Today, I'm going to show you how to generate customized fractals (you know, those fancy ever-repeating mathematical patterns that pop up everywhere in Nature) and transform them into 3D models.

They can then be turned into coasters, key-rings, objects to integrate into other 3D models, phone case decorations, necklace beads...

there's lots of options !

And given the fact that most Fractal patterns can be varied near-infinitely by changing some of the starting values / parameters of their formula, there's infinite possibilities !

Here's an example of Mandelbrot and Rational Map fractal patterns transformed into 3D printable slabs... customization is up to you ;)

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I got the inspiration from this after stumbling upon N-E-R-V-O-U-S System, a design company that specializes in using generative design and custom software to create the most amazing things !

It looks so beautiful XO

While I was trying to find what open-source code they've hidden around their side (I plan on playing around with their simulations and parameters... see what I can come up with), I remembered once seeing an online fractal generator using Javascript to produce PNG images of fractals.

My brain immediately put the following workflow in place:

Fractal generator --> png to svg --> Vectary --> ?? --> Profit + Pleasure

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The tools

So, to make this work, we need:

1. A way to create fractals

Luckily, this was the tool I remembered once seeing, and after trying a few keyword combinations on Google I found it.

The Generator was made by one Christopher Williams, and although the app itself is copyrighted the libraries are free to use, so I'll have to put that on my "to play with" list :)

1. A way to convert the generated png images into svg images for import into a 3D modeller

This is an easy one, as I've used pngtosvg.com for that very purpose multiple times in the past already !

1. Vectary (or any other 3D modelling tool that supports SVG-to-3D conversion)

Generating a fractal

So, first things first.

Let's play with the fractal generator !

As you can see above, the main interface looks pretty clean, with some numbers on the side that we can't really affect.

There's a total of 10 different Fractal patterns listed as possible, each with their own unique appearance.

• The Quadratic Julia

The Julia Constant can be changed to generate differents sets

• The Multibrot set

Exponent=2 gives the normal Mandelbrot set we all know and love

• Polynomial Julia Set

Exponent=2 being the Quadratic Julia set from above

• Rational Map

like the one from the image at the beginning

• Newtonian Fractal

Looks like DNA, but that might just be the biologist in me speaking ;)

• Nova

Hmmm... Looks like it could be adapted into a freaky tiara XD

• Phoenix Fractal

Very symmetric... me likey !

• Burning Ship fractal

This one is pretty strange... adapting it to 3D might me a tad more difficult than the rest :/

• Burning Julia set

interesting shapes

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After choosing the different values (depending on the kind of fractal and what appearance you're looking for ) and saving the generated PNG image (), we can proceed to "cleaning" the image a bit before importing it into Vectary.

PNG to SVG conversion

On the pngtosvg site, we can upload our Fractal image and proceed to clean it up a bit.

Say we go with this one:

Importing it into the tool, we can adjust the number of colors, and degree of simplification, we want the tool to generate our SVG in:

Let's try with the default 5 colors:

A tad too complex.

If you've read some of my other tutorials using pngtosvg, you'll see that the colors displayed at the top of the SVG:

Can be selected and changed as much as you like:

Changing the color directly to empty removes the colored layer from the SVG:

Here I've removed all but two of the colors completely using the empty option ()

So, let's try again, setting it at just 2 colors :

Interesting. Maybe we can get rid of some of the smaller holes using the simplify option set at 1:

Better, given the much smaller holes would probably turn out horrible on a 3D printer. (though, if you've got a high accuracy printer, or scale the model up, you can keep the original quality levels intact).

Import into Vectary

Now we simply save the SVG, and drag it into an already-open Vectary project.

Now we're back where we started !

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From here, it's really up to you to decide how you want to use these Fractal designs in your models.

For inspiration, here's one uploaded as a piece of jewelry on Vectary

Though, if you want to see someone who's REALLY into 3D printed Fractals, look here. Their designs look amazing !

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All models and pictures of said models are released under the CC BY-SA 4.0 license

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