Cellular Automata A multi-purpose modeling method Lemont B. Kier, PhD Prof. of Medicinal Chemistry

1. Cellular Automata A multi-purpose modeling method Lemont B. Kier, PhD Prof. of Medicinal Chemistry Senior Fellow, CSBC Visiting Professor, Univ. of Lausanne (Suisse) and Cho-Kun Cheng, PhD Prof. of Computer Science Fellow, CSBC

2. “The role and privilege of a scientist is to study nature and to try to unlock her secrets”

3. Processes used by scientists: observations

4. Processes used by scientists: observations find patterns

5. Processes used by scientists: observations find patterns develop “laws” of the behavior of patterns

6. Processes used by scientists: observations find patterns develop “laws” of the behavior of patterns seek explanations for the patterns

7. Processes used by scientists: observations find patterns develop “laws” of the behavior of patterns seek explanations for the patterns these take the form of hypotheses and theories

8. Processes used by scientists: observations find patterns develop “laws” of the behavior of patterns seek explanations for the patterns these take the form of hypotheses and theories An alternative to observations is to create models

9. Models A simplification (an abstraction) of the system being studied.

10. Models A simplification (an abstraction) of the system being studied. It has fewer states and interactions than the original system.

11. Models A simplification (an abstraction) of the system being studied. It has fewer states and interactions than the original system. It is focused on just one part of the system that interests us.

12. Models A simplification (an abstraction) of the system being studied. It has fewer states and interactions than the original system. It is focused on just one part of the system that interests us. Designed to be used to understand and even predict behavior.

13. Models A simplification (an abstraction) of the system being studied. It has fewer states and interactions than the original system. It is focused on just one part of the system that interests us. Designed to be used to understand and even predict behavior. Used when experiments are difficult, impossible, or unrewarding.

14. Types of Models An equation

15. Types of Models An equation A picture or graphic display

16. Types of Models An equation A picture or graphic display A dynamic sequence

17. Expectations The outcome of models should mirror reality within that part of the system that we are examining.

18. Predictions If a model demonstrates a significant degree of validity in respect to its mirroring reality, then it may be useful in predicting behavior thus far not observed.

19. “The major role of the brain is to create models and to use them to anticipate behavior for survival”

20. Systems  A sub-unit of nature that we study.

21. Systems  A sub-unit of nature that we study.  Each system in nature is composed of parts (agents) that are, themselves, systems. Nature is a hierarchy of systems.

22. Systems  A sub-unit of nature that we study.  Each system in nature is composed of parts (agents) that are, themselves, systems. Nature is a hierarchy of systems.  We define a particular system, within our own context, by focusing attention on it. Whatever we study, that is a system within our realm of interest.

23. Systems  A sub-unit of nature that we study.  Each system in nature is composed of parts (agents) that are, themselves, systems. Nature is a hierarchy of systems.  We define a particular system, within our own context, by focusing attention on it. Whatever we study, that is a system within our realm of interest.  Changes in the contents (agents) of a system or their interactions, lead to changes in the state of a system and thus the behavior of the system.

24. Attributes of systems include  Motion and perpetual novelty among agents and systems.

25. Attributes of systems include  Motion and perpetual novelty among agents and systems.  All events are local, there is no action at a distance.

26. Attributes of systems include  Motion and perpetual novelty among agents and systems.  All events are local, there is no action at a distance.  Patterns evolve from simple relationships (emergence).

27. Cellular Automata A modeling method A lattice (grid) of spaces (cells) that may hold ingredients (agents) representing (modeling) some part of a system under study.

28. Cellular Automata A modeling method The most common shape of the cells is square on a two-dimensional grid.

29. Cellular Automata A modeling method The agents are endowed with rules that govern their state, movement in the grid, union with other agents and separation from them, and other activities that are selected to model a system.

30. Cellular Automata A modeling method The rules govern local events, and are discrete in space, time and state.

31. Cellular Automata A modeling method Cellular automata is designed to model dynamic events that reveal emergent properties (configurations) from initial conditions.

32. Cellular Automata A modeling method The resulting configurations are examined to determine if they mirror reality.

33. The Neighborhood The cell on a grid where state and movement computations are made at a particular time (iteration).

34. The Neighborhood All events relating to x take place in this arena. The influence of y cells is part of the computation.

35. The Neighborhood In some studies, cells beyond y are implicated in the computation.

36. The Neighborhood For this case, the extended von Neumann neighborhood is used.

37. The Neighborhood In this case the z cells are influential on the x cell and it’s movement.

38. The Grid The grid may be bounded by cells that don’t permit penetration.

39. The Grid Alternatively, when the model is of a large ensemble of agents, the grid is the surface of a torus.

40. The Grid In this case, passage of an agent across an edge puts the agent on the opposite face. This is a no boundary condition of the grid.

41. If the computation of each x agent in the neighborhood is asynchronous then random sequence of computations is made. When all cell in the grid have computed their states and movements, an iteration is counted. A A

42. States The state of a cell is the occupancy yes/no and the type of agent if it is occupied.

43. States The state of a cell is the occupancy yes/no and the type of agent if it is occupied. States can change as a function of time (iteration) or upon contact with another occupied cell.

44. a + b  ab  ac  a + c Examples: an enzyme reaction.

45. a b a a Variegated cells Each edge of a square cell may have a different state.

46. a b a a a a a c a b a c b b c a Variegated cells Each edge of a square cell may have a different state.

47. a b a a a a a d b c b d c c d b a a a a a a c a b a c b b c c d b d b c a d b c Variegated cells Each edge of a square cell may have a different state.

48. Cell Movement Synchronous movement: all cells move simultaneously.

49. Cell Movement Synchronous movement: all cells move simultaneously. Asynchronous movement: each cell, at random, moves.

50. Cell Movement Synchronous movement: all cells move simultaneously. Asynchronous movement: each cell, at random, moves. Deterministic movement: rules are exact.