The Abominable Snowmeng, and other winter fractals


It snowed quite a lot in Portland, yesterday and overnight.  About a foot altogether, which for this town is if not historic at least very rare; a typical Portland winter sees no snow at all, or some brief flurries of fat flakes that don’t survive contact with the wet-from-recent-rain ground.  Every two or three years we’ll get a nice blanket of 2 or 3 inches and the city will shut down for a day or two while everyone panics.

This isn’t the first snow we’ve had this winter, so it’s been a weird one on that front already; last time we got some decent coverage, I scraped a Sierpinski Carpet in the driveway with a chunk of scrap 1×6 we had sitting around:


But this was something else, and so it demanded something else: increased dimensionality.

And so after my wife and I had finished some utilitarian shoveling of sidewalk and driveway, I started building up a good sized cube on front lawn.  Wife helped out for a while too, as we packed snow on sides and top and turned a heap into a squarish heap.

And then it was just a lot of packing and squaring, and then some hollowing out.  The hollowing went comparatively quickly, and there were no disaster collapses which was a relief.


And so: a snow Menger sponge.  A snowmeng.  In the meadow we can build one, etc.


It’s not the cleanest iteration I’ve done, geometrically or literally.  The squares aren’t terribly square and the bottom hole has a bit of snow left in it because it was very difficult to trowel out cleanly (you have to be tall to even catch me cheating, there, but I know I did).  Beyond that, I got clumps of grass and dirt mixed in because I built the thing out of snow I’d already been shoveling off the sidewalk, with all the bits of grass and moss and soil in the cracks.

But also: we went for a walk in the morning to get some exercise and see how the neighborhood was taking the snow.  Which: everything was white and snowy!  A lot of branches had come down under the weight of it, “widowmakers” the word I picked up for those (and their not-fallen-yet cousins) at some point in my youth, probably from Montana family.

But there were also some stuff that had a found-fractal feel:


These chain link accumulations, with the lattice of half-filled triangles, reminded me of some very simple 1D cellular automata patterns.  That’s a whole blog post on it’s own, but for now also:


The accumulation of snow unevenly and seemingly randomly on the hexy trypophobateria that is this TriMet bus stop shelter remind me likewise of some of the complex seeming-randomness of a particular famous 1D cellular automata, the Rule 90 pattern.


Finally, I liked the way the accumulated snow on this tree (and many others) brings out the branching patterns of the, uh, branches — the snow creates a contrast and blocks the view in a way that makes this feel like a cutout diagram of the tree.  All of which feels like a nice echo of a randomized Lindenmayer System model, which is appropriate enough as L-Systems were apparently designed originally to model organic/botanical growth patterns.

Author: Josh Millard

I manage and help moderate the community website MetaFilter, where I go by "cortex"; in my spare time I get up to all sorts of creative nerdery on the internet and in Portland, Oregon.

6 thoughts on “The Abominable Snowmeng, and other winter fractals”

  1. Yeah, it’s a real not-messing-around situation. On the bright side, I think the only people who have been driving around today are people who actually need to, vs. when we get one inch of snow that converts to a layer of ice and baits a ton of unprepared drivers into dumb pileups.

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