Radical Impressionist: A Mathematician Paints

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  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. Whirling Squares (with 'eye' at lower right) My paintings often have Fibonacci number dime...

(Originally published Jan, 2019)  Everyone refers to Betty Edwards' book,  Drawing on the Right side of the Brain .  And I have to admit that it was an important book for me when I began to draw and paint seriously, in fact, so much so that it contributed to my efforts NOT to use the left side of my brain. But I was a Mathematician first and throughout my painting career I kept being bombarded with left-side ideas or logic. I couldn't escape it even if I tried. But I kept pursuing my need Not to allow logic to affect my painting. Finally this year I came to grips with the fact that I am driven by logic; I am an analyst first. And in fact I realized that for me, it's important to accept the logical part in order to grow as a painter.  So I determined that I would not discourage any left-brain ideas popping up while I paint.  And I would marry both sides of my brain perhaps to establish my brand as a painter-mathematician (or mathematician-painter). We all know th...

Golden Ratio Piedra Lumbre Piedra Lumbre II, 15x24, oil The Piedra Lumbre (shining stone) painting has a proportion that is approximately the golden ratio - or the golden mean, an irrational number, approximately 1.610287...., meaning continuing without end.  As an irrational number it cannot be expressed as a ratio of two integers.   I’ve done many paintings, with 10x16 dimension and a few at 15x24, and this 15x24, still with a ratio of 10/16 or 5/8. Note that these are two number in the Fibonacci sequence.  1,1,2,3,5,8, .... The radio of two consecutive numbers gets closer and closer to the golden mean as we progress through the sequence.  Try calculating:  5/3, 8/5/ 13/8, 21/13,... The golden mean is related to the golden spiral, a form found in nature everywhere since it in fact represents how growth takes form (think sunflowers, ferns, tree branches, Nautilus Shell). The ratio is thought to be the most pleasing to the eye, perhaps because it is so perv...