### Whirling Squares Spiral

The light grey squares are marked off within this rectangle. They form what are called the whirling squares. Note that in a golden rectangle with aspect ratio 1.618... a smaller golden rectangle is formed with the part left over after constructing the square. And this continues as we 'whirl' around.

https://en.wikipedia.org/wiki/Fibonacci_sequence:

In mathematics, the **Fibonacci sequence** is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as **Fibonacci numbers**, commonly denoted *F _{n}* . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are:

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

The blue spiral is called a whirling squares' spiral, formed by quarter circles within the squares constructed within this golden rectangle. This spiral approximates the mathematical definition of the Golden Spiral, which is a logarithmic spiral with growth factor PHI. An excellent resource showing the relationship between a Golden and the Whirling Squares' spiral is https://en.wikipedia.org/wiki/Golden_spiral#Approximations_of_the_golden_spiral. For more information on the Golden Mean visit the Bibliography post in this blog.

One especially informative image is:

https://en.wikipedia.org/wiki/Golden_spiral#/media/File:GoldenSpiralLogarithmic_color_in.gif. This is a dynamic 'gif', where you can see the spirals moving.

Here's a snapshot:

This diagram shows how close the Fibonacci Whirling Squares' Spiral is to the Golden Spiral!: