Tuesday: note-age …

Yesterday some more train action, so read more of Revisting the Edge of Chaos: Evolving Cellular Automata to Perform
Computations, by Melanie Mitchell et al (Complex Systems, 7, 89 – 130,
1993).

1. And now for more notes from A response to simplifying complexity, Femke Reitsma, Geoforum 34(1): 13-16
1. Noted by DC Mikulecky (1999, Defintion of Complexity, 2001 — in theory from here http://www.people.vcu.edu/~mikuleck/) that evidence for validity of chaotic dynamics for biological processes involve simple isolated systesms
2. Chaos is found in the idealizalisations or models of read systems, but it is not evidne tin the systems themselves
3. Lorenz’s … weather system was an open byt isolated system
4. C Zimmer 1999 (Life after chaos, Science, 284 (5411), 83 – 86) … it is evident that chaos has only been found in models, not natural systems
5. in chaos theory disorder arises from simple ordered states, in complexity theory large scale order arises from complex apparent disorder at the local scale
6. [Reitsma ] … considers that the types of complexity may be divided into 7 not mutually exclusive groups:
1. Determinisitc omplexity
1. based on information theory
2. measured as the algorithmic content of a string of bits, defined as “the lenght of the shorted program that will cause a standard universal computer to print out the string of bits and then halt” (What is Complexity, Complexity 1 (1) 16 – 19, M Gell-Mann, 1995, p16, http://www.santafe.edu/~mgm/complexity.html)
3. also includes computational complexity, a measure based on processing time
4. complexity is equated with randomness
2. Statistical complexity
1. Statistical measures of complexity attempt to measure the degree of structure or pattern present in a complex system, circumventig the problem of statistical complexity where randomness equals maximal complexity
2. the bounday conditions of extreme order and disorder and satisifed by vanishing at these limits (DP Feldman and JP Crutchfield, 1997, Measures of statistical complexity: Why? Phys. Lett. A 238, 244 – 252)
3. Phase transition
1. Maximal complexity is defined as the mid-point between order and chaos, the edge of chaos (S Kauffman, 1995, At home in the Universe: the serach for the laws of self-organisation and complexity, Oxford Univeristy Press, New York)
4. Chaos derivatives
1. measurses of complexity developed under chaos theory are typically based on the Lyapunov exponent
1. which … “defines in precise mathematical terms a system’s sensitivity to initial conditions” (RV Jensen, 1987, p177, Classical chaos, American  Scientist 75 (Mar-Apr) 168 -181)
2. or the Fractal dimension
1. defines complexity through a measure of the irregularity of an object
5. Connectivity
1. complexity is measured by the degree of connectivity within the system, where the greater the number of connections or interactions, the higher the complexity (S Kauffman, 1995, At home in the Universe: the serach for the laws of
   self-organisation and complexity, Oxford Univeristy Press, New York)
6. System variability
1. complexity is degined whereby an increase in system variability (e.g. spatial variablity or between scale variability) results in an increase in the complexity of the system
7. Relative and subjective complexity
1. these types of complexity … is … relative to the observer; “the complexity of an object is in the eyes of the observer” (GJ Klir and TA Folger, 1988, p193, Fuzzy sets, uncertainty and information. Prentice Hall, New Jersey)
7. Complex system structure degined the complex system as composed of elements and relations or connections
8. Complex system landscape degined the state space of the complex system within which attractors are found and the importance of scale is recognised
9. complex system behaviour is defined by self-organisation and can be devidided into elemental behavior, or element <–> element interaction, system <–> environment behaviour, and the complex whole behaviour that emerges form the two former types of behavior.
10. Coimplex system organisation is described as a continuum, the opposing extermes of which are defined as order and chaos. Between these two end points lies the edge of chaos.

NB you have a review of the the Kauffman reference above: review by Gert Korthof is available on the web.

That’s it for today: need to go through a paper again to confirm some notes, ahead of typing them up (unusual notation style, so presuming I went through it a while back)