Smoke Surfaces of 4D Biological Dynamical Systems

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dc.contributor.authorSchindler, Marwinen_US
dc.contributor.authorAmirkhanov, Aleksandren_US
dc.contributor.authorRaidou, Renata Georgiaen_US
dc.contributor.editorHansen, Christianen_US
dc.contributor.editorProcter, Jamesen_US
dc.contributor.editorRenata G. Raidouen_US
dc.contributor.editorJönsson, Danielen_US
dc.contributor.editorHöllt, Thomasen_US
dc.date.accessioned2023-09-19T11:31:52Z
dc.date.available2023-09-19T11:31:52Z
dc.date.issued2023
dc.description.abstractTo 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].en_US
dc.description.sectionheadersStorytelling and Communication
dc.description.seriesinformationEurographics Workshop on Visual Computing for Biology and Medicine
dc.identifier.doi10.2312/vcbm.20231217
dc.identifier.isbn978-3-03868-216-5
dc.identifier.issn2070-5786
dc.identifier.pages93-97
dc.identifier.pages5 pages
dc.identifier.urihttps://doi.org/10.2312/vcbm.20231217
dc.identifier.urihttps://diglib.eg.org:443/handle/10.2312/vcbm20231217
dc.publisherThe Eurographics Associationen_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Human-centered computing -> Scientific visualization; Applied computing -> Life and medical sciences
dc.subjectHuman centered computing
dc.subjectScientific visualization
dc.subjectApplied computing
dc.subjectLife and medical sciences
dc.titleSmoke Surfaces of 4D Biological Dynamical Systemsen_US
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VCBM 2023: Eurographics Workshop on Visual Computing for Biology and Medicine