1. A New Kind of Science in 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

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

12. This type behavior is very surprising 1.Started from a single black cell 2.Used simple rules 3.Got something that looks to us completely random

18. Is Complexity Special or Common?

19. Turing Machines

22. Substitution Systems

23. 2D Cellular Automata

24. 2D Turing Machines

25. 3D Cellular Automata

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

27. Systems in nature

31. 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

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

37. Why can simple programs produce complex behavior?

38. Computation

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

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

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

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

47. 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.

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

49. Rule 110 is universal Threshold of Universality

51. Where does all the complexity come from? … from the computational sophistication of the system observed compared to the computational sophistication of the observer.

55. Thank you for your attention