Steady visualization of the dynamics in fluids using εε-machines

The visualization of unsteady scientific data is still a challenging problem. Most techniques rely on the animation of individual time-steps. In this paper we propose a steady visualization of the dynamics in fluids using εε-machines. εε-machines are a concept from computational mechanics and can be thought of as finite state machines that can be visualized as directed graphs. The nodes are the causal states of the process. Given a local past of a position, causal states comprise all the information needed to predict the future of this position. As causal states stem from information theory, it can be shown that they are the most compressed representation of local dynamics that still allows for this prediction. Edges in the graph indicate transition probabilities between causal states in successive time-steps. Hence, the visualization of the εε-machine graph provides a concise and highly compressed steady visualization of the system's dynamics that still allows for an in-depth examination. In this paper we describe the construction and visualization of εε-machines and how interaction mechanisms with the physical domain allow for a detailed analysis of data sets describing fluid dynamics.