Renata Raidou and Marwin Schindler from the Research Unit for Computer Graphics won the Best Short Paper Award together with Aleksandr Amirkhanov at this year’s Eurographics Workshop on Visual Computing for Biology and Medicine, from September 20-23, 2023, in Norköpping, Sweden.

Their paper Smoke surfaces of 4D Biological Dynamical Systems shows how they enhanced their approach ManyLands to visualize and compare paths in 4D systems using smoke surfaces. ManyLands is a visualization tool designed to aid domain scientists in analyzing complex multi-dimensional biological systems. This enhancement is crucial as it offers a clearer, more distinct visualization of multiple paths and how they evolve from different initial conditions. This enhancement is vital for more precise analysis, facilitating a deeper understanding of the systems’ behavior and sensitivity to initial conditions.

Abstract

To study biological phenomena, mathematical biologists often employ modeling with ordinary differential equations. A system of ordinary differential equations that describes the state of a phenomenon as a moving point in space across time is known as a dynamical system. This moving point emerges from the initial condition of the system and is referred to as a trajectory that “lives” in phase space, i.e., a space that defines all possible states of the system. In our previous work, we proposed Many- Lands [AKS∗19]—an approach to explore and analyze typical trajectories of 4D dynamical systems, using smooth, animated transitions to navigate through phase space. However, in ManyLands the comparison of multiple trajectories emerging from different initial conditions does not scale well, due to overdrawing that clutters the view. We extend ManyLands to support the comparative visualization of multiple trajectories of a 4D dynamical system, making use of smoke surfaces. In this way, the sensitivity of the dynamical system to its initialization can be investigated. The 4D smoke surfaces can be further projected onto lower-dimensional subspaces (3D and 2D) with seamless animated transitions. We showcase the capabilities of our approach using two 4D dynamical systems from biology [Gol11, KJS06] and a 4D dynamical system exhibiting chaotic behavior [Bou15].

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