My student Colton Baumler has been printing 3d versions of some of the fractal designs I posted about a few months ago:

That’s his three-dimensional interpretation of the first few iterations of this design of mine:

What’s fun about Colton’s version is that each new layer of squares is printed a bit taller than the previous layer. I had really only imagined these as two-dimensional objects, so for me it’s really fun to have 3-dimensional models of them to hold and play with! Colton’s idea of adding some depth really adds another … er … dimension to the overall effect:

His work also gives a nice way to illustrate some of the features of these fractals. For example, visually proving that the “inside” and “outside” in my fractals converge to the same shape can be done by printing the same model at different scales. Here are three copies of the same fractal at different scales, each printed with the same number of iterations:

Not only do these nest tightly inside each other, the *thickness* is also scaled down by the same ratio, so that the upper surfaces of each layer are completely flush.

Colton has been doing this work partly because designing fractals is a great way to learn 3d printing, and he’s now getting some impressively accurate prints. But, I also like some of his earlier rough drafts. For example, in his first attempt with this fractal based on triangles:

there were small gaps between the triangles, which Colton hadn’t intended. But, this gave the piece a sort of rough, edgy look that I like, and it casts shadows like castle battlements:

Colton is still doing nice new work, and we’ll eventually post some more pictures here. But I couldn’t wait to post a preview of some of his stuff!

(Designs and photos © 2018 Colton Baumler and Derek Wise)