Phyllotaxis: Spiral & Fibonacci

Instructor: Brekke Peterson Munks
In this lesson, you'll explore the meaning of phyllotaxis, a term used in the plant world. You'll also learn how to identify a Fibonacci sequence and spiral, as well as some common examples found in nature.

Phyllotaxis and the Fibonacci Sequence

In botany and the plant world, the term phyllotaxis is used to describe the arrangement of flowers, leaves and seeds on a plant stem, an organizational pattern found in the Fibonacci spiral. The Fibonacci spiral is based upon the Fibonacci sequence, a set of numbers that follow a certain pattern, like the ones found on Pascal's triangle. The Fibonacci sequence consists of the following numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The general pattern of these numbers is simple: each term is the sum of the previous two numbers, with 1+1 equalling 2 and 8+13 equalling 21.

Pascals triangle
Pascals triangle

Fibonacci Spirals in Botany

As humans, we tend to look for symmetry and patterns to make sense of objects. Without realizing it our eyes are drawn to Fibonacci sequences, or in the case of a sunflower head, a Fibonacci spiral.

Fibonacci spiral pattern in a sunflower head
sunflower head

The Fibonacci spiral, also known as the golden angle, uses the same numerical pattern found in the sequence. For example, when counting spirals on a seed head, you may count 21 while moving to the right in a clockwise direction and 34 while moving to the left in a counterclockwise direction, both of which are Fibonacci numbers. Spiral arrangements can also be found in plant leaves, where you'll find very little overlap between the top and bottom leaves. Here, the number of clockwise and counterclockwise rotations around the stem, as well as the number of leaves passed along the way, may result in Fibonacci numbers.

In some plants, the number of petals will also be equal to a fibonacci number. For instance, asters and irises may have 21 and three petals respectively. Fibonacci patterns can also be found in tree branches, with two turns around an oak tree resulting in a count of five leaves. By comparison, three turns around a weeping willow tree may yield eight leaves.

Fibonacci spiral
fibonacci spiral

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