The mathematics of avalanche size and frequency follows a power law that can be simulated to
a first approximation by any system that exhibits self-organized criticality (SOC). In “How
Nature Works”" Per Bak reports a simplified model of a sandpile that he, Chao Tang, and Curt
Wiesenfeld developed that shows SOC, the so-called BTW model. Bak also mentions that
Grassberger describes a representation of this model that is fanciful but equivalent to the
BTW model. Imagine an N-by-N grid of office desks and a bureaucrat sitting at each. A folder
is randomly assigned to one desk. The bureaucrat does nothing until four or more folders are
on his desk at which time he sends one to each of his four nearest neighbors. Any bureaucrat
sitting at the edge of this array throws a folder out the window if there is no desk to send
it to. Sometimes, adding one folder can cause multiple redistributions of folders as one
bureaucrat’s actions causes neighbors to exceed three folders, which then ripples through
the office. In principle, just adding one new folder might involve redistribution at every
desk, sometimes multiple times.
The screen after approximately 5000 avalanches.
I’m working on new ways of being able to create and run models in html5 browser-technologies that we used to build with Java and wanted to see how hard it would be to convert one of Bob’s NetLogo models. The avalanche/bureaucrat model was a good first choice because it only uses the patches feature of NetLogo and not turtles.
While it would take a good deal more work to make a whole authoring environment that would be effective and productive for non-professional programmers I think this is a very successful proof-of-concept. At this point I think it would be relatively easy to convert a model that had turtles also.
Seth Tisue, the lead NetLogo developer contributed both Bureaucrats-fast a simplified re-write of Bureaucrats.v6 that runs about 20 times as fast as the original and a version of the model algorithm written in straight Scala Bureaucrats.scala. The speed of the Scala version should be comparable to the speed of a native Java adaptation.
A Google Spreadsheet is available with more complete Avalanche2D-JS Benchmarks comparing the performance of the model and the model, visualization, and grapher in Scala and NetLogo and on various browsers and operating systems including Android and iOS tablets and smartphone systems.
Self-Organised Criticality References
- Review of: How Nature Works: The Science of Self-Organised Criticality, Per Bak, New York, NY: Copernicus Press 1996
- Self organized criticality in earth systems By Stefan Hergarten, page 94
- On the avalanche size distribution in the BTW model
- Wikipedia: Self-Organised Criticality