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Complexity Decomplexified: A List of 200+ Results Encountered Over 55 Years Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Rugged Landscapes and Timescale Distributions in Complex Systems

Authors : D. L. Stein, C. M. Newman

Published in: How Nature Works

Publisher: Springer International Publishing

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Abstract

We review a simple model of random walks on a rugged landscape, representing energy or (negative) fitness, and with many peaks and valleys. This paradigm for trapping on long timescales by metastable states in complex systems may be visualized as a terrain with lakes in the valleys whose water level depends on the observational timescale. The “broken ergodicity” structure in space and time of trapping in the valleys can be analyzed using invasion percolation, picturesquely in terms of “ponds and outlets” as water flows to a distant sea. Two main conclusions concern qualitative dependence on the spatial dimension \(d\) of the system landscape. The first is that the much-used example of a one-dimensional rugged landscape is entirely misleading for any larger \(d\). The second is that once \(d\) is realistically large (above \(6\) seems to suffice), there are many nonmerging paths to the sea; this may be relevant for the issue of contingency vs. convergence in macro-evolution.

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Metadata
Title
Rugged Landscapes and Timescale Distributions in Complex Systems
Authors
D. L. Stein
C. M. Newman
Copyright Year
2014
Publisher
Springer International Publishing
Book
How Nature Works

Print ISBN: 978-3-319-00253-8

Electronic ISBN: 978-3-319-00254-5

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-00254-5_4

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