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.


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)

My paintings often have Fibonacci number dimensions ; eg, 5x8", 8x13" and multiples of the 5x8: 10x16" and 15x24" (near-PHI paintings, where PHI is the golden mean - 1.618...). 13x21 and even 21x34 are dimensions to be exploited in the future.

For these (near) PHI paintings I like to begin my design with a golden spiral superimposed on a dynamic symmetry armature, taking advantage of the benefits of both diagrams:

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!:

Popular posts from this blog

Color Wheel Revisited

(extra) Color Mixing on the web with online Apps with RGB and CMYK

(extra) Color Palette Examples