Starting with fractals

Just took the plunge on a lightly used Glowforge Basic a friend was selling after his Pro showed up. Am pretty excited for the possibilities with this thing, though right now I’m just sorting out my setup (spent today refining my venting a little to avoid stinking up the house) and doing little experiments to see what just works, what needs attention, etc.

I’ve been doing a lot of geometric art the last year and a half, paintings and stencil-based work, and have a particular fixation on the Sierpinski carpet and the Menger sponge, so cutting a few variations on Sierpinski carpets was kind of a gimme early project. At this scale the cuts are pretty satisfactory but accounting for kerf in my Inkscape layout would get the proportions of those smallest square holes more precise.


Well, that’s cool! :grinning:


Beautiful! Welcome!


Uh-oh. Would I be plunging down a rabbit hole if I looked those terms up?

Anyway, your sample is really cool!


As rabbit holes go, fractals are a pretty fun one to fall down and a lot of them lend themselves well to vector design hijinks, so I won’t say don’t!


It is indeed a very deep rabbit hole with many ideas for the :glowforge: particularly Peno-curves and the most extreme case Hilbert curve as has been discussed elsewhere.

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Reminded me of the bottom of a CPU. Looks great!

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And some experimentation this morning with taking this to 3D construction, of a tiny 1-iteration Menger sponge and a 2-iteration pseudo-Menger. Pseudo- because this is just an external facade; a real Menger sponge would have a bunch of guts too, and that’s something I want to tackle in the long run as I continue to get used to thinking through this kind of construction.

There’s both theoretical and practical issues I want to work through in further drafts of this construction:

  • I should work out a kerf-mitigation plan so the joints are flush, which is hopefully just a matter of taking the time to actually do it since I’ve already seen the excellent details folks (especially Jules) have laid out in prior discussions and am comfortable enough with Inkscape for that to be totally doable. In the long run I’d love to see someone build a kerf-nerfing plug-in for Inkscape since my gut tells me that it’d be very doable to automate with a couple of user-specified parameters if someone’s willing to put in the work.

  • I should see if I can make the tab and slot arrangement a little less busy. The holes in this design make it a little more complicated to put a tab or a slot in any given spot, but this was just a first draft this morning and I imagine I can clean it up and get away with full 1/8" inch unit notches.

  • I’d like to sort out a one-piece design for the six faces of the cube, and I’m fairly certain it’s doable; there’s nothing wrong per se with this approach and its distinct pieces, but getting it all symmetrical to the point where I can just tessellate a single 2D piece into a 3D object would be really satisfying.


Here’s the actual cut for those two sponges, for reference. (Looks like I’m too new to add more than one image per comment.)


Wow! Can’t imagine where you’ll take this next!

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I can’t either, but the joins you’ve created for the sides are just fascinating…love they integrate into the whole look. (Definitely something I want to play with.) :smile::+1:

Iterating! Worked on a couple of those things I was talking about: got rid of the tiny tabs and slots in favor of a more balanced arrangement of larger cutouts, and reduced the distinct parts to two very-nearly identical types both of which have 90 degree rotational symmetry.

So you still have two top and bottom pieces and four side pieces, but it’s not as much of an orientation puzzle now and it looks nearly the same from any angle.

I wasn’t able to get it down to a single design, and I think that’s actually not doable with a straightforward GlowForge cut – there’s 8 corners to this cube/sponge structure, and filling 8 corners with 6 square-cut pieces doesn’t work out! A tapered pyramidal type joint on the pieces would work, but that’d require hand-finishing or some elaborate propping-up of partially cut pieces and boy howdy I don’t have the patience for that for something that’s already at 99%.


And here’s the actual cuts for reference. This draft feels good enough that I’m gonna look into truing it up vs. kerfing and see if I can get one to hold itself together snugly.


I had a similar fractal ideas, but in 3D and with triangles. I just don’t know how to pull it into the real world. I drew this up in SketchUp and stopped there. But wouldn’t that be fun to hold?


Sierpinski triangles/pyramids are rad! But, yeah, even setting aside the 3D non-cardinal-angle issue, they’re a tricky variation for real world construction because of the infinitesimal intersections between the constituent triangles/pyramids – one way or the other you have to cheat up the connections from one to the next with a little bit of material.


EXACTLY! That is where I got stuck. Stupid physics.


Cleopatra.s necklace is another fractal that would make a cool design

Here is a quick attempt, but guessing is no substitute for math


Ah! Some sort of cousin of an Apollonian gasket, looks like.