Network Ecologies

Rebecca Norton: Affine Sketches

The Affine Sketches, dating back to 2009, began Rebecca Norton's investigation into various delineated mappings visualizing fields of color vectoring in an ungrounded space of a painting.

Using new geometries and perspectival arrangements, the paintings disrupted habits of vision by joining movements not usually connected in a painting’s traditional visual field. Rather than relying on mimetic impressions and a description of objects, the paintings affirm the potential of imaginative experimentation for the sake of the imagination. They allow the viewer to sense connective or synthesizing processes specific to our perception of the material and physical properties of a painting, offering a window into virtual potentials from which we can think about movements from which our world has unfolded.


Rebecca Norton explores actions and intuitions of intermediacy—what she describes as “a feeling of being suspended in the middle stages of a process. “In her work, representations of people, places and things are mapped with affine geometry—a structure which, for her, models moments of transition. These mathematical transformations chart “free” movements of objects by approximating motion in succession and by delineating spaces of in-betweeness. 

Norton’s first affine sketches (2009) were composed as visual reference to help her understand Felix Guattari and Gilles Deleuze’s use of the term “affine” in their their 1972 publication Anti-Oedipus: Capitalism and Schizophrenia. Norton was most interested in how affine geometry was posed to suggest a “matrix of the world,” and how a (woman’s) body may express an equivalence of this geometry. 

“…Levi Strauss’s kinship atom—with its four relationships; brother-sister, husband-wife, father-son, maternal uncle-sister’s son—presents itself as a readymade whole from which the mother as such is strangely excluded, although, depending on the circumstances, she can be more or less a kinswoman or more or less an affine in relation to her children. Now this is indeed where the myth takes root, the myth that does not express but conditions. As Griaule relates it, the Yourougou, breaking into the piece of placenta he has stolen, is like the brother of his mother, with whom he is united by the fact: “This individual went away into the distance carrying with him a part of the nourishing placenta, which is to say a part of his own mother. He saw this organ as his own and as forming a part of his own person, in such a way that he identified himself with the one who gave birth to him. She was the matrix of the world, and he considered himself to be placed on the same plane as she from the viewpoint of the generations…” -Guattari and Deleuze, Anti-Oedipus: Capitalism and Schizophrenia, p. 157 

From 2009-2012, Norton’s primary interest was in visualizing and composing affine geometry in painting as seen fit for Deleuze. Compositions outlined with affine mappings trace a “ground” within which colors are arranged. Deleuze’s allusive references to the body—as surface of inscription and as the “magical agent” that “acts as if it produces [all things]”—has, for Norton, been a suitable way to think about painting and it is through this idea of a body that she situates the experience of painting. 

To better observe the mathematical and pragmatic nature of affine geometry, Norton partnered with programmer Eddie Elliot. Together they produced Sticks—an interactive site that allows users to see various translations of space following the rules of parallelism that apply to affine geometry. 

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