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Sunday, 2013 March 10, 15:44 — mathematics

better my computer than me

My computer ran for eight solid days to extend this table from six rows — (2 3 7), (2 4 5), (3 3 4), (2 3 ∞), (2 ∞ ∞), (∞ ∞ ∞), each of which is (in some sense) minimal — to 106, by request. I don’t know why anyone would want all those others; I see no qualitative difference between any of them and one or more of the six.

Now that the run is done, I look again at my code and see where it could be made more efficient, by changing from complex to real arithmetic; I’ve already done that in my other hyperbolic programs, the ones that generate the ribbon patterns.

Saturday, 2013 February 16, 11:44 — mathematics, me!me!me!

a bit of randomness

I made a minor improvement to my Doodles page: it now chooses the dragon fractal tile randomly from a series of 243 variants – one for each possible assignment of the five high bits to the three color channels.

Monday, 2012 July 30, 19:31 — mathematics

soap films in curved space

A few of the many triply periodic minimal surfaces can be generated from a quadrilateral slice through a tetrahedron of mirrors, as refined by Surface Evolver. I had the idea that the same concept, applied to one of the analogous tetrahedra that tile spherical 3-space, could result in a pretty model.

To my disappointment, none of the non-prismatic kaleidoscopes — those that generate the six regular polychora — hosts a nondegenerate minimal surface (of this simple form); but each of the duoprism kaleidoscopes gives at least one.

Thursday, 2012 June 14, 09:03 — mathematics, merch

but wait there’s more

This one is a projection of a design on (half of) the surface of a hypersphere: a ribbon spans two orthogonal great circles, wrapping three times around one and five times around the other.

Kitty teeth did break it at one point, but with redundancy that’s not a serious problem. Having got my pix I’ll keep the new toys away from them henceforth.

Thursday, 2012 June 14, 08:59 — mathematics, merch

Baby’s First Klein Bottle™

Not only did it not fall apart in my hands …

Thursday, 2012 June 7, 14:54 — mathematics, merch

first tangible result

The strand — for it is a Klein bottle woven of a single strand — is thinner than I expected, and has broken in at least two places. Ah well, live and learn; I’ve already redesigned it to be more robust.

Monday, 2012 March 19, 10:08 — mathematics

Gray palette

I came up with this concept several years ago (I can’t tell exactly when, because I’ve mislaid the original code!) but never posted any of the images until now.

Some of you may like to guess what’s going on before I tell. For more hints, see these patterns’ 254 siblings.

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