10/21/2015University of Virginia Implications for Everyday Systems Presented by Selvin George A New Kind of Science (Ch. 8) By Stephen Wolfram

2/3/2003University of Virginia Overview Issues with traditional system modelling Mathematical models v/s cellular automata Study specific examples of everyday systems Snowflakes shapes, crystallization Fluid Flow, eddies Branching pattern of leaves Stripes/spots on the skins of animals Model most important features, patterns, shapes etc., using simple cellular automata Critique

2/3/2003University of Virginia Traditional modelling A model is an idealization of a system We capture some aspects, ignore others Compare the behaviour generated by the model to the system for significant similarities Behaviour is often characterised as metrics (stability, hysteresis etc.,) based on mathematical derivations A good model is simple, captures a large number of system features

2/3/2003University of Virginia Issues with modelling From traditional science: if the behavior of a system is complex, then any model for the system must somehow be correspondingly complex Often the models are as complicated as the phenomenon it purports to describe Typically models are complicated and need to be “patched” when differing results are obtained

2/3/2003University of Virginia Mathematical v/s Cellular “In most cases, there have been in the past, never really been any models that can even reproduce the most obvious features of the behaviour we see” Mathematics models describe a system using equations. Numbers represent system behaviour Best first step in assessing a model is not to look at these numbers but rather just to use one’s eyes Easy to set up Cellular automata for most systems Growth-Inhibition is set up using the automaton rules Often Wolfram’s models have been extended

2/3/2003University of Virginia Snowflakes

2/3/2003University of Virginia Snowflakes using Cellular Automata

2/3/2003University of Virginia Breaking of Solids

2/3/2003University of Virginia Fluid Flow and eddies – (1)

2/3/2003University of Virginia Fluid Flow and eddies – (2)

2/3/2003University of Virginia Fluid Flow Model using Cellular Automata – (1)

2/3/2003University of Virginia Fluid Flow Model using Cellular Automata – (2)

2/3/2003University of Virginia Fluid Flow Model using Cellular Automata – (3)

2/3/2003University of Virginia Branching patterns

2/3/2003University of Virginia Branching patterns using Substitution Model – (1)

2/3/2003University of Virginia Branching patterns using Substitution Model – (2)

2/3/2003University of Virginia Mollusc shells

2/3/2003University of Virginia Mollusc shells using Substitution Models

2/3/2003University of Virginia Designs and Patterns on Animal Skin

2/3/2003University of Virginia Stripes using Cellular Automata

2/3/2003University of Virginia Wolfram’s Admissions No control over the underlying rules Must deduce them from phenomena Even his models may not capture many features Some of the models described earlier were found by trial and error

2/3/2003University of Virginia Critique – (1) System Modelling Detail v/s Basic Behaviour Wolfram’s models capture the basic mechanisms However he does not give a framework Panning present-day models is unfair Basic Model Level of Detail Detailed Model

2/3/2003University of Virginia Critique – (2) The rules of a cellular automata does not give us an insight into the system behaviour On the other hand, mathematical models are more descriptive in nature Unless we work at the lowest LOD, cellular automata based models are prone to the same inefficiencies of current modelling methods System modelling with cellular automata will be based more on trial and error rather than repeated refinement of models