a hit of LSD before reading this article.

Here’s something that will help bring the subject back down to Earth: Fractals are found everywhere in nature.

Probably the easiest to describe is Romanesco Broccoli which is a Fibonacci family sequence variation. Notice how each of the buds is made up of even smaller buds below? Yea, fractals man!

Romanesco Broccoli – Fibonacci Fractal Formula (Wikimedia Commons)

Other fractal formulas ubiquitous in nature include trees, mushrooms, pineapples, sunflowers, and ice crystals just to name a few.

The above broccoli fractal example might look a little different than the previous examples.

Around 2010, Swedish members of a fractal forum discovered how to convert two-dimensional fractal formulas into three dimensions. Game changer!

The discovery spawned a whole new genre of art and research revolving around the Mandelbulb which is a Mandelbrot with another dimension added. So, think of the Mandelbrot as a flat plane. The Mandelbulb has x,y, and added z plane making it three dimensional just like a computer-generated 3d model.

Of course, I had to sneak in one of my own pieces of fractal art that I created in fractal learning software Mandelbulb 3D.

Mushhroom Fractal Art created in Mandelbulb 3D
Mushhroom Fractal Art created in Mandelbulb 3D

So, that’s a really compact explanation of what fractals are.

I hope that helped give you a basic understanding of what fractals are and how important they can potentially be. I feel like we’ve only just hit the tip of the iceberg in exploring them and they could have a lot of benefits in many different industries. They’ve already used the technology for much more complex things than what I’ve illustrated above. I encourage you to research and find out more on your own.

So, if you see me posting and talking about fractals on social media, be sure to say hi and hopefully you won’t think I’m a complete weirdo anymore. 😛

While you’re here, be sure to check out my fractal art giclee prints.

Thanks for stopping by and reading!