To learn more about plants and why they grow in such a mesmerizing way, we reached out to Johan Gielis, a Belgian scientist, professor, and author of The Geometrical Beauty of Plants. He was kind enough to have a little chat and share some insights about the balance and harmony we see in the natural world. Gielis started by mentioning that there are several variants of symmetry, but the most common ones are radial and bilateral (mirror) symmetry. 

The radial pattern consists of circular symmetry. When we look down from the top at such a plant, we can see that we could cut it equally from a central point, like you would cut a pie into the same-sized pieces. 

The bilateral pattern means that the plant is equal on both sides if we cut it down the middle. In other words, it resembles a mirror effect. If you want to picture it, draw an imaginary line right down the middle of your face and follow it down your spine. You’ll see that your body looks just about the same on both sides, except for some minor scars, moles, and freckles. 

Environmentalist and microbiologist Swanandee Nulkar wrote that flowers alter their appearance because of their need to attract pollinators. "Evolutionary biologists have observed that floral symmetries have changed over many generations from being radial or bilateral to even asymmetric," she wrote. "Scientists have also found that bilateral flowers facilitated pollinator landing."

Nulkar mentioned a study performed on bumblebees, where "the results showed that bees preferred these more symmetric flowers, owing to their greater nectar-producing capacity." It seems that insects prefer symmetry because of its appeal. "A diverse genome is nature’s most favored pick," she added. 

When asked about why plants grow geometrically, Johan Gielis told us that there are both genetic and developmental components. He provided an example: "On the genetic side, one has Antirhinnum majus, which is the very standard flower for the common snapdragon. One variant—A. majus cycloidea—has a symmetrical flower."

He continued that during the evolution of the plant, deviations may also become prevalent. However, "one of the plant groups with almost no deviations during [their] development is the wonderful Asclepiad," otherwise known as milkweed. 

When you walk around in the natural world, you see patterns everywhere you look. It is often said that the Fibonacci sequence rules the growth of the plants and connects all living things. While it may sound confusing, the Fibonacci sequence is actually not that difficult to understand. It is a series of numbers where each one is the sum of the previous two. Starting from 0 and 1, the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and continues to infinity. 

This sequence is extremely persistent in nature and can be easily noticed in the placement of leaves along the stem, in pine cones, sunflowers, and pineapples. Plus, if you’ve ever heard of the Golden Ratio, it is tightly connected with this sequence. When thinking about the origins of this number, "Leonardo of Pisa [Fibonacci's full name] did not actually discover the sequence," Keith Devlin, a mathematician at Stanford University, said. "It's been around forever."

"Fibonacci numbers are a very popular subject of research and recreation, and one can find innumerable articles in mathematics, science, architecture, and the arts," Johan Gielis told Bored Panda. 

"Especially in the latter fields, they have achieved an almost divine status, because of the relation to the golden mean. From a scientific point of view, however, one needs to be very cautious in the application of the series to actual natural or cultural phenomena."  

He continued: "For example, in the arrangement of leaves, the Fibonacci numbers relate the number of spirals going in one direction, to the number of spirals in the other. In a large-scale experiment of popular science, with over 600 sunflowers only 3 out of 4 of the parastichies on sunflowers were direct Fibonacci numbers. The other 1/4 were approximate or modified Fibonacci and Lucas numbers, derived series, or irregular."

So it seems that nature and math go hand in hand. "As humans, we build models of nature, and our language is indeed mathematical," the professor said. "Mathematics is the ultimate human language," he added, saying that without humans, there would be no math.

When asked why we enjoy looking at geometrical and symmetrical plants and find them incredibly pleasing to the eye, Gielis told us that it’s because of our preference for symmetry. But it also has a cultural component: "Different cultures may have a different idea of beauty. What we learn is what we will prefer later," he concluded. 

So while we try to grasp how such incredible patterns in nature are formed, we can also take our time to appreciate the many wonders it can offer. Whether flowers are symmetrical or not, they are still mesmerizing to look at. So we hope that with posts like these, you will be reminded of how beautiful nature really is.