The Fibonacci-ness of Plants

The Fibonacci sequence provides provocative insights into how numbers relate to nature's creative process.

Fibonacci Sequence

Plant growth is governed by the Fibonacci sequence, which can be understood as a law of accumulation. The sequence is created by adding one number to the one before it to find the next in the sequence, beginning with 0 and 1:

0 — 1 — 1 — 2 — 3 — 5 — 8 — 13 — 21 — 34 — 55 — 89 — 144 ...

In effect, the sequence describes how things grow, building and multiplying according to what's already there. This growth by accumulation is reflected in how trees branch, flowers form, and ferns unfurl.

(All plant growth follows along the Fibonacci sequence; however, you will sometimes find multiples of a Fibonacci number, such as a 4-petaled flower—a double 2—and of course, natural variation does occur!)

Phyllotaxis (Leaf Arrangement)

The Fibonacci sequence governs the placement of leaves along a stem, ensuring that each leaf has maximum access to sunlight and rain. If you look straight down along a stem, the leaves (or branches) emerging from it will spiral such that when you count from one leaf to the one that lines up directly below it, the number of leaves between them and the number of times that group of leaves spirals around the stem will both be Fibonacci numbers.

This same principle is at work in the formation of pine cones, sunflowers, pineapples, and cacti. All have a double spiral structure that allows their smaller elements (seeds, for instance) to pack closely and efficiently. Look at the middle of a sunflower: you will see that the seeds line up in crisscrossing spirals radiating from the center, and if you count the number of spirals turning in each direction (clockwise/counterclockwise), they will always be Fibonacci numbers.

(For more on phyllotaxis, see the resources list below.)

Fibonacci and the Golden Ratio

The Fibonacci sequence relates directly to the golden ratio, nature's perfect proportion. If you divide one Fibonacci number by the number before it to find their ratio, the farther we move down the sequence, the closer it approximates the golden ratio, 1.618.

2/1 = 2

3/2 = 1.5

5/3 = 1.666...

8/5 = 1.6

13/8 = 1.625

21/13 = 1.615...

34/21 = 1.619...

55/34 = 1.617...

Visually, we can see how the growth of the Fibonacci sequence as a progression of squares mirrors a golden rectangle and its golden spiral:

Emerging fern fronds make this same spiral.

We find a wondrous correlation between nature's law of growth and its most beautiful and harmonious proportion.

Putting it all together

Cristobal Vila's "Nature by Numbers" is a beautifully rendered visualization of the Fibonacci sequence in nature.

The role of the Fibonacci sequence in the growth of plants is a compelling example of the unifying order behind creation. These patterns permeate the universe, reminding us that the same swirling energy is shaping ferns, sunflowers, whirlpools, spinning galaxies, and our own DNA.

Learn more:

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