Presented for your consideration: the somewhat disappointing results of an experiment in using piecewise polynomial spirals, of varying degrees of continuity, to fit the Takana — disappointing in that few if any of the curves are as pretty as I hoped.

I treat here only those that can be drawn with a single stroke. (The others can be built by combining subsets of these strokes.) In each chart, the degree of continuity increases downward, and the degree of the polynomials increases to the right.

A polynomial spiral is a curve whose tangent angle is a polynomial function of arc length; it has the form integral(exp(i*f(t))). (I implement it as a Taylor series.) In principle, f could be any real-valued function. If f is constant, you get a straight line; if f is linear (leftmost column in these small charts), you get a circle; if f is quadratic, you get an Euler spiral or Cornu spiral or clothoid, which is much used in railroads and highways to avoid sudden changes in lateral acceleration.

Here f is a least-squares fit to the step function which is the direction of the squared stroke. The top row of the chart shows continuity of degree zero: the component arcs meet, but that’s all; f is discontinuous. Degree one: the tangent angle is a continuous function of arc length. Degree two: the first derivative of tangent angle with respect to arc length, i.e. the curvature, is continuous. Degree n: the (n-1)th derivative of tangent angle, i.e. the (n-2)th derivative of curvature, is continuous.

Click each chart to extend it.

Later: I have come to a couple of conclusions. In most of these charts, the best entry to my eye is where f is piecewise quadratic with one continuous derivative. More than one degree of polynomial above the continuous degree adds little fidelity and detracts from beauty.

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I can’t remember how much I knew of Elvish languages before The Silmarillion, with a glossary, appeared in 1978. Can you tell from the text of The Lord of the Rings (not counting the Appendices) that Quenya and Sindarin are related? Are any words explicitly given in both?

Each month I check my HTTP referral logs, and find that nearly all of the “referring” pages that I haven’t seen before are spam. Usually there are also a few sites showing one of my images as examples of some theme or other. Now here’s one of both classes: a page of auto-generated SEO drivel containing one of my pix, apparently because the description contains the word “binary”.

About a dozen years ago I made a page of links to my favorite webcomics. Looking at that list now, I find that twelve that are still going (though a few are very sporadic), ten have stopped but remain accessible through a system of tubes, and eight have vanished:

• Fluble by Christopher Mastrangelo
• Bobbins by John Allison
• When I Grow Up by Jeff Rowland
• JoBeth by BJ Hiorns and Joey Hetzel
• Shaw Island by Zach Stroum
• The New Adventures of Bobbin! by Joycelyn Yik
• Catharsis by Jen Boeke
• Everyone Drunk But Me by Laura Beth Brandt

Other favorites now missing include

• Malfunction Junction by Matt Milby
• As If! by Amy Hebberson
• Life on Forbez
• meh~! (mathematically enhanced hares) by wing mui
• Warp 9 to Hell
• Knowledge Is Power by Laura Chapple
• Yourmometer by Hobbes (Laura LeGault)
• Killer Robots from Space by Adam Greengard
• Don’t Forget to Validate Your Parking by Mike Le
• Cyberbooty by Tony B
• everything at Graphic Smash, Modern Tales, ComicSpace, Webcomics Nation, Girlamatic, Activate, and (in about 2021) Smackjeeves

Maybe when a favorite series stops updating for a year I ought to save the content for myself before it vanishes!

My new telephone has dozens of ringtones and I hate them all: Newagey lo-fi orchestral crap, mostly laden with snare drums for some reason.

My last phone played the sound of an old-fashioned mechanical bell; the one before that, a pizzicato passage from a Ravel string quartet; before that, the quick part of Pachelbel’s Canon – in frankly electronic timbres that did not pretend to be an orchestra.

I want a ringtone that says “a digital device seeks your attention,” not one that sounds like something overheard on a cheap radio belonging to someone with no taste.

I was in the kitchen. Rocky came in, crying. I scritched him. He ran to the comfy chair, stood beside it, looked at me, called once again. I went and sat in the comfy chair, and Rocky jumped up to claim his usual seat on my knee.