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- W2049453807 abstract "The National Academy of Sciences convened an Arthur M. Sackler Colloquium on “Self-organized complexity in the physical, biological, and social sciences” at the NAS Beckman Center, Irvine, CA, on March 23–24, 2001. The organizers were D.L.T. (Cornell), J.B.R. (Colorado), and Hans Frauenfelder (Los Alamos National Laboratory, Los Alamos, NM). The organizers had no difficulty in finding many examples of complexity in subjects ranging from fluid turbulence to social networks. However, an acceptable definition for self-organizing complexity is much more elusive. Symptoms of systems that exhibit self-organizing complexity include fractal statistics and chaotic behavior. Some examples of such systems are completely deterministic (i.e., fluid turbulence), whereas others have a large stochastic component (i.e., exchange rates). The governing equations (if they exist) are generally nonlinear and may also have a stochastic driver. Many of the concepts that have evolved in statistical physics are applicable (i.e., renormalization group theory and self-organized criticality). As a brief introduction, we consider a few of the symptoms that are associated with self-organizing complexity.The classic example of self-organizing complexity is the frequency-size distribution of earthquakes. Earthquakes are certainly complex yet they universally satisfy the relation (to a good approximation) ![Formula][1] where N is the number of earthquakes in a specified time interval and region with their rupture area greater than A . This is the well known Guttenberg–Richter relation (1). The scaling exponent D is the fractal dimension introduced by B. Mandelbrot (2). In his book, Mandelbrot (3) pointed out the wide range of validity of the fractal scaling relation ![Formula][2] where Ni is the number of objects of size ri . Power-law scaling is second only to the Gaussian distribution in terms of applicability. Its relatively recent acceptance, in terms of the fractal paradigm, can be attributed to the fact that it cannot be used as … [1]: /embed/tex-math-1.gif [2]: /embed/tex-math-2.gif" @default.
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- W2049453807 title "Self-organized complexity in the physical, biological, and social sciences" @default.
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- W2049453807 doi "https://doi.org/10.1073/pnas.012579399" @default.
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!["The National Academy of Sciences convened an Arthur M. Sackler Colloquium on “Self-organized complexity in the physical, biological, and social sciences” at the NAS Beckman Center, Irvine, CA, on March 23–24, 2001. The organizers were D.L.T. (Cornell), J.B.R. (Colorado), and Hans Frauenfelder (Los Alamos National Laboratory, Los Alamos, NM). The organizers had no difficulty in finding many examples of complexity in subjects ranging from fluid turbulence to social networks. However, an acceptable definition for self-organizing complexity is much more elusive. Symptoms of systems that exhibit self-organizing complexity include fractal statistics and chaotic behavior. Some examples of such systems are completely deterministic (i.e., fluid turbulence), whereas others have a large stochastic component (i.e., exchange rates). The governing equations (if they exist) are generally nonlinear and may also have a stochastic driver. Many of the concepts that have evolved in statistical physics are applicable (i.e., renormalization group theory and self-organized criticality). As a brief introduction, we consider a few of the symptoms that are associated with self-organizing complexity.The classic example of self-organizing complexity is the frequency-size distribution of earthquakes. Earthquakes are certainly complex yet they universally satisfy the relation (to a good approximation) ![Formula][1] where N is the number of earthquakes in a specified time interval and region with their rupture area greater than A . This is the well known Guttenberg–Richter relation (1). The scaling exponent D is the fractal dimension introduced by B. Mandelbrot (2). In his book, Mandelbrot (3) pointed out the wide range of validity of the fractal scaling relation ![Formula][2] where Ni is the number of objects of size ri . Power-law scaling is second only to the Gaussian distribution in terms of applicability. Its relatively recent acceptance, in terms of the fractal paradigm, can be attributed to the fact that it cannot be used as … [1]: /embed/tex-math-1.gif [2]: /embed/tex-math-2.gif"](?object=%22The%20National%20Academy%20of%20Sciences%20convened%20an%20Arthur%20M.%20Sackler%20Colloquium%20on%20%E2%80%9CSelf-organized%20complexity%20in%20the%20physical%2C%20biological%2C%20and%20social%20sciences%E2%80%9D%20at%20the%20NAS%20Beckman%20Center%2C%20Irvine%2C%20CA%2C%20on%20March%2023%E2%80%9324%2C%202001.%20The%20organizers%20were%20D.L.T.%20(Cornell)%2C%20J.B.R.%20(Colorado)%2C%20and%20Hans%20Frauenfelder%20(Los%20Alamos%20National%20Laboratory%2C%20Los%20Alamos%2C%20NM).%20The%20organizers%20had%20no%20difficulty%20in%20finding%20many%20examples%20of%20complexity%20in%20subjects%20ranging%20from%20fluid%20turbulence%20to%20social%20networks.%20However%2C%20an%20acceptable%20definition%20for%20self-organizing%20complexity%20is%20much%20more%20elusive.%20Symptoms%20of%20systems%20that%20exhibit%20self-organizing%20complexity%20include%20fractal%20statistics%20and%20chaotic%20behavior.%20Some%20examples%20of%20such%20systems%20are%20completely%20deterministic%20(i.e.%2C%20fluid%20turbulence)%2C%20whereas%20others%20have%20a%20large%20stochastic%20component%20(i.e.%2C%20exchange%20rates).%20The%20governing%20equations%20(if%20they%20exist)%20are%20generally%20nonlinear%20and%20may%20also%20have%20a%20stochastic%20driver.%20Many%20of%20the%20concepts%20that%20have%20evolved%20in%20statistical%20physics%20are%20applicable%20(i.e.%2C%20renormalization%20group%20theory%20and%20self-organized%20criticality).%20As%20a%20brief%20introduction%2C%20we%20consider%20a%20few%20of%20the%20symptoms%20that%20are%20associated%20with%20self-organizing%20complexity.The%20classic%20example%20of%20self-organizing%20complexity%20is%20the%20frequency-size%20distribution%20of%20earthquakes.%20Earthquakes%20are%20certainly%20complex%20yet%20they%20universally%20satisfy%20the%20relation%20(to%20a%20good%20approximation)%20!%5BFormula%5D%5B1%5D%20where%20N%20is%20the%20number%20of%20earthquakes%20in%20a%20specified%20time%20interval%20and%20region%20with%20their%20rupture%20area%20greater%20than%20A%20.%20This%20is%20the%20well%20known%20Guttenberg%E2%80%93Richter%20relation%20(1).%20The%20scaling%20exponent%20D%20is%20the%20fractal%20dimension%20introduced%20by%20B.%20Mandelbrot%20(2).%20In%20his%20book%2C%20Mandelbrot%20(3)%20pointed%20out%20the%20wide%20range%20of%20validity%20of%20the%20fractal%20scaling%20relation%20!%5BFormula%5D%5B2%5D%20where%20Ni%20is%20the%20number%20of%20objects%20of%20size%20ri%20.%20Power-law%20scaling%20is%20second%20only%20to%20the%20Gaussian%20distribution%20in%20terms%20of%20applicability.%20Its%20relatively%20recent%20acceptance%2C%20in%20terms%20of%20the%20fractal%20paradigm%2C%20can%20be%20attributed%20to%20the%20fact%20that%20it%20cannot%20be%20used%20as%20%E2%80%A6%20%5B1%5D%3A%20%2Fembed%2Ftex-math-1.gif%20%5B2%5D%3A%20%2Fembed%2Ftex-math-2.gif%22){kind=link}