Does the Fibonacci sequence really appear throughout nature?

Partly. Fibonacci numbers are well documented in the spiral arrangements of leaves, petals and seeds in many plants, a field called phyllotaxis. They are not a universal rule of growth, and many widely repeated examples, such as the nautilus shell, human proportions and art, are not supported. Even in plants, real specimens are messier than the textbook version. [1] [2]

The sequence runs 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, with each number the sum of the previous two. In sunflowers, seeds form two sets of spirals, one curving each way, and the counts are usually a pair of neighbouring Fibonacci numbers, such as 34 and 55 or 55 and 89. Pine cones show the same kind of paired spirals, and come in both clockwise-dominant and anticlockwise-dominant forms. A Nature article by Amar Klar notes that the numbers of petals, sepals and spirals in many plants follow the series. [1] [3]

Popular articles also point to fruit cross-sections, such as a five-pointed star in an apple, and to the cells of a pineapple. These are presented as common, though such accounts are less rigorous than the plant research. [4]

A 2016 crowdsourced study of 657 sunflowers, reported in Science, found that nearly one in five had non-Fibonacci spirals or patterns more complicated than previously reported, including near-Fibonacci sequences and other competing patterns. The report adds that plant biologists have not worked out a mechanistic model that fully explains how sunflower seed patterns arise. [3]

Mathematician Keith Devlin, quoted by Live Science, says the sequence is not a secret code governing the universe and that many plants do not follow it. He says the nautilus shell does not grow according to the sequence, and that links to the human body, art and architecture go from tenuous to fictional. He states that claims that the golden ratio is uniquely pleasing to the eye fail when tested. HowStuffWorks similarly cautions that a coincidence is sometimes just a coincidence, while noting the numbers appear often enough to reflect real patterns. [2] [5]

The cause is not settled. Klar describes two main hypotheses. The field model holds that existing primordia, the sites where new organs form, emit inhibitory biochemical fields that determine where the next one appears. The mechanical model holds that tissue mechanics and physical forces shape the pattern. Klar argues that neither yields easily testable predictions or convincing experimental support, and that both explain only how an established pattern continues, not how it starts. [1]

Klar proposes a third idea: an asymmetric cell division, in which one daughter cell can divide at once while the other must wait one extra cell cycle, would produce cell numbers matching the Fibonacci series. He presents it as a theoretical proposal and says the challenge is to link such divisions to actual patterns and design tests to distinguish the models. His small check of pine cones, 20 dexter and 17 sinister from one tree, fits his prediction of equal proportions, but it is a minimal sample. [1]