Radical Impressionist: A Mathematician Paints

Santa Fe River Turbulence, with Dynamic Symmetry Armature, 10x16.  (golden ratio) Notes: (in progress: return again from time to time to see additions or modifications) 9/15/25: Edited a bit.  For example, the Wise Photo App Dynamic Symmetry Grid now works properly with a 2 to 3 proportion image (AR 1.5) since SLR cameras use this proportion. 5/15/23:    Added "Golden Rectangle" to the title to emphasize that this post is about the golden PHI proportion. Added an image with the Rule of Thirds superimposed over a PHI grid for the viewer to see the difference visually. Removed comment about other proportions since they are not represented in this post. Removed the Wise Photo App version of the Dynamic Symmetry grid applied to this golden proportioned painting since it distorted the size in its downloaded version.  In the App, it's best to use the PHI/Golden Triangle/Spiral 'grids' for golden rectangle proportions and the Dynamic Symmetry Grid for 3 to 4 or 2 to 3 ...

Notes I am beginning a series of shorter posts. Each post will concentrate on one topic and in an order such that they will build on each other. The series is open-ended but they will begin with topics on composition.  The underlying mathematics will be explained where ever possible or at various points. Introduction  I want to preface this post with my usual 'disclaimer'. When I first began to paint I wanted to make sure that the left-side of my brain didn't take over, which -as a Mathematician- it's prone to do; I wanted to be expressive !  However, as the years went by I couldn't avoid seeing how often mathematics entered into discussions of composition, for example. So I decided to spend time investigating for my own self the symbiotic relationship of math and art. My usual approach to a painting now is to start off analytically, with measurements and thoughts about proportions and unequal measures, and perspective in the landscape and the direction of light and...