Patterns with square and compass

I found a pattern after I painted this 5″ x 9″ sketch. Something pulled  my eye to the left edge. It seems too empty and not enough was happening.  I drew with white pencil on the sketch with a square and a compass and found  I could make a cube root rectangle ( 1 x 1.732+ ) grow from a square if I cropped the left edge slightly. I will use this new proportion when I paint the full size painting of these Chilean mountains.
Our eyes look first for simple stable proportions like the square, the double, the half, or the third. Our eye takes the height and tries to fit it in to the length in even numbers. When we can’t do that are eyes continue to move searching for a fit, giving a sensation of movement. I have found rectangles proportioned to √ and √3 ( square root and cube root) can give a sense of motion.
I made a square root rectangle ( 1 x  1.4142+ ) by making a square and drawing its diagonal. I pinned the compass in the lower left corner of the diagonal of the square, and set it to the length of the diagonal. I arced a line down from the top left corner to the extended base line of the square. the rectangle is completed by a vertical drawn drawn at that point.
As the square root  rectangle came from the square by means of the diagonal, so the cube root  rectangle grows from diagonal of the square root rectangle.The motivating force that turns the square from a seeming blank into a living dynamic space is the diagonal. The diagonal to the square is endowed with the energy to create new spaces.
I also found that the height of the white spot that represents the sun was located by a diagonal line of the cube root rectangle crossing the first vertical line of the square. I felt something and reacted to it before I knew why. Seeing, drawing and painting are a way of knowing before words and numbers.
This is the completed 18″x32″ acrylic painting ‘Las Torres Del Paine’