second-guessing by halves

Posted on Saturday, 2018 February 24 by Anton

Early strips of some webcomics carry the author’s much later comments. Christopher Baldwin (Bruno) and David Willis (Roomies!) are reposting old series that ended. David Morgan-Mar’s (Irregular Webcomic!) schedule these days is two new strips and five comments on old strips each week.

If it were me, I think I’d want to keep coming back to older strips, with ever decreasing frequency. Perhaps like this:

if n even:
    n /= 2
    comment on n
    while n even:
        n /= 2
        add n to backlog
else:
    pop a number from backlog and comment on it
Posted in cartoons | 5 Comments

un-meander

Posted on Wednesday, 2018 February 14 by Anton


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.

Posted in curve-fitting | Leave a comment

meander

Posted on Sunday, 2018 February 11 by Anton

(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.

Continue reading →

Posted in curve-fitting | 2 Comments

recruitment options

Posted on Tuesday, 2017 November 07 by Anton

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.

Posted in pets | 1 Comment

shibboleths?

Posted on Saturday, 2017 November 04 by Anton

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”.)

Posted in language | 1 Comment

a poster

Posted on Saturday, 2017 September 09 by Anton


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.

Posted in merch | 2 Comments

mutant dragons

Posted on Monday, 2017 July 03 by Anton

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? Continue reading →

Posted in eye-candy, mathematics | Leave a comment