Forgive my waxing hyperbolic . . .

This is a tiling of the hyperbolic plane by triangles whose angles are π/2, π/3, π/7 – the smallest possible tile. I present it in a conformal mapping analogous to the Mercator projection, which I’ve never seen done before.

Here’s a pretty thing: an animated fractal mountain generator (Java). The text unfortunately doesn’t explain anything about the algorithm, but it’s evidently the familiar triangle-subdivision mountain – with the offsets oscillating, so you see the land rising and tilting and falling back into the sea, while the smaller hills change more slowly and are carried along with the grand movements.

Vladimir Bulatov makes and sells pretty things in metal, wood and stained glass. I haven’t bought any of them — yet!

Nearly eight hours in the making, here it is: all the 24-bit colors in a tasteful, tilable fractal arrangement — 16million.png.gz (1 megabyte). And since Mads asked for it, the Python sourcecode: two files.

Another way to flatten the color cube is by traversing both the cube and the square with Hilbert curves, and continuously mapping one to the other. I’ll try that, one of these weeks.

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.

Jamie Zawinski has ported his gorgeous screensaver collection to MacOS.

My favorites are Demon, a colorful cellular automaton; CloudLife, a fuzzy variant of Conway’s Life; Substrate, whose randomly growing arcs suggest the street plan of an old city; Galaxy, a simulation of gravitic interactions; Polytopes, which displays one of the six convex regular polychora, rotating in 4-space.

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.