Authors: Marwin Schindler, Aleksandr Amirkhanov, Renata Georgia Raidou
Venue: VCBM 2023
DOI: https://doi.org/10.2312/vcbm.20231217
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 ManyLands—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 and a 4D dynamical system exhibiting chaotic behavior.
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BibTeX
@inproceedings {10.2312:vcbm.20231217,
booktitle = {Eurographics Workshop on Visual Computing for Biology and Medicine},
editor = {Hansen, Christian and Procter, James and Renata G. Raidou and Jönsson, Daniel and Höllt, Thomas},
title = {{Smoke Surfaces of 4D Biological Dynamical Systems}},
author = {Schindler, Marwin and Amirkhanov, Aleksandr and Raidou, Renata Georgia},
year = {2023},
publisher = {The Eurographics Association},
ISSN = {2070-5786},
ISBN = {978-3-03868-216-5},
DOI = {10.2312/vcbm.20231217}
}