![]() Keep spiralling around, adding bigger and bigger squares. The entire outside shape will always be a rectangle. Make the next square fit next to both together - that is, each side is length two. Start with one square and draw another next to it that is the same height. Better draw more slug cats.Here's one way to draw a really perfect spiral. Those other spirals can't help but be jealous of this clearly superior kind of spiral. You could draw a snail or a Nautilus shell, an elephant with a curled up trunk, the horns of a sheep, a fern frond, a cochlea and an inner ear diagram, an ear itself. But you can bring the wonk back by exaggerating the bumps, and it gets all optical-illusiony.Anyway, you're not sure what the second kind of spiral is good for, but I guess it's a good way to draw snuggled up slug cats, which are a species you've invented just to keep this kind of spiral from feeling useless.This third spiral, however, is good for all sorts of things. Probably something to do with how the ratio between two different numbers approaches one as you repeatedly add the same number to both. You can start with a wonky shape to spiral around, but you've noticed that as you spiral out it gets rounder and rounder. Or you could start tight but make the spiral bigger as you go out.The first kind is good if you really want to fill up a page with lines or you want to draw curled up snakes. Or you can start big but make it tighter and tighter as you go around, in which case the spiral ends. There's the kind where as you spiral out you keep the same distance. Oh, and because of overcrowding in your school, your math glass is taking place in Greenhouse No.3 - plants.Īnyway, you've decided there's three basic types of spirals. Probably a good time to start doodling, and you're feeling spirally today, so, yeah. Initial phyllotactic transformations, occurring already in the very early stages, indicate great plasticity of cactus growth and seem to support the hypothesis of the ontogenetic increase of phyllotaxis diversity due to transformations.Say you're me in your math class and your teacher's talking about… Well, who knows what your teacher's talking about. Discrepancy in the range of phyllotactic spectra in seedlings and in mature plants suggests that phyllotaxis diversity emerges during further plant growth. the main Fibonacci and the decussate pattern. Only two, the most common phyllotactic patterns occurred in the early development of studied seedlings, i.e. Differences in the initial stages of pattern formation do not fully explain the phyllotaxis diversity in mature cacti. It was either areole pair (mainly in Mammillaria), starting a decussate pattern, or a single areole (mainly in Thelocactus) quickly followed by areoles spirally arranged, usually in accordance with the main Fibonacci phyllotaxis. ![]() In seedlings from the Cacteae tribe ( Mammillaria and Thelocactus), cotyledonal areoles were never observed and the first areoles always appeared in the space between cotyledons. ![]() ![]() This pattern was subsequently transformed into bijugate or into simple spiral phyllotaxis. Usually, next pair of areoles was initiated perpendicularly to cotyledonal areoles, starting the decussate pattern. In seedlings from the Trichocereeae ( Gymnocalycium, Rebutia) and Notocacteae ( Parodia) tribes, two opposite cotyledonal areoles developed as the first elements of a pattern. The analysis of the sequence of areole initiation revealed intertribal differences. To assess the origin of this diversity, early stages of phyllotactic pattern formation were examined in seedlings. Representatives of the family Cactaceae are characterized by a wide range of phyllotaxis. ![]()
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