Blanketing my friends and family and social media network with fractal imagery for months on end is paying dividends: I get people throwing found imagery and straight up craft projects my way now, which basically always makes my day.
And so I’m gonna celebrate a lazy, snowy (in Portland, again, somehow) Saturday by showing off other folk’s stuff instead of my own.
Above: two second-iteration lego Sierpinski carpets, at one-pip and two-pip scales. I like ’em both, and like the visual contrast between the two both at a detail level and via the palette inversion, but the smaller is I think particularly interesting for showing off how complicated it is to make an odd-valued design (9×9) work with block pieces that tend to come in power-of-two dimensions like 2×2 and 1×4.
There ends up being a nice conflict between the symmetry of the design and bits of asymmetry in the implementation — you can see some rotational regularity with some of the pieces but there’s also a couple of 2×3 blocks showing up, and the central 3×3 square is a marriage of three distinct block sizes.
(There’s a rainy day puzzle: least number of power-of-two blocks you can use to construct a carpet shape, for various iteration levels?)
All of which raises the question of adding a dimension and building a lego Menger sponge. With solid colors standing in for holes it probably wouldn’t be too much of a challenge, but doing it with negative space for the holes/tunnels could be a real challenge of finding the right arrangement of long pieces to create flush edges but also allow enough continuity from one vertical level to the next to hold the whole thing together.
This is pretty rad: plinth used a 3D printer to build out a model of exactly half of a three-iteration Menger sponge, as if sliced along a multiaxial diagonal from the full shape. And it’s obvious here (though the detail falls apart at the smallest holes due to printer resolution limits) that the resulting pattern of that diagonal bisection is, not square tunnels, but six-pointed stars. Which makes sense on paper once you go looking, but is a pretty delightful visual surprise the first time you encounter it.
I also seem to have gotten into my friend Phil’s head; he sent me this render the other day of what’s essentially a variation on the “skeleton” negative space inside an interation-one Menger sponge. A traditional Menger would have prongs as large as the central cube there, rather than skinnier spokes, but the basic tri-axial cross shape is in shouting distance.
Also from Phil, this nice little three-iteration Sierpinki carpet, rendered within the engine for a little slow-gaming sim he’s working on called Badlands, which you can go check out for free. I think he maybe cheated here, though, since the game doesn’t have triangular tiles yet as far as I can tell.
Speaking of Sierpinski triangles: my friend Joel spotted this in Somerville, Massachusetts, and I’m curious what the story is. Quick googling didn’t turn up anything obvious, and he didn’t have any other context — apparently it’s attached to a perfectly ordinary looking house. Curious!
Finally, sent to me by my friend esch, a floor tiled with 3×3 meta-tiles of palette-alternating one-iteration Sierpinski carpets. Linoleum carpets! Confusing.
At this scale my assumption is it’s a coincidence, just someone aiming for a little bit of visual dazzle in otherwise utilitarian flooring rather than an intentional nod to the fractal, but I’m not gonna complain.
Thanks again to everybody who tossed stuff my way; no reason this whole fractal fixation should be a one-way street.