Radical Impressionist: A Mathematician Paints

Much literature exists about how Plato and Pythagoras approached numbers and measurements as can be seen in my post of references. But I will use as my reference here the book written in the 1970's by Morris Kline, a friend of mine from my graduate school years. I used his definitive textbook, Mathematical Thought from Ancient to Modern Times *  for a required course that I taught at NYU: " Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these — the search for beauty . Mathematics is an art, and as such affords the pleasures which all the arts afford." A newer version exists:   Mathematics for the Non-mathematician . Another book by Kline: Mathematics of Certainty. He considered Pythagoreans 'superficial' but they did develop two very important doctrines (pg 15): Nature is built according to mathematical principles. Number relations underly, unify and

In November-December of 2020 I continued a series of High Desert Color paintings, more colorful and abstract than previous paintings. This is the tale of one of the paintings, once titled "Hope on the Horizon" to accompany the new era in our country, to illustrate hope that soon we will be able to travel again.  I find solace in painting. It's a magical life. But I changed the title to Prismatic Spectrum. Stages of "Prismatic Spectrum (aka,Hope on the Horizon)", 9x12, oil I. Initial Wash The palette used is my usual Cobra Water-based Oil palette, prismatic from Cad yellow Light through different oranges and reds, mixed purple (cobalt blur plus permanent rose), blues  (cerulean blue hue, cobalt blue, ultramarine blue and greens (viridian and sap) as well as yellow ochre and burnt sienna. A brush was used primarily for this initial wash to establish the range of values (color-based). One can see touches of paper towel in the sky.  In addition, one can see palette

 I've been experimenting with the palette knife, perhaps using it as if it were a pastel stick, layering colors on top of previous colors to create a new color perhaps. For this post I will use or demonstrate a 3-color palette of a red, blue and a yellow to create 'all' colors. The specific colors I will be using are: Cobra Water-Mixable Oils - Madder Lake (R), Ultramarine Blue (B) and Permanent Yellow Light (Y) and Titanium White (W). The initial plein air layer was painted at the foot of the Catalina Mountains near Tucson. I then used my mountains, the Santa Rita Mountains, in my back yard to refine the painting. This might be the final version for this first example after applying several layers (click to enlarge to see the texture): Details for texture: Catalina Mountain Foothill Painting Site: And the painting while onsite. My painting buddies really liked this at that time.Perhaps I should have left it alone. But the dark shadows on the mountain bothered me. And the s

Notes Under Construction Recently I became aware of an interest in the study of turbulence in paintings. Googling turbulence in paintings leads to several sites with artists from Leonardi da Vinci to Van Gogh and Jackson Pollack. For example*, "a mathematical analysis of the works of Van Gogh reveals that the stormy patterns in many of his paintings are uncannily like real turbulence, as seen in swirling water or the air from a jet engine".  Some Links of Interest   Painting with Turbulence:  https://www.npr.org/sections/13.7/2015/04/01/396637276/van-goghs-turbulent-mind-captured-turbulence https://tigerprints.clemson.edu/cgi/viewcontent.cgi?article=3292&context=all_theses - a master's thesis, very technical involving simulations. But it includes information about the history of the term, turbulence, in art beginning with Leonardi da Vinci: "More than five hundred years ago, Renaissance artist and engineer Leonardo da Vinci identified turbulence as a distinct n

 Turbulence Series: Hillsides Documentation of the development of a larger scale painting of Turbulent Hillsides in the High Desert of New Mexico. I have been painting a series of works titled High Desert Colors. They use the prismatic colors seen here in the high desert, perhaps pushed to emphasize the full color palette. Several paintings are currently (Dec 2020) in the Marigold Arts Gallery on Canyon Road in Santa Fe, NM. They can also be seen on my website,  www.karenhalbert.com . The very first in the series (I: sold) was inspired by a painting by Lois Griffel in her excellent Impressionist Landscapes' book, based roughly on her Sunny Day Marsh (with the water removed). Some of the inspiration came from paintings by Erin Hanson, Open Impressionist ( https://www.erinhanson.com/ ), Her use of exaggerated color, bold mosaic of patterns and thick brushwork is very attractive to me.  Her colors are built from a limited palette of red, blue and yellow. I have experimented with such

What does Mathematics have to do with Art? There's no connection. Right!?? But isn't Mathematics all around us in the environment?  I would say that the answer is a resounding "YES!". Mathematics underlies the patterns found everywhere in nature and this influences our paintings. A funny thing happened while becoming an artist and landscape oil painter (after my first careers as a Mathematician and Computer Programmer). I noticed how often the 'bibles' of painting included chapters on design and what I perceived as mathematical elements: aerial perspective, dimensionality, proportions, unequal measures, patterns and motif, self-similarity, informal sub-division, symmetry, dynamic symmetry, the golden mean, etc..  Then terms like fractals, Mandelbrot, self-similarity and fibonacci series began to crop up everywhere. Almost 20 years after beginning my painting journey I realize that it has brought me full-circle back to my roots in mathematics. And my paintings