“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

– Benoit Mandelbrot, introduction to The Fractal Geometry of Nature

At this time of year many of the trees and shrubs in our landscapes are mere skeletons of their summer glory. Their beautiful canopies of leaves have been shed and they provide little visual interest. Unless you look a bit closer…


This is actually a great time to observe the branching patterns of deciduous trees. A closer look reveals that they are eerily similar to our own vascular and respiratory systems. As each system goes from the main trunk to the larger limbs to the smaller branches and then the twigs we see the same fractal branching that occurs in the network of blood vessels in our lungs. How incredible that such like systems are actually performing a reverse process. Trees are taking in our exhaled carbon dioxide and releasing oxygen (O2) into the atmosphere.  In turn, we inhale that O2 rich air into our lungs where it travels through the increasingly smaller vessels until it reaches the capillaries where it passes through into our bloodstream. As the oxygen-rich blood travels through our body our cells use the oxygen and release CO2 back into the bloodstream where it travels back to our lungs before releasing CO2 as we exhale.


The important thing to remember is that for both of these systems to work well they need to cover a large surface area and fractal branching is the most efficient way for that happen. Fractal branching is a pattern that repeats itself in either larger or smaller scales, each step looking like a copy of the same overall shape. These patterns are called self-similar and are found in many areas in nature from trees to rivers and many more. Ferns are a great example of a self-similar fractal as each pinnate leaf is a miniature version of the larger frond that it branches off from although natural branching fractals do not go on infinitely as mathematical fractals can. Remember the Fibonacci Sequence from your high school math class?


Most of the fractals that we are familiar with and see on a regular basis fall into the category known as spiral fractals. Spiral fractals are responsible for some of the most beautiful forms that can be found in nature. Many galaxies are spiral fractals. The marine animal known as the Nautilus is perhaps one of the most well-known examples of the spiral fractal. But there are also so many spiral fractals that we encounter in the plant kingdom on a daily basis.

Ferns exhibit fractal properties in two ways. The uncurling of a new fiddlehead in the spring is a lovely example of a spiral fractal while a mature Japanese Painted fern (Athyrium niponicumn) pictured above shows the self-similar pattern of a branching fractal.

The Monkey Puzzle tree (Araucaria araucana)  has a most interesting growth pattern with each branch a continuing spiral of tough, scale-like leaves. Although native to Chile and Argentina, these images are of a specimen that is located on the Long Island campus of Hofstra University.

Closer to home are some plants that are in many of our gardens during the summer season. The compact spirals of Stonecrop, also known as Sedum, help to form the tight clusters of thick leaves that give it its distinguishing look. I always love the way that dew or rain collect in the in little cups that are formed.

Sunflowers (Helianthus annuus), Gerbera (Gerbera) daisies, and Coneflowers (Echinacea purpurea) show their spirals on a grand scale.

Decorative cabbage and kale (Brassica oleracea) are seasonal plants that bring their cold-resistant beauty to our fall landscaping and thus complete a full year of natural fractals that can be found all around us .


Susan Pelton