Flow Simulation with Vortex Elements

Flow Simulation with Vortex Elements

Mark Stock (Independent artist, scientist and programmer, USA)
DOI: 10.4018/978-1-4666-0942-6.ch002


While fluid flow is a ubiquitous phenomenon on both Earth’s surface and elsewhere in the cosmos, its existence, as a mathematical field quantity without discrete form, color, or shape, defies representation in the visual arts. Both physical biology and computational physics are, at their roots, very large systems of interacting agents. The field of computational fluid dynamics deals with solving the essential formulas of fluid dynamics over large numbers of interacting elements. This chapter presents a novel method for creating fluid-like forms and patterns via interacting elements. Realistic fluid-like motions are presented on a computer using a particle representation of the rotating portions of the flow. The straightforward method works in two or three dimensions and is amenable to instruction and easy application to a variety of visual media. Examples from digital flatwork and video art illustrate the method’s potential to bring space, shape, and form to an otherwise ephemeral medium. Though the rules are simple, the resulting behavior frequently exhibits emergent properties not anticipated by the original formulae. This makes both fluid simulations and related biological computations deep, interesting, and ready for exploration.
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Particle Simulations

Very simple systems of interacting elements can produce non-deterministic, emergent behavior. Conway created a set of rules governing the life cycle of a square pixel in a grid (a cellular automaton): it becomes “alive” if exactly three of its 8 neighbors are alive, survives if two or three are alive, and dies otherwise (Gardner, 1970). Despite the simplicity of these rules, this “Game of Life” generates a remarkable diversity of behaviors—such as the Gosper Glider Gun seen in Figure 1 (Britton, 2011)—and is still the subject of active research forty years after its creation. A limitless number of cellular automata are possible, though most research focuses on emergent behavior of simple rule sets (Wolfram, 2002).

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