Biological Sciences

Fossil study sheds light on famous spirals found in nature

A 3D model of a 407-million-year-old plant fossil has overturned thinking on the evolution of leaves. The research has also led to fresh insights about spectacular patterns found in plants.

Fibonacci spirals in the leaves of a monkey puzzle tree
Fibonacci spirals in the leaves of a monkey puzzle tree

Leaf arrangements in the earliest plants differ from most modern plants, overturning a long-held theory regarding the origins of a famous mathematical pattern found in nature, research shows.

The findings indicate that the arrangement of leaves into distinctive spirals, that are common in nature today, were not common in the most ancient land plants that first populated the earth’s surface.

Instead, the ancient plants were found to have another type of spiral. This negates a long held theory about the evolution of plant leaf spirals, indicating that they evolved down two separate evolutionary paths.

Nature's Secret Code

Whether it is the vast swirl of a hurricane or the intricate spirals of the DNA double-helix, spirals are common in nature and most can be described by the famous mathematical series the Fibonacci sequence.

Named after the Italian mathematician, Leonardo Fibonacci, this sequence forms the basis of many of nature’s most efficient and stunning patterns.

Spirals are common in plants, with Fibonacci spirals making up over 90% of the spirals. Sunflower heads, pinecones, pineapples and succulent houseplants all include these distinctive spirals in their flower petals, leaves or seeds. 

Why Fibonacci spirals, also known as nature’s secret code, are so common in plants has perplexed scientists for centuries, but their evolutionary origin has been largely overlooked.

Based on their widespread distribution it has long been assumed that Fibonacci spirals were an ancient feature that evolved in the earliest land plants and became highly conserved in plants. 

Holly-Anne Turner the first author of the study started this project as a Plant Science Honours student
Holly-Anne Turner the first author of the study started this project as a Plant Science Honours student

Digital Reconstruction of a Plant Fossil

However, an international team led by the University of Edinburgh has overthrown this theory with the discovery of non-Fibonacci spirals in a 407-million-year old plant fossil. 

Using digital reconstruction techniques the researchers produced the first 3D models of leafy shoots in the fossil clubmoss Asteroxylon mackiei – a member of the earliest group of leafy plants.

The exceptionally preserved fossil was found in the famous fossil site the Rhynie chert, a Scottish sedimentary deposit near the Aberdeenshire village of Rhynie.

The site contains evidence of some of the planet’s earliest ecosystems – when land plants first evolved and gradually started to cover the earth’s rocky surface making it habitable.

The findings revealed that leaves and reproductive structures in Asteroxylon mackiei, were most commonly arranged in non-Fibonacci spirals that are rare in plants today.

Evolution of Plant Spirals

This transforms scientists understanding of Fibonacci spirals in land plants. It indicates that non-Fibonacci spirals were common in ancient clubmosses and that the evolution of leaf spirals diverged into two separate paths.

The leaves of ancient clubmosses had an entirely distinct evolutionary history to the other major groups of plants today such as ferns, conifers and flowering plants.

The team created the 3D model of Asteroxylon mackiei, which has been extinct for over 400 million years, by working with digital artist Matt Humpage, using digital rendering and 3D printing. 

The research, published in the journal Science, was funded by UK Research and Innovation (UKRI), The Royal Society and the German Research Foundation. 

The study also involved researchers from, University College Cork, Ireland, University Münster, Germany and Northern Rogue Studios, UK.


Our model of Asteroxylon mackiei lets us examine leaf arrangement in 3D for the first time. The technology to 3D print a 407-million-year old plant fossils and hold it in your hand is really incredible. Our findings give a new perspective on the evolution of Fibonacci spirals in plants.

Dr Sandy HetheringtonEvolutionary Palaeobiologist and Project Lead , School of Biological Sciences 


The clubmoss Asteroxylon mackiei is one of the earliest examples of a plant with leaves in the fossil record. Using these reconstructions we have been able to track individual spirals of leaves around the stems of these 407 million year old fossil plants. Our analysis of leaf arrangement in Asteroxylon shows that very early clubmosses developed non-Fibonacci spiral patterns.

Holly-Anne TurnerFirst Author of the study, Former Undergraduate Student, School of Biological Sciences

Related Links

Leaves and sporangia developed in rare non-Fibonacci spirals in early leafy plants, Science

Sandy Hetherington