Waiting for a warranty repair on 3D printer so I'll write instead

[pcallahan]

My Flashforge ran into a problem (electronic not mechanical) but it is still under warranty so I'm staying hopeful. I need to make some detailed writeups anyway, but here are two things I've done. The first is improved (smaller) Robinson triangles, which I have made public in Tinkercad https://www.tinkercad.com/things/1cw8py ... -triangles

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This is what they look like assembled. The flippable shape enforces a Penrose kite and dart tiling and they also group into rhombs.

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I also finally made a set of tiles for Margolus Critters. The bump in the middle enforces the diagonal shift between layers. They work as intended but aren't as much fun as I had hoped, especially since you can't see the layer beneath as you place them.

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[pcallahan]

My designs seem to be getting more attention on Printables than on Thingiverse, so maybe that's the right place for them. I'll put up the Margolus tiles soon, but first I want to photograph a few layers to demonstrate.

Meanwhile, here are the Robinson triangles: https://www.printables.com/model/832709 ... ing-variat

After taking a closer look at Robinson's deflation rule, I see that he makes the obtuse triangles bigger than the acute triangles, so they assemble into rhombs rather than kite and dart. I started to wonder if I should do that (but I like kite and dart better). One thing to consider is that if you make the obtuse (dart half) small and the acute (kite half) large, then you have two distinct side lengths, but you have three if you take Robinson's approach. I hope this picture clears it up.

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[pcallahan]

The 3D printer has been up and running for a while already, but it took me time to get back to this. After making the kite and dart half triangles, I realized they did not follow Robinson's deflation rule after all, so I did a redesign here: https://www.printables.com/model/905407 ... ve-version

I wanted to make a pair of triangles that did (changing "color" when flipped) but there is a problem, observable in Robinson's deflation:

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Because there is no two-coloring of tiles consistent with flipping, I can't put the (jigsaw) nubs all on one side and the voids on the other. That makes it impossible to print a tile without an overhang.

I solved this by printing the tiles in two halves that slide together on a dovetail and snap in back. In some ways, it's inelegant, but it's an interesting 3D printing challenge.

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I spent a lot of time coming up with this, but I will note that another approach is just to print some of the kite halves in a color to match the darts. This will also give you the look of a rhomb tiling.

I am starting to like the look of the rhomb tiling, though I previously preferred kites and darts. Since I'm limited to three image uploads, once again, here's a link to the Printables page: https://www.printables.com/model/905407 ... ve-version

[pcallahan]

Small update: I decided to try printing the thick rhomb half in one piece with a snap-off support. See details on printables page: https://www.printables.com/model/905407 ... ve-version

It works OK, but it is a little rougher. I am not sure which approach I like better. The two-side solution shows how to make tiles that use different colors on each side. I have room to add a picture of some rhomb tilings in this post.

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Here is the new piece before and after snapping off support.

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[tommyaweosme]

idea: make some blocks in three different colors/materials.

color 1: alive now, dead next
color 2: alive now, alive next
color 3: dead now, aive next

and also make a grid to fit those blocks.

when you switch to the next generation, get rid of color 1s, and change color 3s to color 2. then, check all the color 2s and change them into color 1s as nessecary. then, put the color 3 downs where nessecary and then switch to the next generation.

now you are emulating cgol.

[pcallahan]

Here is one more variation on these triangles, this time keeping the tabs hidden. The details are here: https://www.printables.com/model/948066 ... les-with-h

You can make a kite and dart tiling or a rhomb tiling depending on your color choice.

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Here's how they snap together into kites and darts. They're a little more fragile than the jigsaw version, but keep the tabs hidden so the pure tiling is emphasized.

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[pcallahan]

I wanted a reason to practice two color printing (switching the filament in the middle so top and bottom are different) and I decided to make a checked Penrose tiling using triangles that are black on the bottom and red on the top. The Printables page is here : https://www.printables.com/model/113650 ... -triangles

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I like this way of displaying Penrose tiles. In principle, it is possible to pick out both a kite-dart tessellation and a rhomb tessellation. In less garish colors, it might work well as a floor tiling.

Since I wanted to make a new printable model instead of just reusing an old one, I changed the internal boundaries so they slide together for a firm hold. There is a bump in the middle for resistance and I also printed a tool for pushing them together reliably, though you don't need it. Here is a dart before and after assembly.

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