Whirling Squares Spiral

Construction of the 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 Fn . 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.

Whirling Squares (with 'eye' at lower right)

We often use Fibonacci numbers as lengths for our canvases; eg, 5x8", 8x13" and multiples of the 5x8: 10x16" and 15x24" (near-PHI paintings, where PHI is the golden mean - 1.618...).

Now we superimpose the spiral on our golden rectangle dynamic symmetry armature; this it the armature we are using for our near-PHI paintings.


The blue spiral is called a whirling squares' spiral, formed by quarter circles within the squares constructed within this golden rectangle with aspect ratio 1.618... 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 digram shows how close the Fibonacci Whirling Squares' Spiral is to the Golden Spiral!:



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