Implications for Everyday Systems

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

2. 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 University of Virginia

3. 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 University of Virginia

4. 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 University of Virginia

5. 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 University of Virginia

6. Snowflakes University of Virginia

7. Snowflakes using Cellular Automata University of Virginia

8. Breaking of Solids University of Virginia

9. Fluid Flow and eddies – (1) University of Virginia

10. Fluid Flow and eddies – (2) University of Virginia

11. Fluid Flow Model using Cellular Automata – (1) University of Virginia

12. Fluid Flow Model using Cellular Automata – (2) University of Virginia

13. Fluid Flow Model using Cellular Automata – (3) University of Virginia

14. Branching patterns University of Virginia

15. Branching patterns using Substitution Model – (1) University of Virginia

16. Branching patterns using Substitution Model – (2) University of Virginia

17. Mollusc shells University of Virginia

18. Mollusc shells using Substitution Models University of Virginia

19. Designs and Patterns on Animal Skin University of Virginia

20. Stripes using Cellular Automata University of Virginia

21. 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 University of Virginia

22. 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 University of Virginia

23. 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 University of Virginia