Originally, I planned for this lesson to be about the principle of design *patterns*. However, I started to go down the Golden Ratio and Fibonacci Sequence rabbit hole, and quickly realized it needed it’s own lesson. Hope you find this information as fascinating as I do!

### What is the Fibonacci Sequence?

One of the most common patterns in nature is the Fibonacci Sequence (also, known as the “Golden Ratio”). This mathematical pattern is found throughout nature. It creates a spiral. This spiral is the same one found in a the curl of a fern, and in a spiral galaxy. I will admit, that like many artists before me, I did have a period of time where I was obsessed with this spiral. Suddenly, I saw it everywhere. A great thing about knowing this spiral, is that you can then easily get the shapes of pine cones and sunflower seeds correct.

### Yes, Okay, But what *IS* the Fibonacci Sequence?

The Fibonacci Sequence is a series of numbers that builds up on itself. You take the two most recent numbers in the sequence and add them together. You have to start with a 0 and a 1. The sequence looks like: (0) 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. This plain math line doesn’t really tell us what this *looks* like. For that, here is a quick video I made to show you.

## How to Use the Fibonacci Sequence

One way artists can use the Fibonacci sequence is by creating compositions that follow this golden ratio, (which is a proportion of 1.618). This proportion is found in many natural objects, such as seashells, flowers, and even human faces. To use the golden ratio in your artwork, you can divide your canvas or paper into sections that follow the ratio of 1:1.6. This can create a sense of balance and harmony in your composition.

Another way artists can use the Fibonacci sequence is by creating spirals or curves that follow the sequence. For example, a Fibonacci spiral is a logarithmic spiral that expands outward at a constant rate. Each quarter turn of the spiral is based on the next number in the Fibonacci sequence, creating a spiral that grows according to the sequence. Artists can use these spirals in their work to create a sense of movement and flow.

The Fibonacci sequence is used to understand the spirals in sunflowers and pinecones. To make these, layer many spirals on top of each other, all starting from the same point, and half of them spiraling in the opposite direction.

Artists can also use the Fibonacci sequence to create patterns or designs that repeat in a sequence of Fibonacci numbers. For example, a pattern that repeats every five or eight units can create a sense of harmony and balance in your artwork. (The 5 and the 8 came from the sequence of numbers. As a reminder, they are, 1, 1, 3, 5, 8, 13, 21, 34, 55, 89, etc.)

## Using Fibonacci for Composition

Artists can use the Fibonacci sequence as a tool to help them decide on the placement and proportions of elements in their composition. By using the sequence to divide up the space on your canvas or paper, you can create a composition that is balanced and visually pleasing.

Artists have used the “golden ratio” for centuries. The first mention of this spiral was in 300 BCE by Euclid in his work on geometry and mathematics. The term “golden ratio” didn’t start until the 1800s. However, we see that nature seems to have used it from the beginning of time (or maybe shortly after).

The “Rule of Thirds” is a simplification of this ratio.

The Fibonacci sequence is a powerful tool for artists to use in their work. By understanding the principles of the sequence, artists can create compositions that are harmonious, balanced, and visually pleasing. Whether you are a painter, sculptor, or graphic designer, the Fibonacci sequence can help you take your artwork to the next level.