The image above was created using a program called Mandelbulb3D, which is a fractal generating and imaging software. If you don't know what fractals are, here's a good explanation, but basically a fractal is an infinitely complex pattern that is self-similar across all scales.
It's not just pretty, the math behind this picture has many useful applications in fields ranging from computer science, engineering, medicine, understanding the shape and formation of coastlines, clouds, lightning, trees, vegetables, bacteria, and even galaxies.
I could keep naming things, but essentially it explains a lot about the natural world around us, which I find extremely cool.
Since I'm not an engineer or scientist, I just like to use fractals as a way to find cool shapes. The pictures below were also made using Mandelbulb3D, but there are other programs out there that do similar fractal renderings on PC and iOS/Android. One I like to use on my phone is Fraksl.
One of the first I made. I found this mountain-like structure with this thin arch, and a hole right through it. This one was really fun to play with...
As soon as I saw the horns on that cave I knew it had to look evil.
The formula for this one created so many crazy wavy forms.
There's an awesome feature in Mandelbulb3D where you can create random mutations of your formula to get new shapes. I used it to get these towers - really love the floating bits at the top!
This one looked like a jellyfish no matter what colors I put, so it had to be placed underwater.