
(Left) Mammillaria elongata, or golden star cactus, displays a helical morphology. (Right) A magnetic cactus of dipole magnets on stacked bearings assumes phyllotactic spirals, similar to the biological cactus. With the magnetic cactus, physicists have investigated the dynamics of phyllotaxis.
In a recent study, researchers have experimentally demonstrated for the first time a celebrated model of "phyllotaxis," the study of mathematical regularities in plants. In 1991, S.L. Levitov proposed a model of phyllotaxis suggesting that the appearance of the Fibonacci sequence and golden mean in the pattern of spines on a cactus can be replicated for cylindrically constrained, repulsive objects. Now, researchers have constructed a "magnetic cactus" with 50 outward-pointing magnets acting as spines, which are mounted on bearings and free to rotate on a vertical axis acting as the plant stem. With this setup, the researchers, from Los Alamos National Laboratory in New Mexico; Cornell University in Ithaca, New York; and The Pennsylvania State University (PSU), have verified Levitov's model, and their study has been published in a recent issue of Physical Review Letters.
In their experiment, the researchers put the system in a low-energy state by mechanical agitation. Then the scientists observed as the magnets (spines) arranged to form phyllotactic spirals, generating a so-called Farey tree of unfavorable angles. The unfavorable angles are fractional multiples of 2π (i.e. 2πi/j, such as 2π/3, 4π/3, etc.). The spines on the magnetic cactus, like those on a plant, form a helix around the cylindrical stem by growing around these particular angles.









