four million colors
You may know from The Art of Computer Programming §4.1 (citing W. Penney, 1965) that, just as any positive real number can be represented by a bit string in base 2, any complex number can be represented by a bit string in base –1±i. Here I express the bits of that representation as bits of color values.

This is only an arbitrary crop of an image consisting of 218 pixels; get 222 colors (png, 373 KB). The full 24-bit version will have to wait for me to get cleverer about use of memory. (Later: Success.)
When I say I make mathematical pictures, the response often is: “Like fractals?” Some of my designs have chaotic reflections, but this is my first fractal in many years.
fun with eigenvectors
After installing that matrix math library, I spent a week’s evenings pushing several abstract graphs through my “topological coordinates” program and finding, to my lack of complete shock, that none of them had any neat three-dimensional embedding.
Then I tried a torus, and was again far from amazed that it didn’t work well either: all the vertices being equivalent under the inherent symmetries, there’s nothing to distinguish the “inner” from the “outer”.
I cut a seam of the torus to make a cylinder, and then I got a surprise: the free ends curl in like an apple. If anything I’d expect the opposite: the vertices along the edges, being topologically outermost, “ought” to curl outward.

One of these days I’ll get around to fullerenes.
what, if anything, were you thinking?
I hear some surprising things in this job. I trust I’m not violating confidence if I repeat this doozy from a discharge report:
At this point the etiology of the [symptom] is still unclear to me; it could possibly be idiopathic but, given that his symptoms have resolved and [test results], most likely his [symptom] has unclear etiology.
Idiopathic or unclear? We report, you decide.
Finagle’s Law
I hoped to have some new math pictures for you (or at least for me) today, but my attempts to install a code library that I need have come to nothing. The makefile invokes gcc with options that version 3.3 won’t take. I try to install gcc 4, and Fink says before I can do that I need to recompile Fink with gcc 4.
So I’m having a depressive episode instead.
But I can tell you anyway about what I wanted to do. ( . . more . . )
umbra Saturni
the view from Saturn’s shadow
My latest finding of “dictionary translation”, at a pet store:
ONE-STORY CAT CAVE
UNE CAVERNE À CHATS D’HISTOIRE
I’d make it caverne à chats à une étage.
Funny that I missed this three years ago — Joseph Hertzlinger has a provocative idea about drugs:
I don’t think a suggestibility drug such as marijuana should be encouraged. . . . I suspect that marijuana might be particularly dangerous from the point of view of inducing groupthink. I have not had any direct personal experience but I have noticed that it is defended as reinforcing the approved habits in the social group of the user. [examples elided] If we put that together we can see that marijuana is a conformist drug – probably because of its ability to make people suggestible. (That might explain the thoroughness of the collapse of trendy drug use in the ’80s. Once its use declined, the remaining users would start conforming to the new trend and stop.) . . . Declare that any drug whose use declines will be legalized. That will encourage drug users to keep their friends off the drug and will eliminate the “everybody does it” defense.
it takes an expert?
Kaiser Permanente has a radio spot with this bit of dialogue:
So what did your doctor say?
Oh, she prescribed the same medication she always does.
And it worked?
M-hm! My doctor is awesome.
What’s wrong with this picture?