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Generalized Pythagoras Trees: A Fractal Approach to Hierarchy Visualization

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Computer Vision, Imaging and Computer Graphics - Theory and Applications (VISIGRAPP 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 550))

Abstract

Through their recursive definition, many fractals have an inherent hierarchical structure. An example are binary branching Pythagoras Trees. By stopping the recursion in certain branches, a binary hierarchy can be encoded and visualized. But this binary encoding is an obstacle for representing general hierarchical data such as file systems or phylogenetic trees, which usually branch into more than two subhierarchies. We hence extend Pythagoras Trees to arbitrarily branching trees by adapting the geometry of the original fractal approach. Each vertex in the hierarchy is visualized as a rectangle sized according to a metric. We analyze several visual parameters such as length, width, order, and color of the nodes against the use of different metrics. Interactions help to zoom, browse, and filter the hierarchy. The usefulness of our technique is illustrated by two case studies visualizing directory structures and a large phylogenetic tree. We compare our approach with existing tree diagrams and discuss questions of geometry, perception, readability, and aesthetics.

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Acknowledgements

We would like to thank Kay Nieselt, University of Tübingen, for providing the NCBI taxonomy dataset.

Author information

Authors and Affiliations

  1. VISUS, University of Stuttgart, Stuttgart, Germany

    Fabian Beck, Michael Burch, Tanja Munz & Daniel Weiskopf

  2. Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy

    Lorenzo Di Silvestro

Authors
  1. Fabian Beck
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  2. Michael Burch
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  3. Tanja Munz
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  4. Lorenzo Di Silvestro
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  5. Daniel Weiskopf
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Corresponding author

Correspondence to Fabian Beck .

Editor information

Editors and Affiliations

  1. Dip. di Matematica e Informatica, Università di Catania, Catania, Catania, Italy

    Sebastiano Battiato

  2. Inria/ZIRST, Saint Ismier, France

    Sabine Coquillart

  3. INRIA-Rennes/MimeTIC Tean, Rennes cedex, France

    Julien Pettré

  4. Swansea University, Swansea, UK

    Robert S. Laramee

  5. Computer Science, Linnaeus University, Växjö, Sweden

    Andreas Kerren

  6. do IPS, Escola Superior de Tecnologia, Setúbal, Portugal

    José Braz

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Beck, F., Burch, M., Munz, T., Di Silvestro, L., Weiskopf, D. (2015). Generalized Pythagoras Trees: A Fractal Approach to Hierarchy Visualization. In: Battiato, S., Coquillart, S., Pettré, J., Laramee, R., Kerren, A., Braz, J. (eds) Computer Vision, Imaging and Computer Graphics - Theory and Applications. VISIGRAPP 2014. Communications in Computer and Information Science, vol 550. Springer, Cham. https://doi.org/10.1007/978-3-319-25117-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-25117-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25116-5

  • Online ISBN: 978-3-319-25117-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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