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A New Kind of Science in a Nutshell

A New Kind of Science in a Nutshell. David Sehnal QIPL at FI MU. Motivations. How does anything complicated get produced in nature? Traditional Science – i.e. calculus, Newtonian physics, … What if there is a more general underlying principle? Simple programs. 1D Cellular Automata.

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A New Kind of Science in a Nutshell

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  1. A New Kind of Sciencein a Nutshell David Sehnal QIPL at FI MU

  2. Motivations • How does anything complicated get produced in nature? • Traditional Science – i.e. calculus, Newtonian physics, … • What if there is a more general underlying principle? • Simple programs

  3. 1D Cellular Automata

  4. Cell to be updated Left neighbor Right neighbor New color

  5. This type behavior is very surprising • Started from a single black cell • Used simple rules • Got something that looks to us completely random

  6. Is Complexity Special or Common?

  7. Turing Machines

  8. Substitution Systems

  9. 2D Cellular Automata

  10. 2D Turing Machines

  11. 3D Cellular Automata

  12. To sum it up… • Simple rules do not imply simple behavior • It seems that complex behavior is a very common phenomenon

  13. Systems in nature

  14. Snowflakes • When a piece of a snowflake solidifies, heat is released • This heat prohibits ice nearby • New rule: Piece solidifies if exactly on of the neighborhood cells is solid

  15. More systems in nature • Fluid flow • Patterns on shells • Fundamental physics • And many others …

  16. Why can simple programs produce complex behavior?

  17. Computation

  18. Computation • All cellular automata can be though of as doing computations • One does not need to know the point of the computation beforehand

  19. Universality • Some automata can simulate all others • One only needs to specify the initial conditions

  20. Universality • Once universality is reached, the behavior is maximally sophisticated (from the computational point of view)

  21. More questions • What about systems such as rule 30? • Or systems in nature? • How sophisticated are these?

  22. Principle of Computational Equivalence Essentially any time the behavior of a system looks to us complex, it will end up corresponding to a computation of exactly equivalent sophistication.

  23. Simple behavior (repetitive or nested) corresponds to simple computations • Complex behavior corresponds to sophisticated computations

  24. Threshold of Universality • Rule 110 is universal

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