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...

 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...

  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 ...