Rudyard Kipling may have told us how the leopard got his spots, but it was mathematician and father of computer science Alan Turing who showed how patterns in nature come from a chemical reaction.

Inspired by Turing, West Windsor-based artist Andrew Werth, a former computer engineer, creates patterns in colorful abstract paintings that will appear in two area exhibitions opening this week. The first is “Energy in Mind” where he joins artists Jennifer Cadoff and Debra Weier at ArtTimesTwo Gallery at the Princeton Brain and Spine Institute on Alexander Road in Princeton Junction. The second is “Patterns & Meaning: Alan J. Klawans and Andrew Werth” at Artists’ Gallery in Lambertville.

During a recent visit to Werth’s home-based studio, the autumn leaves outside pale in comparison to his canvases. Gallery goers have seen Werth’s patterns and optical illusions since 2007, when he began winning awards from the Gallery at Mercer County Community College, Trenton City Museum at Ellarslie, the Philadelphia Sketch Club, and, most recently, at the Prince Street Gallery in New York.

Werth’s interests in psychology, philosophy, consciousness, perception, thinking and the self underlie the optical effects. “The titles of my paintings are clues to concepts that I find fascinating in the philosophy and science of mind,” says Werth.

“The I in Disguise,” “The Plasticity of Perception,” and “Approaching Equilibrium” — each painting seems to have its own inner light, beckoning the viewer inside. Trying to grasp it is a challenge. With undulating shapes and patterns, and highly detailed markings over an under layer, it’s near impossible to figure out how these could have been constructed. Following one path in a maze takes you somewhere else altogether.

When Werth comes across an idea in his readings, he writes it down for a possible painting. “I then try to figure out ways to suggest that idea in the painting through formal means, such as the use of color or shape. I don’t expect a viewer to know that and don’t need the viewer to be interested in cognitive science, since above all my goal is to make intriguing and compelling visual images.”

When ArtTimesTwo Gallery curator Madelaine Shellaby met Werth last year, the two began discussing ideas about the mind/body connection. The works by each of the artist in the exhibition, says Shellaby, “spark in the viewer an interest in questions of where does consciousness physically reside, what is its quantum texture, what is the quality of the energies that permeate mind and body, what is its relationship to the broadest range of existence.”

“Andrew is interested in the perceptual intricacies of embodiment, how our human experience is directly shaped by our bodies, with attention going back to the nature of our self-awareness and our awareness of the world around us,” says Shellaby.

Even before he started using Turing patterns, Werth writes, “I had been playing around with hand-drawn interweaving curves as a structural starting point for my paintings. After quite a bit of experimentation, I developed some techniques on the computer that let me turn a starting image into a balanced, positive/negative pattern that I later learned was essentially the same thing Turing had proposed.”

Sometimes the artist may start with a photograph, other times a random “seed” image. “Along the way I apply other transformations and adjustments to the image until I’m happy with the flow of the design.” The flow comes from a mixture of planning, intuition, and trail and error.

But the Turing patterns are just the starting point. Then come color and how the colors transition through the painting. The puzzle the artist sets himself up to solve, with positive and negative layers, has its roots in the thought challenging “Brainiac” puzzles he did as a child growing up with a market analyst father, stay-at-home mother, and a brother in central and northern New Jersey.

After the under painting is complete, Werth hand paints thousands of individual marks, using a maulstick to keep his hand steady, giving the images an optical depth. “The marks take much longer than the under painting,” he says.

Werth uses metallic pigments for a reflective quality. The paintings look different from different angles, and they seem to move and pulsate.

Vision impairment, or corrected vision, can also affect the way the paintings are seen. Werth had Lasik surgery to correct his vision a few years ago, and the doctor suggested leaving one eye slightly near-sighted to help with reading. But Werth didn’t like the effect. “My paintings didn’t work the same because the stereoscopic vision wasn’t crisp.”

“The colors we see are due to the pigmentation in our eyes as well as the neural structure of our brain,” he writes. “We generally think of vision as being like photography, where an entire image is presented to us at once.” But vision might better be compared to touch, he says, “since it is only through the continuous probing and movement of our eyes that we are able to construct the world around us.”

This approach is described in the term “enaction” coined by Francisco Varela, Evan Thompson, and Eleanor Rosch in “The Embodied Mind: Cognitive Science and Human Experience.” “The mind is not just a passive receiver of data,” says Werth, who has titled one of his paintings “Enaction.” “We have a spacio-temporal sense as we move through the world.”

After studying computer engineering and information networking at Carnegie Mellon, the New Jersey native worked in software development for Bellcore and CNET. When he rose to management, he missed the creative side, and so at age 29 decided to try something else.

Thinking he might like to study psychology or philosophy and go on to an academic career, he moved to Manhattan. There he got sidetracked by taking cooking classes at Peter Kump (now the Institute of Culinary Education) and art classes through the Art Students League.

He also took the Viewing Art Intelligently courses with Jon Zinsser at the New School from 2001 to 2009. Zinsser would give his students a list of exhibitions they should see, then discuss the influences on the contemporary art world. “That’s what got me in the museum and gallery-going habit,” says Werth.

Learning drawing, color theory, and landscape painting, his earlier works were representational. Even now, his studio includes a realistic portrait of his wife, Karen Yee, and a self-portrait. “I liked representational painting, but didn’t have that much fun that I’d want to do it professionally. The subjects I’m interested in are abstract.”

The 42-year-old artist took classes in abstract painting at Cooper Union and the 92nd Street Y. It reminded him of the maze drawings, or Brainiac puzzles.

During one of his classes in abstraction, while painting a still life, “in frustration I started doing marks in colors, and it triggered something in my brain. I was interested in perceptual things, and I developed my technique, learning by experimenting.”

Putting different colors next to one another could push something forward or back, he discovered. Using color gradients, the brain perceives a fading into the distance.

One of the biggest compliments Werth has received was at an opening of an exhibit at D&R Greenway’s Johnson Education Center, when a woman told him she felt as if she had in her dreams been to the place he painted.

Werth says, “As a software developer, most of what you write fades away, but I hope my paintings allow me to be a part of people’s lives for a long time.”

“Patterns & Meaning: Alan J. Klawans and Andrew Werth,” Artists’ Gallery, 18 Bridge Street, Lambertville, November 9 through December 2. Opening reception: Saturday, November 10, 3-6 p.m. www.lambertivillearts.com

“Energy in Mind,” ArtTimesTwo gallery at Princeton Brain and Spine Care Institute, along with the work of Jennifer Cadoff and Debra Weier, 731 Alexander Road, November through March, opening reception Thursday, November 8, 5-7 p.m. www.artimestwo.com

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