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Monday, 2014 January 27, 16:28 — mathematics

some thoughts about packing

My bundle of 19 fullerenes is arranged in a face-centred cubic lattice, each ball occupying one of the 24 even-numbered cells of a 4×4×3 array (and parts of the adjacent cells). The spacing of the grid planes is determined by the sums of the radii of the circumspheres of nearest-neighbor balls.

There appears to be much more ‘daylight’ between balls than necessary. That’s not a problem here, as the size of the bounding box is not near the limits of the process; but still it got me thinking about how to tighten the packing. ( . . more . . )

Friday, 2014 January 24, 22:23 — neep-neep

in which I curse my lack of omniscience

I want to push several hundred greyscale images through a threshold filter, so that an output pixel is black or white according to whether the corresponding input pixel is less or more than 1/2 bright. (My goal is a ‘woodcut’ effect.)

ImageMagick can apparently do this with one command, but I lack a library that it needs.

GIMP has a menu command with this function, but to do it from a script it seems I’d need to learn Scheme.

I could write a program using Python Imaging Library (which I’ve used to output most of my mathematical designs in recent years), but so far in RTFM I can’t tell how to, y’know, access the pixels it reads in. Later: Found a better FM.

Wish me luck.

Friday, 2014 January 24, 22:08 — merch, sciences

small irregular fullerenes

Shapeways has thirteen models of (the most symmetrical and famous form of) C60, but none of the thousands of smaller fullerenes. So I designed models of the 35 smallest, i.e. up to C36; this includes the smallest with no symmetries, and the smallest with no ‘peaks’ where three pentagons meet. One bundle has the 19 forms with mirror symmetry; two other bundles will have the 16 or 32 chiral forms (arbitrarily divided), so that the buyer can choose to have both or only one of a pair distinguished only by handedness.

I’ll make them available when I have them in my hands and am satisfied of their strength.