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Kristin Holder can pick up a paintbrush or pencil and take it to a canvas, but most of what happens during the process is out of her hands. For Holder, the finished product is either determined by happy accident or mathematical equation.

From a distance, the installation Heavy Thinking (His View, Her View)—which appears on a wall at the Warehouse Gallery’s third floor as part of Holder’s exhibition, “The Last Next”—seems to be two imperfect geometric shapes floating on a weathered, pockmarked wall. Get closer, though, and you’ll see hundreds of lines measuring down the space of the wall, slowly dividing into smaller and smaller cubes.

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“It’s called a Menger Sponge. In theory, you could take a cube and subdivide it down until you get to the idea of a massless cube,” says Holder of the work. “It’s self-generated—the dimensions of the cube determine the divisions, and you can take it to infinity. I didn’t make any decisions about the distance between them or how high on the wall they would be. It was all predicated on the math.”

Heavy thinking, indeed. Though the formula for a Menger Sponge involves complicated mathematic symbols resulting in iterations of 20N, Holder insists the process is quite simple. “It’s like dividing the edges of a Rubik’s Cube,” she says.

The 34-year-old Georgetown artist, who received her MFA from American University in 1999, relies on trial and error, both of which are highly visible in the show. Her numbered works, 17, 8, and 32, depict her multiple attempts to paint the branches of a tree for that many days, each time in the same muted gray color. However, since the light and wind constantly change the tree, and since Holder mixes her paint fresh each day, the color and shape are never exactly the same. Look underneath the frame of the canvas, and you can see her notation of each day’s attempt.

“I’m showing you my failures,” says Holder. “From day to day, your point of view changes, as well as your patience with your skills. If I’m telling you that I’m looking at the same thing day after day and painting the same thing day after day, why isn’t it more accurate?”

Holder’s untitled works made of soot and shellac, rust, or ink are also the product of multiple attempts. Made by singeing a piece of paper held to a match above her head, then drawing naturalistic patterns on and around the burn mark, the works are especially delicate.

“The soot that accumulates when you burn the paper—if it gets touched, the drawing is ruined, so the durability of the drawing is not reliant on the drawing but how it’s handled,” says Holder. “There’s a lot of fumbles.”

But while chance—of fumbles, of where a match will land, of how the paint will mix, or in the case of one untitled work, how wetting the paper will produce attractive blue flecks against her gold dye—is a big part of her work, Holder doesn’t rely on it.

“I feel a certain resignation to what’s available for me to work with—the

parameters of what’s available to me physically,” says Holder. “It’s not the same kind of chance as throwing paint around. It’s more calculated.”

Calculated, literally. On the corner of some of Holder’s geometric drawings, you’ll see faded traces of a long division problem worked out by hand.

“The Last Next” is on view from 4 p.m. to 8 p.m. Thursdays and Fridays and 1 p.m. to 6 p.m. Saturdays and Sundays, to Sunday, Oct. 28, at the Warehouse Gallery, 1019 7th St. NW. Free. (202) 783-3933.