Mark Stock

“Mesh #3 Iso”

Digital archival print, 20" x 20" (frame) 12" x 12" (print), 2000.

Mesh #3 Iso illustrates a frame from the evolution of an initially-tetrahedral (non-physical) vortex sheet using a triangulated vortex method developed as part of the artist's dissertation research. Circulation is attached to the edges of the triangles, and triangles are split and merged to accommodate stretching and folding of the sheet. The ill-posedness of vortex sheet dynamics is suppressed in this simulation via regularization of the Biot-Savart kernel. The parallel projection and realistic rendering add two more layers to the real and unreal natures of the image.


Mark Stock, Research Scientist, Applied Scientific Research, Inc.

"All of my work depicts imaginary scenes that derive their complexity from the deceptively simple behavior of large numbers of independent actors/agents/particles/elements. The rules governing the action of each element are often based on primary natural and physical forces and can be described in a single mathematical statement or a few lines of code. Alone, each element emits a trivial and boring solution, like a single star floating motionless in space. Together, though, these elements create massively-complex galaxies of shapes and forms inspired by, and reflecting, the natural origin of their rules. This is the way of computational science: to break complex, real problems up into many smaller and easily solvable problems such that the ensemble predicts the behavior of the real system. That was my education, and is now my creative inspiration."

Other works by the artist

“Green Streamlines”

Digital archival print, 20" x 20" (frame) 12" x 12" (print), 2006.

Green Streamlines depicts individual traces through a vector potential field. The field is populated with random thick-cored vortex particles, and each path is created by integrating the Biot-Savart equation in both directions from an initially-random point. Barnes and Hut's multipole treecode algorithm is used to accelerate the calculations. My goal for this image was to allow appreciation of ubiquitous fluid forms by instantiating a small tangle of turbulence.


“Untitled #92”

Digital archival print, 20" x 20" (frame) 12" x 12" (print), 2007.

This sketch consists of thousands of lines drawn through a three-dimensional vector field. The data represents the vorticity at an intermediate stage of a simulation of vortex sheet motion at high Reynolds number. The initial strength of the spherical vortex sheet was set using potential flow theory such that the interior of the fluid volume had a uniform upward velocity. This is a common simulation in the study of three-dimensional vortex methods. A small random perturbation in every step of the space curve integration assists in finding stable "orbits" in the field, which show up as dark bands.