Tessellated Visions: An Interview

Tessellation Studies on View at Backdoor Studios

Editor’s note: In the interest of full disclosure, the subject in this story is the writer’s partner.

What are tessellations?

The quick answer is they are patterns of shapes, such as polygons, that fit together to completely cover a surface without any gaps or overlaps. These repeating patterns are found in mathematics, nature, art and architecture, with common examples including honeycomb structures in beehives, tiled floors and the artwork of M.C. Escher.

Designer, engineer and an artist, Douglas Johnson creates the unexpected with his kinetic, color-drenched tessellation paintings. Each one of his 12 works presents distinctive forms and personalities. Some flow and float on the canvas, as if rushing past you; others display angles, rendering foundation or structure. Only with close inspection will these works reveal intricate layers of certain repeated patterns. 

Tessellation Studies is on view at Cherry Wood’s Backdoor Studios through Sept. 4 

Douglas said his works represent mathematics. It started by experimenting with basic shapes. This led to a system for creating new forms. A shape cut out of one side of a square and placed on the other side gives a shape that tessellates as it did before the change, and no matter how complex the change, it continues to tessellate.

“This led to further exploration to find a more complex form and more complex rules that would lead to more interesting results,” the announcement read. “The work on display represents an attempt to demonstrate these concepts.” 

Douglas spoke to Random Lengths News about his works and what it is about tessellations that have kept him intrigued with creating them for nearly two decades.

“I’ve enjoyed the idea of tessellations and where it can go and how delicate it can get,” said Douglas. “The different possibilities of what a tessellation can be used for.”

At one point, the designer said he was even thinking that it could be used as a possible way to hold molecular engines together.

“If you can build your molecular engine into one of these forms that I’ve been working on, then they’ll hold onto each other and not drift apart.”

He noted that it’s not something he knows very much about, but one possible use for them is to be used for oil cleanup on oceans.

“I’m imagining all these individual, man-made, microscopic machines floating around the ocean, consuming oil and transforming it into a biodegradable byproduct. And they are just floating around so it would be good if they could be held together. I always meant to find somebody who works in this area to discuss it with them but I never have. The point is, I think there’s a use for what I’m doing, I just don’t know what. It’s a solution without a problem. But it’s a good solution so I’m looking for a good problem.”

Creating these was a fun project; Douglas enjoyed what he distilled it into, saying it’s an endless concept that has legs, where he can keep finding more variations of the idea.

His process starts with developing a new shape through sketching, then moving into 3D design software for fine tuning and to ensure a perfect fit from one instance to the next. The 3D design software affords the automatic repetition of the shape to fill space that he can then export into 2D design software for color studies and morphing the top layer to add visual drama. Line work gets transferred to the canvas, and finally he begins the process of filling in each shape with color. He mixes his own colors to match what he designed on the computer and modifies as needed. He aims to make the paint as flat as possible, minimizing any brush strokes. It’s a look that he strives for to make the shapes jump off the canvas.

“I look for color combinations that will shock the eye, so the form becomes the star,” he said. “Like a designer dress, the color is just there to accentuate the form. But I put a lot into the color choices so in some ways, as with a designer dress, the form becomes a vehicle for the color.”

Douglas is also a math fan. When asked if the mathematical aspect of this work seems like he’s working on a different or higher plane, he recalled approaching it with every bit of intellectual exercise he could muster, pushing his cognitive abilities, to come up with the tessellation form that he finally achieved. He thought he might have discovered a new wallpaper group, the mathematical term for the categories of form that make up all possible basic tessellations. He consulted with an expert, who said what he’s doing is a combination of two existing wallpaper groups.

“I enjoyed learning about that side of the idea of a tessellation and how seriously this stuff gets taken in some small circles,” he said. “There have been more than two people who have come up with new areas in that realm. A couple people came up with [the same new tessellation] simultaneously. That happens occasionally in mathematics. Oftentimes with science and math, something will be ripe for discovery and multiple people will make the same discovery simultaneously. Then they will publish right away and the … publishers will get the submissions at the same time from different parts of the world. It’s wild how that happens.”

In mathematical subject matter, which includes tessellations, Douglas said, it’s broken down carefully and is proven. Each wallpaper group is a different type of tessellation; There are approximately 17 or 19 different wallpaper groups (forms that can be repeated and create tessellations) that have been discovered up until a few years ago. He added there’s now two more, but it’s being debated if they are conventional wallpaper groups because “they’re kind of a different animal.” People that follow this regularly know each one by the number.

Tessellation designs

Like so many artistic endeavors, Douglas said, in terms of his designs something has to spark a reaction inside his head. 

“It’s a complex thing to figure out, because I can make a shape but it has to fit with another one next to it and they have to work together to be visually pleasing,” he said. “It takes a bit of massaging to make each shape that fits together [do so] in a way that’s pleasing to the eye.” 

It boils down to a lot of work. The initial idea is almost completely obscured by the work it takes to finish the form that will tessellate and look good, and be different from any one that happened before, he explained.

While creating and painting tessellations presents a worthy challenge, before Douglas started studying tessellations, he contemplated transferring them into 3D tessellations and what that could mean. He said he tried and tried, but couldn’t find a way to create a tessellation sculpture that made sense. 

“Other people have worked on this concept and the results are mixed but it’s really difficult to make something tessellate in three dimensions,” he said. “It’s fascinating to think about. It’s not impossible but it is another level of effort that I can try, maybe after I’ve retired to ponder endlessly. It’s an area that I haven’t gotten bored with. There are different directions [that] I can go, within the same vein and other things I can do with it.”

Something Douglas likes to do intellectually, but doesn’t often get a chance to do, he said, is to take a concept and just stay with it. 

“In my work as an engineer, I start out with a concept and carry it through until it’s ready to build and then I transfer the plans to someone else to build it. To accomplish that I’ve got to carry that piece of furniture in my head until it’s done — [then] someone comes by and says ‘hello’ and it’s gone,” he quipped. “Really it’s not that big a deal.” 

This is how Douglas came up with these works, he was able to take an entire weekend to just figure it out. 

“I’d like to make it clear that I’m not a fine artist,” Douglas said. “I know how to paint a great painting like a traditional landscape or a still life but I’m not good at it. What I’m doing is a representation of a mathematical concept. I try to make it as fun as I can for myself and the viewer but it’s mathematics, an obscure area of mathematics at that. People seem to respond to it from an artistic perspective and a mathematical concept.” 

Tessellation Studies

Time: 5 to 9 p.m., closing reception Sept. 4 and Thursdays, Saturdays 12 to 5 p.m.

Cost: Free

Details: Contact: Cherry Wood on Instagram @cherrysgalleryon7th. Or Douglas Johnson @dougified

Venue: Backdoor Studios, 374 W. 7th St., San Pedro