Radical Impressionist: A Mathematician Paints

The Wise Photo App is available on the iPhone or iPad to apply overlays of 'rules' to your photographs or painting images on the device. Some examples applied to a well-known painting image are provided below. But there's a caveat that took me a while to figure out completely. The app changes the proportion of the photo to fit the grid as explained below.  (I even communicated with the main technician about this; he said that he didn't expect someone to apply two types of grids to the same photo. I was interested in comparing a dynamic symmetry grid with a PHI grid to see the difference. But more than this though is the changes made to the image provided unless it fits exactly a certain proportion). I've experimented with the Wise Photo App at length and it's great fun!! Here's a link to order it:  https://apps.apple.com/us/app/wise-photos/id1406085029  (the first two rules are free from apple; otherwise it costs a few dollars) for the iphone or the ipad. An

A Brief Presentation of Several Compositional Armatures with Examples from Historic Paintings: Rule of Thirds PHI Grid Golden Triangle Dynamic Symmetry Expanded Dynamic Symmetry Harmonic Armature Fibonacci Spiral Vanishing Point Grid Informal Subdivision Golden Mean "Caliper" System Orthogons Divisions into Fifths (Kimberly Elam) Introduction As a Mathematician, I have become intrigued with several Armatures used by current and historic artists. In this post I have applied the armatures to several historic paintings. I wanted to analyze the armatures further. Which ones seem most helpful? I have tried to choose examples by artists that consciously utilized the given armatures. I may use one example for now, but have to select the most appropriate for this analysis.  Many historic paintings have used a complex design scheme consisting of more than one armature, but I will begin with a simple armature.  But for example some classical works were based on combinations of Root 2,

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) 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.  It's best to use the PHI/Golden Triangle/Spiral 'grids' for golden rectangle proportions and the Dynamic Symmetry Grid for other formats. Note that formats other than 3:4 crop the images somewhat (or sometimes a lot) with the Dynamic Grid in this App. Moreover, the only additional aspect ratios handled by the Dynamic Grid need t