Smoke Surfaces of 4D Biological Dynamical Systems

Information

• Publication Type: Conference Paper
• Workgroup(s)/Project(s): not specified
• Date: September 2023
• ISBN: 978-3-03868-010-9
• Publisher: The Eurographics Association
• Lecturer: Marwin Schindler
• Event: EG VCBM 2023
• Editor: Höllt, T. and Jönsson, D.
• DOI: 10.2312/vcbm.20231217
• Booktitle: VCBM 2023: Eurographics Workshop on Visual Computing for Biology and Medicine
• Pages: 5
• Conference date: 20. September 2023 – 22. September 2023
• Pages: 93 – 97
• Keywords: rendering, Human-centered computing, scientific visualization, Applied computing, Life and medical sciences

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 [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].

Additional Files and Images

Weblinks

• Entry in reposiTUm (TU Wien Publication Database)
• DOI: 10.2312/vcbm.20231217

BibTeX

@inproceedings{schindler-2023-sso,
  title =      "Smoke Surfaces of 4D Biological Dynamical Systems",
  author =     "Marwin Schindler and Aleksandr Amirkhanov and Renata Raidou",
  year =       "2023",
  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 [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].",
  month =      sep,
  isbn =       "978-3-03868-010-9",
  publisher =  "The Eurographics Association",
  event =      "EG VCBM 2023",
  editor =     "H\"{o}llt, T. and J\"{o}nsson, D.",
  doi =        "10.2312/vcbm.20231217",
  booktitle =  "VCBM 2023: Eurographics Workshop on Visual Computing for
               Biology and Medicine",
  pages =      "5",
  pages =      "93--97",
  keywords =   "rendering, Human-centered computing, scientific
               visualization, Applied computing, Life and medical sciences",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2023/schindler-2023-sso/",
}