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Wednesday, 2008 July 9, 22:09 — eye-candy, mathematics

the greatest thing ever!

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.

Saturday, 2008 January 5, 13:15 — eye-candy

LiveLand

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.

Saturday, 2007 September 22, 01:13 — eye-candy, mathematics

just don’t throw it indoors

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

Thursday, 2007 July 5, 08:37 — eye-candy, mathematics

16 million colors

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.

Sunday, 2007 June 10, 17:42 — eye-candy, mathematics

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.

Thursday, 2007 March 22, 21:50 — eye-candy, neep-neep

long-awaited

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.

Saturday, 2007 January 13, 11:08 — astronomy, drugwar, eye-candy, language

umbra Saturni