It’s not rare for mathematical sequences to be used in the art world. After all, many artists are deliberate in how they organize their pieces in order to design a more appealing structure.
One distinct yet somewhat unfamiliar sequence for many is the Fibonacci Sequence; praised in the mathematics world for creating the “perfect spiral”, the Fibonacci Sequence can be seen in multiple settings like the arts, but how has the beloved pattern elevated artworks since its discovery?
What is the Fibonacci Sequence?
First discovered by Leonardo of Pisa (aka Leonardo Fibonacci) in the early 13th century, the Fibonacci Sequence is a Math sequence in which each value is the sum of the two preceding values.
SEQUENCE
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
This ongoing list is represented as a sequence. Sequences can only occur because of rules/formulas which help determine their pattern.
RULE
x_n = x_n-1 + x_n-2
How does the Fibonacci Sequence create such perfect spirals?
The Fibonacci sequence uses what is widely regarded as the Golden Ratio: a number at approximately 1.618 which acts as the multiplier for each value in the sequence.
The Golden Ratio is only an approximate approaching value, meaning that there is a small margin of error for each calculation. Despite this, there is a notable decrease in error as the value increases! Let’s look at an example using some of our larger values in the sequence.
EXAMPLE
…13, 21, 34, 55…
13 x 1.618 = 21.034
21 x 1.618 = 33.978
34 x 1.618 = 55.012
The results were pretty close, huh!? Because the Golden Ratio is the consistent multiplier in the Fibonacci Sequence, the spiral will only grow in size without disrupting the pattern of the sequence.
How Can we Find the Fibonacci Spiral in Art Pieces?
Although the Fibonacci Sequence is profound in nature, it is also highly valued in the art community. In fact, many artists regard the “perfect spiral” as being aesthetically pleasing to the human eye. Take a look at some of these famous art pieces which utilize the Fibonacci Sequence!
Whilst the spiral is not explicitly present in many works, artists have cautiously followed the Rule of Thirds: Separating a portrait or painting into three parts to allow the subject of the piece to be focused in one or two of the three frames rather than simply being centered.
This strategy aids the use of the Fibonacci Spiral, ultimately creating a balance of tranquility in the image and therefore developing a more flowy feel.
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