Sun, 22 Aug, 2004

Cactus Flower Math

Those (few) who have been following ELECTRON BLUE from its beginnings know that I keep cacti. In March I lamented the death of one of my cacti, "Spinoza." But this time I have much better cactus news to report. One of my cacti, out on my terrace for the summer, has bloomed. Cactus flowers are often rare, brief events, and so was this one. I was glad to catch it. During the day, I saw the buds appear on the top of the plant, where I had noticed activity some weeks earlier. When I came home from work in the evening and looked at the plant, I was thrilled to see that the buds were in bloom. Knowing that these glorious white flowers would only last one night, I quickly grabbed my new digital camera and snapped some shots. I took some by the light of a fluorescent camping lantern, but they were slightly blurred so the shot you see here was illuminated by the flash.

By the next morning, the flowers were folded up, and would not bloom again. I don't know what kind of cactus this is; I'd love to know its Latin name. I suspect it is of the Mammillaria or Echinopsis genus. For all I know, it may put up more blossoms. But most likely, that is its big moment for this year.

To get this entry back onto the topic of math, take a look at the body of the cactus in the bud photo. The areoles, or the points where the spines emerge, are arranged in a regular interlocking hexagonal pattern, which if joined would cover the hypothetical surface of the round plant, rather like the famous geodesic dome associated with Buckminster Fuller.

But this plant isn't really spherical, it is an oblate spheroid, a sphere flattened at top and bottom. Its green surface is not smooth, but actually made of cones which support the spiny areoles. The spines of this cactus are curved inward and crisscross to form a tesselated pattern that is not quite regular, but subdivides the basic triangular planes which the areoles define. The spines form a three-dimensional network of curved lines. Other spines have the same inward curve, but are set at a higher angle, to make the outward-facing points which protect the plant. So this little cactus, if you look at it closely, is a marvel of geometry.

Posted at 2:41 am | link


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