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 dimensions ; eg, 5

  Taos Gorge Fusion, 20x16, oil We did not use a Dynamic Symmetry Armature during the design of this painting. We decided to analyze the design against an armature to see how the painting could be improved - or not. First we layered a Dynamic Symmetry Armature plus Rebated Squares on the painting as is: Taos Gorge Fusion with Dynamic Symmetry++ Armature Visit Karen's website to read the Description of this painting.In the description we remark on the inspiration artists have derived from this gorge's configuration; it does lend itself to analysis via an armature.  However, we 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. We do see an alignment of edges of the canyon with the armature. We also note the parallel of the river with a reciprocal line.  But we decided

 In my quest to learn everything about how we can use an iPhone effectively when setting up for a Plein Air Session, I learned a lot. I hope what I have learned can be as helpful to my readers as it has been for me. I wrote this post while staying in San Diego near my son's house in Jan 2023. I took the photo of the view from the back patio.  I just read through the post (Jun 11) and rather then try to perfect it, I think it has enough useful information to publish the post.  June 11, 2023: published. iPhone Editing/Cropping and Aspect Ratios Tip #1. iPhones automatically take photos at a 9x12 (horizontal) or a 12x9 (vertical) ratio  This is well-known, but I mistakenly have tried to edit a photo to my desired measurements incorrectly.  This leads me to .. Tip #2. The edit/crop tool provides a set of aspect ratios  that you may use to adjust and crop your image (see arrow). You many watch a short uTube video illustrating this also:  https://www.youtube.com/watch?v=1Q6euEpcqDc . The

6/10/23: Note that several of these paintings are in fact now planned for the exhibit.  Some were not (though I still have time to include them in the exhibit - which can be accessed with the qr-code or the link below it in the 5/27 update). 5/27/23 Update with QR-code for immediate access to the Exhibit on my website: Focus smart phone camera on this QR code to access my website's exhibit. You may also access the exhibit directly at: Radical Impressionist: A Mathematician Paints Exhibit 5/27/23 Changed painting titles to the current names reorganized in May by category, Chromatic Lands, Land Abstractions, Luminous Lands, Turbulent Lands, Turbulent Waters, Turbulent Winds. April 24, 2023: To prepare for the Los Alamos show this coming July, I am going to decide which of my current paintings best fit in with the theme of the show, Radical Impressionism: A Mathematician Paints. There are some obvious choices - either paintings of the Los Alamos Area or paintings I've analyzed alr