The Geometry of Plants

Apr 27, 2015 2 comments

Looking around, you might imagine that branches, leaves and flowers grow at random, haphazardly. The truth is, however, that the points at which every branch, leaf, stem, bud or petal emerge, have all been set out according to fixed laws and miraculously precise measures. There are patterns everywhere you look in the natural world, the most persistent of which is the Fibonacci sequence. The sequence was first described by ancient Indian mathematicians hundreds of years before the birth of Christ, even though it’s named after the Italian mathematician Leonardo of Pisa, who was more famously known as ‘Fibonacci’. It was Fibonacci’s book “Liber Abaci”, published in the early 13th century, that introduced this magical sequence to the Western world.


The Fibonacci sequence is so simple it’s almost baffling. Here each number is created by adding together the previous two, so starting from 1 1 2 3 5 8 13 21… it continues to infinity. The Fibonacci sequence is so persistent in nature that it’s a challenge to find a plant or fruit structure that does not conform to it. For instance, the placement of leaves along a stem is governed by the Fibonacci sequence, ensuring that each leaf has maximum access to sunlight and rain. The same principle is at work in the formation of pine cones, sunflowers, pineapples, and cacti. The Golden Ratio, which you might have heard before, is just another manifestation of the Fibonacci sequence.

All plants are geometrical one way or the other. However, there are plants whose geometry is more pronounced than others. Here are some famous examples.

Romanesco Broccoli


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Romanesco broccoli, also known as Romanesque cauliflower, is light green in color and has a striking appearance because its form is a natural approximation of a fractal. When compared to a traditional cauliflower, its texture as a vegetable is far more crunchy, and its flavor is not as assertive, being delicate and nutty.

Crassula ‘Buddha’s Temple’


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Crassula ‘Buddha’s Temple’ is a hybrid between Crassula falcata and Crassula pyramidalis, made in 1959 by Myron Kimnach from the U.S.A. But because it's a very slow growing cultivar, it has never been propagated commercially in large numbers. So even over 50 years after the creation of it, Buddha's Temple is still hard to find.

The plant grows about up to 6 inches tall and start branching at varying levels from the sides of each column. The flat, thin leaves which are silvery-grey to greyish-green in color are stacked tightly and folded up at the edges, forming a perfectly square column.

Aloe polyphylla


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Aloe polyphylla grows in high, mountainous, grassy slopes of Drakensberg mountains in the Kingdom of Lesotho, near South Africa, where the plant is endemic. Here it clings to rocky crevices and well-drained scree slopes. The climate is cool in the summer and in the winter the aloes are often covered in deep snow. Because of its strikingly symmetrical, five-pointed spiral, the species is highly sought after as an ornamental but is difficult to cultivate and usually soon dies if removed from its natural habitat. In South Africa, buying or collecting the plant is a criminal offense.



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The Dahlia is a common garden flower, but have you looked at one closely? There are 42 species of dahlia, with flowers as small as 2 inches in diameter or up to 1 feet.



The seed head of sunflower follows the Fermat's spiral which is based on the Fibonacci sequence. Photo credit

Red Cabbage


Red Cabbage sliced in half horizontally showing Fibonacci spirals of leaf arrangement. Photo credit

Pelecyphora aselliformis


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Pelecyphora aselliformis is gray-green and round with lateral, flattened tubercles that have scale-like spines and are arranged in a spiral. It can grow to up to 10 cm in height with flowers that grow up to 3 cm across and are a brilliant violet color. The plant is relatively rare and is only found in northern Mexico.

Ludwigia sedioides


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Ludwigia sedioides, commonly known as Mosaic flower and False loosestrife, is a herbaceous perennial plant that grows on wet and swampy locations. It is native to Brazil and Venezuela.

Lobelia deckenii


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Lobelia deckenii is a species of giant lobelia that grows on the mountains of East Africa. The plant usually produce multiple rosettes, consisting of between one and eighteen rosettes, connected underground. Each rosette grows for several decades, produces a single large inflorescence and hundreds of thousands of seeds, then dies.



View from below of Angelica flowerhead. The flowerhead is roughly spherical; each part is similar to the whole head in having a stalk and its own sphere of flowers. Photo credit

Angelica is a genus of about 60 species of tall biennial and perennial herbs in the family Apiaceae, native to temperate and subarctic regions of the Northern Hemisphere, reaching as far north as Iceland and Lapland. They grow to 1–3 m tall, with large bipinnate leaves and large compound umbels of white or greenish-white flowers.

Sources: Divine Template Creations / / Bored Panda


  1. Absolutely amazing. Nature used Fibonacci before he existed.


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