Movatterモバイル変換

[0]ホーム
URL:

Skip to main content

Advertisement

Springer Nature Link
Log in

Generalized Pythagoras Trees: A Fractal Approach to Hierarchy Visualization

  • Conference paper
  • First Online:

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.

This is a preview of subscription content,log in via an institution to check access.

Access this chapter

Similar content being viewed by others

References

  1. Andrews, K., Heidegger, H.: Information slices: visualising and exploring large hierarchies using cascading, semicircular disks. In: Proceedings of IEEE Symposium on Information Visualization, pp. 9–11 (1998)

    Google Scholar 

  2. Balzer, M., Deussen, O., Lewerentz, C.: Voronoi treemaps for the visualization of software metrics. In: Proceedings of Software Visualization, pp. 165–172 (2005)

    Google Scholar 

  3. Battista, G.D., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs (1999)

    MATH  Google Scholar 

  4. Benson, D.A., Karsch-Mizrachi, I., Lipman, D.J., Ostell, J., Sayers, E.W.: Genbank. Nucleic Acids Res.38(suppl 1), D46–D51 (2010)

    Article  Google Scholar 

  5. Bosman, A.E.: Het wondere onderzoekingsveld der vlakke meetkunde. N.V. Uitgeversmaatschappij Parcival, Breda (1957)

    Google Scholar 

  6. Burch, M., Konevtsova, N., Heinrich, J., Höferlin, M., Weiskopf, D.: Evaluation of traditional, orthogonal, and radial tree diagrams by an eye tracking study. IEEE Trans. Vis. Comput. Graph.17(12), 2440–2448 (2011)

    Article  Google Scholar 

  7. Burch, M., Raschke, M., Weiskopf, D.: Indented pixel tree plots. In: Proceedings of International Symposium on Visual Computing, pp. 338–349 (2010)

    Chapter  Google Scholar 

  8. Carrière, S.J., Kazman, R.: Research report: interacting with huge hierarchies: beyond cone trees. In: Proceedings of Information Visualization, pp. 74–81 (1995)

    Google Scholar 

  9. Devroye, L., Kruszewski, P.: The botanical beauty of random binary trees. In: Proceedings of Graph Drawing, pp. 166–177 (1995)

    Chapter  Google Scholar 

  10. Eades, P.: Drawing free trees. Bull. Inst. Comb. Appl.5, 10–36 (1992)

    MathSciNet MATH  Google Scholar 

  11. Grivet, S., Auber, D., Domenger, J., Melançon, G.: Bubble tree drawing algorithm. In: Proceedings of International Conference on Computer Vision and Graphics, pp. 633–641 (2004)

    Google Scholar 

  12. Holton, M.: Strands, gravity, and botanical tree imaginery. Comput. Graph. Forum13(1), 57–67 (1994)

    Article  Google Scholar 

  13. Jürgensmann, S., Schulz, H.J.: A visual survey of tree visualization. In: IEEE Visweek 2010 Posters (2010)

    Google Scholar 

  14. Kleiberg, E., van de Wetering, H., van Wijk, J.J.: Botanical visualization of huge hierarchies. In: Proceedings of Information Visualization, pp. 87–94 (2001)

    Google Scholar 

  15. Koike, H.: Generalized fractal views: a fractal-based method for controlling information display. ACM Trans. Inf. Syst.13(3), 305–324 (1995)

    Article  Google Scholar 

  16. Koike, H., Yoshihara, H.: Fractal approaches for visualizing huge hierarchies. In: Proceedings of Visual Languages, pp. 55–60 (1993)

    Google Scholar 

  17. Kruskal, J., Landwehr, J.: Icicle plots: better displays for hierarchical clustering. Am. Stat.37(2), 162–168 (1983)

    Google Scholar 

  18. Lin, C.C., Yen, H.C.: On balloon drawings of rooted trees. Graph Algorithms Appl.11(2), 431–452 (2007)

    Article MathSciNet  Google Scholar 

  19. Machado, P., Cardoso, A.: Computing aesthetics. In: de Oliveira, F.M. (ed.) SBIA 1998. LNCS (LNAI), vol. 1515, pp. 219–228. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Mandelbrot, B.: The Fractal Geometry of Nature. W.H. Freeman and Company, New York (1982)

    MATH  Google Scholar 

  21. McGuffin, M., Robert, J.: Quantifying the space-efficiency of 2D graphical representations of trees. Inf. Vis.9(2), 115–140 (2009)

    Article  Google Scholar 

  22. Nocaj, A., Brandes, U.: Computing voronoi treemaps: faster, simpler, and resolution-independent. Comput. Graph. Forum31(3), 855–864 (2012)

    Article  Google Scholar 

  23. Peitgen, H.O., Saupe, D. (eds.): Science of Fractal Images. Springer, New York (1988)

    Google Scholar 

  24. Reingold, E., Tilford, J.: Tidier drawings of trees. IEEE Trans. Softw. Eng.7, 223–228 (1981)

    Article  Google Scholar 

  25. Rosindell, J., Harmon, L.: OneZoom: a fractal explorer for the tree of life. PLOS Biol.10(10), e1001406 (2012)

    Article  Google Scholar 

  26. Schulz, H.J.: Treevis.net: a tree visualization reference. IEEE Comput. Graph. Appl.31(6), 11–15 (2011)

    Article  Google Scholar 

  27. Shneiderman, B.: Tree visualization with tree-maps: 2-D space-filling approach. ACM Trans. Graphics11(1), 92–99 (1992)

    Article  Google Scholar 

  28. Stasko, J.T., Zhang, E.: Focus+context display and navigation techniques for enhancing radial, space-filling hierarchy visualizations. In: Proceedings of the IEEE Symposium on Information Visualization, pp. 57–65 (2000)

    Google Scholar 

  29. Ware, C.: Information Visualization, Second Edition: Perception for Design (Interactive Technologies), 2nd edn. Morgan Kaufmann, Burlington (2004)

    Google Scholar 

  30. Wertheimer, M.: Untersuchungen zur Lehre von der Gestalt. II. Psychol. Res.4(1), 301–350 (1923)

    Article  Google Scholar 

  31. Wetherell, C., Shannon, A.: Tidy drawings of trees. IEEE Trans. Soft. Eng.5(5), 514–520 (1979)

    Article  Google Scholar 

  32. Wilson, E.O.: Biophilia. Harvard University Press, Cambridge (1984)

    Google Scholar 

  33. Yang, J., Ward, M.O., Rundensteiner, E.A., Patro, A.: InterRing: a visual interface for navigating and manipulating hierarchies. Inf. Vis.2(1), 16–30 (2003)

    Article  Google Scholar 

Download references

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

    You can also search for this author inPubMed Google Scholar

  2. Michael Burch

    You can also search for this author inPubMed Google Scholar

  3. Tanja Munz

    You can also search for this author inPubMed Google Scholar

  4. Lorenzo Di Silvestro

    You can also search for this author inPubMed Google Scholar

  5. Daniel Weiskopf

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence toFabian 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

Rights and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

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

Download citation

Publish with us

[8]ページ先頭
©2009-2025 Movatter.jp