Let's try this again

It's been a decade since the last time I tried something like this. Let's see if this time goes any better.

My goal is 250 words per day. Extra words from previous days can roll over to subsequent days (so I can build up a buffer), but I can't slosh in the other direction (so each day has a hard deadline). In other words, the goal is that by the end of the Nth of November, I'll have published a total of 250N words. For sleep-schedule reasons, the deadline is 23:00 UTC.

...and I'm at like 100 words so far. Not ideal.

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The thing I want to talk about right now unfortunately requires pictures to really convey properly, but let's have a go at it.

Suppose you have a square grid where each cell can be in one of two states, and you want to smooth out stairstep diagonals into proper diagonals. You can subdivide each cell into a central diamond and four triangular corners. Let the diamond be colored according to the initial/naive state of the cell; let each corner follow the rule that it's colored according to the majority of the four cells that meet at its right-angled vertex. (Break ties by matching the center.)

The need to break ties makes this slightly ugly. On a grid of hexagons, we can similarly inscribe a smaller hexagon whose vertices are the midpoints of the edges of the cell. This lets us smooth out lines with no special cases.

How do we generalize this to three dimensions? On a cube, we have two different types of diagonals: the "wide staircase" where we cut off an edge, and the "Q*bert staircase" where we cut off a corner. If we pick one or the other, it's not too horrible, but ideally we want to handle both cases.

The 3D analogue of the hexagon might be the rhombic dodecahedron?

[318 words.]