I chose to feature this photograph because of the beautiful spiral formed by the unfurling inflorescence. It reminds me of many a grade-school math book. It also reminds me of a few years in my late teens that I spent marveling at “sacred geometries”. I remember one book that went through the numbers one through ten, discussing all of the ways that each number related to our bodies, the world, the universe, etc. I am not sure if this is a phase that all teens go through, or whether I am particularly unusual in this regard. In either case, life is now far too busy to contemplate such esoteric things, but this photo does remind me that there are some underlying mathematical principles that underlie the beauty of the botanical world.
A 2007 article in the online magazine Science News discusses “The Mathematical Lives of Plants” (2018 review — the linked page is now subscription only, but the content can be found elsewhere by searching for the article title). This article explains plant parastichy, or the number of clockwise versus counterclockwise spirals found in many plants, and points out that these numbers are almost always two consecutive Fibonacci numbers. The Fibonacci sequence is composed of a series of numbers in which each number is the sum of the previous two: 1, 1, 2, 3, 5, 8, 13, and so forth. This sequence can also mathematically describe the spiral formed by unfurling ferns, and in this case the unfurling Heliotropium angiospermum. Scientists have been puzzling over this phenomenon since at least the 19th century. Only fairly recently has major progress been made on why plant development should follow the Fibonacci sequence. According to the article, the answer lies in the placement of newly forming primordia. A primordium is an organ or tissue in its very early stages of development; in plants, the primordia appear as little bulges that will later form leaves, roots, flowers or other plant parts depending on their type. These primordia absorb the hormone auxin, which promotes their growth. It has been deduced that as each primordium is formed, it grows in a location furthest from the other primordia so that it may obtain the most auxin. The pattern created by initiating each primordia as far from its neighbours as possible results in patterns, such as the Fibonacci sequence.
Heliotropium angiospermum is commonly called scorpions-tail, in reference to the way that its inflorescence curls open. The inflorescence bears two matching rows of tiny flowers. Scorpions-tail is a small perennial shrub that is native to Florida, Texas, and much of Mexico and the Caribbean. It is touted as an excellent plant for pollinator gardens, as it blooms profusely much of the year. That being said, the overall shrub is rather straggly and does not bring to mind the order and mathematical precision elicited by the close-up photo of its bloom. For an image that shows more of the plant, see Selg@Flickr’s photograph.
One person who apparently hasn’t allowed maturity and responsibility to compromise the wonder he finds in the natural world is Charles Jencks, who has designed and built the “Garden of Cosmic Speculation” in Scotland. This garden is half serious and half tongue-in-cheek. Garden vignettes represent black holes and quarks; a cascade explains the history of the universe. This garden does not feature Heliotropium angiospermum, or even that many plants, but instead uses spectacular grading and sculpture to explore the ideas of fractals, quarks, and other cosmic phenomena. The Garden of Cosmic Speculation opens only one day per year, but can be explored virtually through Charles Jencks’ website: Garden of Cosmic Speculation.