Here, each curve hits alternate dots: first exactly (above), then with offsets pushing it toward the other curve. Below is the result of eight iterations.

With enough iterations, the top of ‘s’ eventually gets a more symmetrical arch, as the change in curvature is spread more evenly.

But many runs get stuck in the fitting phase, and I don’t yet know why. Attacking one likely flaw didn’t help.

(Previously: 2014, 2011, 2010; also, less closely related, 2015)

I tried to smoothen a stroke by shifting each dot toward the Euler spiral (aka clothoid, aka Cornu spiral) determined by its four nearest neighbors. That didn’t work so well: small wiggles were removed, but big ones were magnified.

( . . more . . )

Mom mentioned a friend who once had two dogs, and when one died both she and the surviving dog took it hard; so now she keeps three dogs of staggered ages.

My cats are brothers, now six years old. I have long had in mind that in 2021 I’ll look to add one about 5yo – rather than get a kitten now, because older animals are harder to place.

But today at the shelter I saw many kittens whose data sheet said “would prefer to go home with a sibling,” and thought of saying, “Next time a batch of kittens is down to an odd one, call me and I’ll take it, if it’s not solid black (like Rocky and Bramble).” A sad proviso, but one must be practical.

In The Fall and Rise of Reginald Perrin, there are two yes-men: Tony, who likes to say “Great!”, and David, who likes to say “Super!”.

If I were writing it, their distinctive tics would instead be “in terms of ——” and “from a —— standpoint”. (They can share “on a —— basis”.)

Sometimes I search my blog for this picture and scratch my head in puzzlement that it’s not here, before remembering that I posted it on Google Plus back when I used that.

So here it is. Stephen Guerin (the shaven one) displays his canvas print of one of my designs.

The colors came out better than I hoped, in stark contrast to a couple of mugs with related designs that I got from the same shop.

In 2007 I thought of a pretty way to paint a square so that all pixels are different, but similar colors are clustered. For each pixel, set x,y to its coordinates; if their sum is odd, set the low bit of one of the color channels to 1. Replace x,y with (-x+y)>>1, (-x-y)>>1; this has the effect of rotating the grid by 3/8 turn and shrinking it by a factor of √2, so that the former even points, which formed a larger oblique grid, now fall on the original grid, and the odd points have their new half-coordinates truncated away. Repeat until a bit has been assigned to each bit of the three color channels.

(More concisely: considering the pixel’s coordinates as a complex number, express it as a bit string in base (-1+i).)

Colors that match in their higher bits form twindragon fractals, thus:

In 2012, I thought: what if the rotation alternates clockwise and counterclockwise?

A bit on the boring side.

But in 2017, I thought: what about less trivial sequences? ( . . more . . )

In the last couple of years I’ve looked at thousands of webcomics. Sometimes I wish I’d kept a list of those whose first page is captioned “It begins” or “So it begins” or “And so it begins.”