Fractal Fern Vase

Hey there, wonderful people!

I have a sordid past as a math nerd and software person - shocking revelations, I know - and those interests have combined in this ferny-looking vase!  The organic patterns that sprout from the base and make their way up the sides are mathematical in nature, and the whole vase itself is the result of many, many hours of calculations.  Fortunately, computers are good at doing those things!

The short story

A certain kind of simulation was used to build up a fern- or lightning-like pattern, then that pattern was wrapped around a vase shape!

The long story

https://en.wikipedia.org/wiki/Diffusion-limited_aggregation

That's the basis for the pattern involved - Diffusion-limited aggregation.  Basically, it involves simulating randomly moving particles on a grid, and fixing them in place when they happen to end up near an existing one, leading to those characteristic fern shapes.  

I love this algorithm!  It's a very simple process but it yields these amazing patterns that seem so familiar.  So, I wrote an application to create those patterns, storing the result as a big matrix of ones and zeroes.  I figured for our purposes we could probably do just fine with about 800,000 points in the grid, which led to a few tens of thousands of ones in a sea of zeroes.  But those ones depicted strange and beautiful shapes!

Next it was a matter of forming that into an interesting three-dimensional, printable form, and for that I fired up OpenSCAD.  I took the grid, mapped one axis to angles around the vase, and mapped the other to the height.

The first version of this was very dull, though.  I just had tiny points on a cylinder, and it was very hard to make out.  So, that needed improvement.  Each point instead became represented by a kind of flared, faceted cone pointing outwards, and that was far more dramatic!

From there, making the cylinder into a more flowing curved thing meant coming up with an interesting curve formula that could be used to scale the distance of the points from the centre based on their height.  Less complicated than it sounds :)

Once all that was done, I just had to wait a few days while OpenSCAD dutifully processed all of the geometry!  

Printing Tips

Nothing tricky here, but it's a big file!  There's more detail in there than is strictly necessary, but having computed it all it seemed a shame to go throwing information away!

This is a vase mode print, of course, so set your slicer accordingly!

Print Dimensions

The Fractal Fern Vase occupies 87mm x 85mm on the print bed and is 160mm tall.

File Locations

You'll find this one on dropbox under 700 Fractal Vern Vase

Link to dropbox post: https://www.patreon.com/posts/31697592

Further Thoughts

I had no idea whether this would actually be a practical thing to attempt!  Conceptually, it isn't that complicated, but computationally it's fairly hefty, and I really didn't have any way to know what kind of computational complexity I was going to cause inside the innards of OpenSCAD when I asked it to merge tens of thousands of objects together!  I started the process and just had to wait and see whether it would finish before the heat death of the universe.  It took a couple of days :)

xoxo

Sven.