Radical Impressionist: A Mathematician Paints

 Scroll down for construction steps for the basic dynamic symmetry. In ascending order of aspect ratio: Construction Example: Step 1: main diagonals and one reciprocal (perpendicular to the 'baroque' diagonal) Step 2: main diagonals and all 4 reciprocals. Note the red x indicating a possible focal point. Final Step: horizontals and verticals through the intersections of the diagonals and their reciprocals. See also: blog post on the Spiral:  https://karenhalbert.blogspot.com/2023/06/whirling-squares-spiral.html Whirling Squares Spiral: We superimpose the whirling squares' spiral onto the Dynamic Symmetry Armatures for PHI* rectangles, as indicated in the following diagram: *or near-PHI such as 10x16, 15x25, 5x8, 8x13

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...

  Taos Gorge Fusion, 20x16, oil I did not use a Dynamic Symmetry Armature during the design of this painting. I decided to analyze the design against an armature to see how the painting could be improved - or not. First I layered a Dynamic Symmetry Armature plus Rebated Squares on the painting as is: Taos Gorge Fusion with Dynamic Symmetry++ Armature Visit my website to read the Description of this painting. In the description I remark on the inspiration artists have derived from this gorge's configuration; it does lend itself to analysis via an armature.  However, I can see several points to make: if the brightness of the sky is to be a focal point, it's not close to our usual focal points: the intersections of diagonals and their reciprocals.  In fact, though, perhaps a better focal point would be within the gorge itself. I do see an alignment of edges of the canyon with the armature. Also note the parallel of the river with a reciprocal line.  But I decided to ana...

  June 5, 2023: Updated with new title, Painting in Los Alamos-2022. Sept 2022: I am participating in a Paint Out in Los Alamos, Sept 20-22, 2022 with a group from the Plein Air Painters of New Mexico.  A show of the paintings from the paint out will be held at the Fuller Lodge in Los Alamos from Sat, Sep 24 - Oct. 8, 2022.  See  https://www.papnm.org/2022-Los-Alamos-Nonjuried-Paintout-and-Show I wanted to prepare for the event by scouting out the locations, taking photographs and perhaps doing painting studies, using composition tools described elsewhere on this blog. I have included here my attempt at a painting and then my preparatory studies of a similar scene. Note that I took part in the same paint out 4 years ago, so in fact I know the spots I want to paint. I will try to keep an open mind though in case another site seems promising. I painted at the White Rock Overlook then and intend to paint there again.  One scene I would love to paint are the cliffs ...

 I have completed two paintings of the Los Alamos Cliffs, titled Turbulent Lands I and II. A 15x25 panel with a partial Dynamic Symmetry Armature constructed on it has been waiting for me to do another version. I wanted to experiment with a few tools I now use, a squeegee and rubber foam shape among them - oh and yes, a trowel from the hardware store. Cliffs lend themselves to painting with straight edges. I did use these tools on paintings that needed work a few weeks ago (as well as the Turbulent Lands II) and these are the paintings I decided to title Land Abstraction I and II. . Steps for this new painting without comment: