Line into Color, Mesh into CFD

Painter Helen Frankenthaler's work has been on my mind since seeing the exhibition Fluid Expression: The Prints of Helen Frankenthaler at Fort Worth's Amon Carter Museum of American Art earlier this week. While there I also purchased and then read John Elderfield's book on her painting, Line Into Color, Color Into Line. Both left me with a much stronger appreciation for her work.

As often happens to me, certain concepts, ideas, or statements about art trigger analogies to my work in computational fluid dynamics and mesh generation. Such was the case when Frankenthaler was quoted in the book as saying

I felt more and more that the drawing should come from what the shapes of the colors are; rather than, "I am arranging this with lines or confinements or patterns." And I do very much believe in drawing, especially when it doesn't show as drawing... When I talk about drawing, I mean "how are you getting your space," not where the pencil is going.

To put that quote in context, the book's theme was how Frankenthaler exercised three types of lines (drawn lines, the perimeter of regions of color, and the edge of the canvas) to great effect in her paintings that are more typically known for their ethereal washes of color - poured, stained, painted or otherwise.

Helen Frankenthaler, Sesame, 1970. source

But first a bit of background. Within the world of computational fluid dynamics, the mesh is the digitalized version of the object around which you wish to solve the equations of fluid motion - digitalized so the computer can understand it. Think of it as the scaffolding on which the fluid will be simulated. In the illustration below (image source), the mesh lines around a ship's hull define where the computations will be performed.

When the equations of fluid motion are solved on the mesh, the results are often presented as graphical contours of a some property of the fluid like pressure as shown below on the ship's hull (image source). In this picture, red represents high pressure and blue represents low pressure.

The analogy I'm making between Frankenthaler's paintings and computational fluid dynamics is lines are meshes and color is the CFD results. When she says "drawing should come from what the shapes of the colors are" I hear the case for mesh adaptation (closely coupling the mesh to the actual flow of fluid instead of just the geometry). When she says she believes in drawing "especially when it doesn't show as drawing" I hear the case for "invisible" mesh generation (because meshing is not and end unto itself, only a means to an end). Regardless of whether we're talking about lines in terms of mesh or lines in terms of boundaries of the regions of color, it's true that the mesh is how you're getting your space, the space within which the simulation will be performed.

Other than the fluidity with which she applies pigment to canvas, there's little that visually ties her paintings to CFD (the images above make this clear). The drawn lines in Sesame don't look anything like lines in a mesh and the regions of color don't look much like fluid flow. But it's Frankenthaler's process and approach and her way of thinking about the interplay of line and color, mesh and CFD, creating and defining space, that brings art and science, a bit closer, at least in my mind.