Talk to mathematicians and they’ll do their best to explain how beautiful their chosen field can be, but it probably won’t make any difference: if you’re not quite so expert, you won’t have the faintest idea what they’re talking about.

3D Fractals have the power to change all that. Some will appreciate the way they shift the geometrical properties of the complex plane and shift them into 3D space. But the rest of us can enjoy spectacular fractal art which is a mix of H R Giger’s sketchpad, old sci-fi novel cover art, and the weirdest dreams Terry Gilliam has ever had.

Mandelbulb 3D is a free portable application for Windows and Mac which can help you discover and generate fractal scenes of your own. It’s not a polished commercial product (the download link is on a forum thread, the interface is a cluttered mess), but can still produce some amazing results: landscapes, deep space scenes, strangely organic shapes, more (the Mandelbulb website has lots of examples).

3D fractals can look like places, landscapes, objects, lifeforms – there’s plenty to explore

If you’re not the mathematical type then the program can seem intimidating, at least initially. The interface is crammed with panels, buttons, values and options, and it’s not at all obvious how to begin.

Fortunately it’s easier than it looks, at least for basic operations. The program opens with a basic 2D formula, and producing your first fractal object is as simple as clicking “Calculate 3D”.

Click “Formulas”, hover your mouse over one of the formula types (3D, 3Da, 4D etc) and select a new formula. You don’t have to understand anything about it, just click “Calculate 3D” again to produce a very different image. Tweak the formula figures to change how it looks, maybe adjust the image size to suit your needs, and save anything you like as an image, ready to share with others.

Better still, the MandelBulb site has plenty of example images you can use. Click something you like on this page, and you’ll see both the source image and the settings that generated it. Select and copy the settings to the clipboard, click Open > Text > Calculate 3D in Mandelbulb 3D and it’ll generate a local copy of the image, ready for you to customise and explore further.

Mandelbulb 3D’s interface really needs work, but it’s still not too difficult to use and you’ll be creating fractal masterpieces within minutes. Go take a look.