If you begin with the oldest leaf and move up the twig, the next will be 180 degrees away. The third leaf is 90 degrees from the second, the fourth 180 degrees from the third, and the fifth 270 degrees from the fourth. After that, the sequence starts again.

A few other unrelated plants, including the red-flowered torch lily of South Africa and a popular flowering tree called the crepe myrtle, also display this leaf layout, which is called “orixate” after its main showcase.

It’s a “peculiar pattern” previously unexplained by science, said Munetaka Sugiyama, a plant physiologist at the University of Tokyo. In a study published Thursday in PLOS Computational Biology, Dr. Sugiyama and his colleagues present the first mathematical model that successfully accounts for this unusual arrangement.

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Dr. Sugiyama, who often walks past Orixa japonica shrubs at his university’s botanical gardens, has long been intrigued by leaf arrangements, or phyllotaxis. But it was “just my hobby,” he said, until he found a kindred spirit in Takaaki Yonekura, now a graduate student. About five years ago, he joined Dr. Sugiyama’s lab, and the two began studying orixate patterns.