Algorithmic Dynamics of Cellular Automata
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The document discusses the classification and dynamics of elementary cellular automata (ECA), emphasizing the different classes based on their behaviors and providing examples for each. It explores various research findings related to complexity, symmetry breaking, and the effects of initial conditions, with references to relevant publications. Additionally, applications of this research in network theory, biology, and algorithmic information are mentioned, along with acknowledgments of collaborators and contributions to the field.
Algorithmic Dynamics of Cellular Automata
- 1. ALGORITHMIC DYNAMICS OF CELLULAR AUTOMATA In celebration of Prof. Harold McIntosh Hector Zenil www.hectorzenil.net
- 2. An example of an ECA: Rule 255
- 4. Wolfram’s original ECA classification • Class 1. Symbolic systems which rapidly converge to a uniform state. Examples are rules 0, 32 and 160. • Class 2. Symbolic systems which rapidly converge to a repetitive or stable state. Examples are rules 4, 108 and 218. • Class 3. Symbolic systems which appear to remain in a random state. Examples are rules 22, 30, 126 and 189. • Class 4. Symbolic systems which form areas of repetitive or stable states, but which also form structures that interact with each other in complicated ways. Examples are rules 54 and 110.
- 5. What classification? 1001 (Left) versus starting from 1011 (Right) ECA rule 22 Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems, vol. 19, No. 1, pp. 1-28, 2010
- 6. Gray Code First 50 initial configurations based on a Gray-code enumeration for binary CAs. H. Zenil et al., Asymptotic Behaviour and Ratios of Complexity in Cellular Automata Rule Spaces, International Journal of Bifurcation and Chaos vol. 23, no. 9, 2013.
- 7. Strong symmetry breaking in the initial condition produces a phase transition leading to the production of high statistical randomness Bi-stable behaviour of ECA Rule 22 H. Zenil et al., Asymptotic Behaviour and Ratios of Complexity in Cellular Automata Rule Spaces, International Journal of Bifurcation and Chaos vol. 23, no. 9, 2013.
- 8. Compressing space-time evolutions of ECAs Evolution of rules 95, 82, 50, and 30 together with the compressed (dashed line) and uncompressed (solid line) lengths. Compression-Based Investigation of the Dynamical Properties of Cellular Automata and Other Systems, vol. 19, No. 1, pp. 1-28, 2010
- 9. AIT-based separation found Discrepancies: ECA Rule 73 and 94 are class 2 in Wolfram’s original classification H. Zenil et al., Asymptotic Behaviour and Ratios of Complexity in Cellular Automata Rule Spaces, International Journal of Bifurcation and Chaos vol. 23, no. 9, 2013.
- 10. The asymptotic bevahiour of CAs towards greater complexity Consistent across all measures: block entropy, lossless compression (Compress) and algorithmic probability (CTM/BDM) H. Zenil et al., Asymptotic Behaviour and Ratios of Complexity in Cellular Automata Rule Spaces, International Journal of Bifurcation and Chaos vol. 23, no. 9, 2013.
- 11. CA block emulation (compilers) Rule 54 emulates 51 J Riedel, H. Zenil, Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Turing Universality, 2016.
- 12. Cross-boundary breaking of classes J Riedel, H. Zenil, Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Turing Universality, 2016.
- 13. Cross-boundary breaking of classes Rule 54 emulates 51 J Riedel, H. Zenil, Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Turing Universality, 2016.
- 14. Cross-boundary class breaking J Riedel, H. Zenil, Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Turing Universality, 2016.
- 15. Main figure Reprogrammability landscape of abstract computer programs As a function of program length and compiler size J Riedel, H. Zenil, Cross-boundary Behavioural Reprogrammability Reveals Evidence of Pervasive Turing Universality, 2016.
- 16. Prime rules and new universality result in ECA Boolean composition of prime ECA rules 15, 118 and 170 simulates ECA rule 110
- 17. The 2D CA Game of Life (GoL) Density diagram showing the persistence of structures:
- 18. GoL’s glider (a ‘moving’ particle) A piece of information moving through the grid from one side to another
- 19. Pattern algorithmic dynamics GoL’s glider algorithmic dynamics The amount of information is preserved, neither lost or increased
- 20. Characterization of evolving patterns H. Zenil, Algorithmic-information Properties of Dynamic Persistent Patterns and Colliding Particles in the Game of Life
- 21. Characterization of local dynamic patterns What about the characterization of events
- 22. Types of symmetric particle collisions Free particle 2-particle front collision 2-particle side collision 3-particle collision 4-particle side collision
- 23. Dynamics of a 4-particle collision New particles Fixed point H. Zenil, Algorithmic-information Properties of Dynamic Persistent Patterns and Colliding Particles in the Game of Life
- 24. Algorithmic dynamics of a stable ‘near miss’ H. Zenil, Algorithmic-information Properties of Dynamic Persistent Patterns and Colliding Particles in the Game of Life
- 25. Sensitivity of dynamics to initial conditions Periodic fixed point H. Zenil, Algorithmic-information Properties of Dynamic Persistent Patterns and Colliding Particles in the Game of Life
- 26. Particle annihilation H. Zenil, Algorithmic-information Properties of Dynamic Persistent Patterns and Colliding Particles in the Game of Life
- 28. All cases can be reduced to 4 density plots (+ annihilation) 3 cases with (periodic) fixed points and 1 open-ended case Algorithmicdynamics ofglidercollisions
- 29. Algorithmic Dynamics characterization H. Zenil, Algorithmic-information Properties of Dynamic Persistent Patterns and Colliding Particles in the Game of Life
- 30. Interventional Calculus H. Zenil, N.A. Kiani, F. Marabita, Y. Deng, S. Elias, A. Schmidt, G. Ball, J. Tegnér, An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems, 2017.
- 31. Reconstructing space-phase dynamics We are generalizing this to continuous dynamic systems such as strange attractors H. Zenil, N.A. Kiani, F. Marabita, Y. Deng, S. Elias, A. Schmidt, G. Ball, J. Tegnér, An Algorithmic Information Calculus for Causal Discovery and Reprogramming Systems, 2017.
- 32. Reducing Dimension (compression/coarse-graining/ normalizing) by minimal information loss Rule22
- 33. Rule158 Reducing Dimension (lossy compression/coarse- graining/normalizing) by minimal information loss
- 34. Detecting generating mechanisms by decoupling signals and programs We have generalized these ideas to graphs and networks Rule255and110
- 35. Applications in network theory and molecular biology • A 3-million USD lab to produce models of human cells and steer cells at will using these tools that we have developed: H. Zenil, N.A. Kiani and J. Tegnér Methods of Information Theory and Algorithmic Complexity for Network Biology Seminars in Cell and Developmental Biology, vol. 51, pp. 32-43, 2016.
- 36. Journal of Complex Systems • Founded by Stephen Wolfram in 1987 • First journal in the field of Complex Systems • Has published most of the most landmark papers in the field • Over 675 papers from 950 authors • Free open access and free publication �������� �������� �������� ������� ���������� ����������� ������� ���������� ������ ��������� ������� �������� �������� ����� ���������� ��������� ��������� ������� �������� ������ �������� ���������� ������������������� ������ ��������� ����� ������������� �������������� ��������������� ������� ��������� ����������� ������ ������������ ������ ��������� ���� ��������� ������������ ������� ����������� ������������ �������� �������������� �������� ������� �������� ���� ���������� ����� ���������� ��������� ����� ������� ������� ����������� ����������� �������� �������� �������� �������� ���������� ���������� �������� ������ �������� �������� ������ ��� ������ ��������� �������� ��������� ���������� ����� �������� ������� ������ �������� ����� ������ ������� ������ ������ ������� �������� ����� ���� ��� ������ ����� ������ ������ ���� ���� ���� ���� ����� ���� Word cloud of titles http://www.complex-systems.com/
- 37. Thanks Collaborators: Narsis A. Kiani Jesper Tegnér Juergen Riedel Others from CompMed and AlgoNature