### notes on dynamic systems

- course notes on dynamic systems http://www.cs.colorado.edu/~lizb/chaos-course.html
- Visualizing Local Properties and Characteristic Structures of Dynamical Systems http://www.cg.tuwien.ac.at/~helwig/diss/
- the mathematical low-down from Mathworld → http://mathworld.wolfram.com/DynamicalSystem.html
- graphical examples » http://www.dynamical-systems.org/

### CA

using cellular automata for modeling 2d + 3d fluid dynmaics

### tools/code/etc+

R is `GNU S' - A language and environment for statistical computing and graphics. R is similar to the award-winning S system, which was developed at Bell Laboratories by John Chambers et al. It provides a wide variety of statistical and graphical techniques (linear and nonlinear modelling, statistical tests, time series analysis, classification, clustering, …).

R is designed as a true computer language with control-flow constructions for iteration and alternation, and it allows users to add additional functionality by defining new functions. For computationally intensive tasks, C, C++ and Fortran code can be linked and called at run time.

### unsorted / tangents /etc+

Kimber, D. and Marcia Bush

“Situated State Hidden Markov Models”

Xerox Parc, Palo Alto, 1993

http://citeseer.nj.nec.com/254069.html

Abstract: We introduce a probabilistic model called a Situated State Hidden Markov Model (SSHMM), in which states are `situated' (i.e. assigned positions) and assumed to correspond to regions of an underlying continuous state space. Transition probabilities among states are induced by the assigned state positions in such a way that transitions occur more frequently between nearby states. The model is formally defined, and a maximum likelihood estimation procedure is described. Experiments on synthetic data are described and demonstrate that SHMM's can learn the structure of an underlying continuous state space even when observed through high dimensional discontinuous functions….

Stevens, Roger and Rok Sosic

Griffith Univ. Research Report CIT-95-14

“Emergent Behaviour in Slime Mould Environments”

http://citeseer.nj.nec.com/93380.html

Abstract: Slime moulds are well studied organisms in biology. They are some of the simplest organisms that exhibit complex emergent behaviour. Although individual organisms interact with the environment only by following local rules, slime moulds produce a collective behaviour on a global scale. The modelling of slime mould patterns provides a good testbed for studying emergent behaviour. We have simulated the behaviour of slime moulds on a computer model. In the model, each organism is guided by rules, derived from studies of real organisms. By changing parameters of the simulation, we were able to study some underlying mechanisms behind the emergent behaviour. We have concentrated on the strength of the communication signal and the distance at which the signal is effective. Results show rather unexpected results that a stronger communication signal does not necessary reinforce the emergent behaviour and that the effective signal distance does not depend on the density of organisms.

fluid dynamics → http://www.eng.vt.edu/fluids/