View of Samantha Thomas’s exhibition “Texture/Parameter,” 2013; at LAXART.

Abstract painting's meteoric rise to the sine qua non of modern art history was less linear than erratic, a trajectory aptly charted earlier this year in MoMA's "Inventing Abstraction." If such grand surveys aim to reveal the history of a period by mapping it expansively, Los Angeles-based artist Samantha Thomas mines the canon of abstraction by working intensively, creating canvases that quote from a century-long history of modern art while questioning some its most hallowed assumptions through a sly use of materials.

The works (all 2013) in Thomas's exhibition "Texture/Parameter" were mostly easel-size and installed salon-style on one wall, with two larger pieces nearby. They venture down a path of familiar citations: actual tangled and matted yarn alludes to Pollock's skeins, a tilted frame conjures Mondrian's lozenges, a vertical band pays homage to Newman's zips. The artist's most explicit interlocutor is Kazimir Malevich, whose early 20th-century Suprematist paintings of nearly monochromatic squares—each offset just enough so as not to merely echo the canvases' shape, but rather to exist as an autonomous form—became the stuff of avant-garde legend. Today, the once-austere surfaces of Malevich's squares—especially the famous black ones—are cracking; the deleterious effects of corrosion and decay have qualified the work's promise of truth as embodied in geometry. Thomas intimates as much in two works, each the chromatic inversion of Malevich's black-on-white schema. The raw canvas of Texture/Parameter #12 hides an egg carton, resulting in a bulging, spectral grid. Texture/Parameter #20 is plagued with holes, the result of the canvas having been burned.

While some narratives of abstract art celebrate the purging of figural references in favor of pure line and color, Thomas's work strongly suggests the body in a variety of ways. After all, latent within proposed narratives of abstraction's purely "optical" experimentation was always its shadowy other: the sense of touch. For Thomas, the canvas is far from flat, and materials form an entry point for testing a range of textures. In some pieces, oil and acrylic are built up and smoothed over so as to take on a quality of vinyl or latex. In addition to creating these more synthetic effects, Thomas is persistent in her use of coarse vegetal fibers: burlap, linen and rope.

Several cruciform reliefs appear wilted and slightly slouching, evoking not a universal language of forms, but rather the course of gravity and age. Elsewhere, the canvases seem to sprout appendages. In Texture/Parameter Study #2, vertical bands of vermilion flank a section of burlap, its raised seam suggesting both the bumpy flesh of scar tissue and the curvature of the human spine. Thomas's vocabulary of orifices and sinewy coils, conjuring Eva Hesse and others, invites further bodily associations: a bulky girth of rope becomes entrails, the creasing and wrinkles of linen a protruding navel.

Ambitious in scope, "Texture/Parameter" portended to take on a modernist art history, but it most successfully considers the temporality of a distinctly bodily register: the rhythms of fecundity and rot. Thomas seems to understand that exploring abstraction's parameters is less about interdicting the possibilities of canvas than marshaling its excesses.