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Exactly 50 years after the US-American meteorologist Edward Lorenz
(remember the "butterfly effect
"?), the topic is still as fascinating as ever. A new visualization technique developed at the University of Vienna helps to make chaos visible to the naked eye.
The vibratory states of a dynamical (chaotic) system could to date only be visualized with methods requiring several graphs that are hard to interpret for non-mathematicians. Now a working group led by biophysicist Christian Herbst
from the Department of Cognitive Biology
, University of Vienna, has developed a new method for documenting chaotic phenomena: the phasegram. This novel approach, created in collaboration with chaos expert Hanspeter Herzel
from the Charité in Berlin, Germany, can visualize symptoms of systems "on the way to chaos" in a single graph. The method, which is being published in Royal Society Interface, allows for the intuitive interpretation of chaotic or nearly chaotic phenomena, and thus makes the fascinating world of chaos theory more accessible to the scientific community.
Herbst CT, Herzel H, Svec JG, Wyman MT, Fitch WT. 2013 Visualization of system dynamics using phasegrams. J R Soc Interface 20130288. doi:10.1098/rsif.2013.0288
- Please follow the link for an open source (i.e. free) PDF version of the manuscript.
Download our press release in English (PDF
or Word document
) or German (PDF
or Word document
). The press release contains an easily-digestable explanation of the phasegram method. The analyzed signal
and the images contained in the press release can be downloaded separately (Fig. 1
, Fig. 2
and Fig. 3
). You can also download a biography (English
) and a portrait image
of Christian Herbst from this web site.
prototype for creating phasegrams, written in Python, is available from this web site. Please make sure you read the contents of the file readMe.txt
carefully before installing/running the software.