Original abstract oil painting, 30 inches by 30 inches, 2011
A somewhat abstracted and fanciful painting of a vector field. Of course there is (to my knowledge) no non-abstracted way to paint a vector field. This particular vector field features patterns from liquid crystal physics, along with the general div, grad and curl + cross and dot product definitions, and the non-chiral terms of the Frank elastic free energy for liquid crystals (twist, splay, and bend deformation contributions). The first thing the hubs said when he saw it was “ooooh, nabla!”
A scalar field is simply a space with a quantity assigned to each point. Each set of coordinates pulls up a value for the field in addition to a location in the space. A vector field is populated with vectors. Each set of coordinates pulls up a vector magnitude and direction. Many of the features of nematic liquid crystals are described in terms of where the molecule (or optical or dipolar) axes point on average, how uniformly they point, and how the pointing direction varies in a liquid or solidified material. Vector fields come in handy.
There are also tensor fields. I’d have to really put my painty thinking cap on to tackle a tensor field.
Painted using a series of dripped washes to create a richly colored and textured background. Hints of a grid and obscured vectors were painted on and solvent was used to loosen their forms. Plain paint and gel impasto were used to finish adding the arrows, equations, and the twist blend splay schematics. Another artist suggested including equations. For this painting I think they work. (and I still remember this stuff!)
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