Cellular Automata and Artificial Life

1. Cellular Automata and Artificial Life

2. Cellular Automata (元胞自动机) Each Unit Is an Automata Connectivity: Each Automata Is Linked With Its Neighborhood

3. a d b c b c An example of Cellular Automata every unit has a value: a, b, c and d.

4. 1 0 0 0 0 0 An example of Cellular Automata • Rule 90

5. An example of Cellular Automata • There are 2^3=8 different input states. • There are 2^8 =256 different state change rules. • Each rule is numbered from 0 to 255.

6. An example of Cellular Automata • See the pictures of the dynamics of these rules. • Text book: Gerard Weisbuch, Complex Systems Dynamics, an introduction to automata networks, Addison-Wesley Publishing Company, Inc. USA. P25-P27

7. Strong attractors • Rule 250: all 1 • Rule 128: all configurations with at least one 0 converge toward the attractor containing only 0’s, ( exception of configuration of all 1’s )

8. Short-period attractors • Rule 108 and 178: periods of 1 or 2.

9. long-period attractors • Rule 90 and 126: too long to be easily observable.

10. One dimensional cellular automata with three inputs • One dimension ( two dimensions ) • With three inputs ( with more than 3 inputs) • Neighbors: 3, 5, … The nearest neighbors

11. One dimensional cellular automata with two inputs • Even-numbered automata; • Odd-numbered automata; T T+1 T+2

12. One dimensional cellular automata with two inputs

13. Two-dimensional Cellular Automata • The first cellular automata proposed by von Neumann were on the nodes of a two-dimensional square grid. • Have a relatively ancient history, from von Neumann’s self-reproducing automata of the 1940’s to Conway’s “game of life”.

14. The grid is infinite. When it has edges, we connect the right edge of the figure to the left edge; …… 2D Cellular Automata

15. 2D Cellular Automata • Homogeneous: The state change rules are in principle the same for all of the automata in the lattice. (inhomogeneous) • Parallel iteration mode; • The connectivity structure is related to the symmetries of the lattice.

16. Two kinds of neighborhood • Von Neumann neighmorhood (left) k=5 • Moore neighborhood (right) k=9

17. 2D threshold automata • Threshold t: -1 <= t <= k+1 • New State = 1 iff S >= t. S: the sum of the states of the neighbors

18. If T is small or large • Weak thresholds ( T <= 0 or is close to 0 ) favor the growth of zones of automata in state 1. • Strong thresholds ( T is close to k ) favor the growth of zones of automata in state 0.

19. t=0, t=1, t=2, t=3, t=4 from left to right, up to bottom. T =1.5, k=5

20. T =1.5, k=5 • Isolated 1’s are destroyed. • The condition for growth is that at least two neighbors must be in state 1. • If the groups of 1’s are far enough apart, the growth stops when the convex envelope of the initial configurations is full of 1’s

21. t=0, t=1, t=2, t=3, t=4 from left to right, up to bottom. T =1.5, k=5

22. T =1.5, k=5 • A good representation of the growth of crystals (quartz) in thermodynamic equilibrium. • Convex envelope of the seeds corresponds to the equilibrium shapes.

23. Window Automata and Dendritic Growth • If an automaton is in state 1, it stays there; • If an automaton is in state 0, it changes to 1 only if one of its neighbors is in state 1. • See a picture.

24. It modeled snowflake growth • Snowflakes are crystals which undergo dendritic growth to lacy shapes • When the solid seed is much colder than the solution it will grow. • Not allowing the transition toward the state 1 when the number of neighbors in state 1 is too large because of heat dissipating

25. Conway’s “game of life” • An automaton in state 0 switches to state 1 if three of its neighbors are in state 1( born ). Otherwise, it stays in state 0. • An automaton in state 1 stays in state 1 if 2 or 3 of its neighbors are in state 1. It switches to state 0 in the other cases. ( dies, either of isolation or of overcrowding ).

26. Square Game of life

27. honeycomb Game of life

28. Honeycomb Glider Game of life

29. After four iterations, it returns to its initial configuration, having undergone a translation. Binary signals that propagate down the diagonals of the lattice. The collision of two gliders destroys them both. See demo Game of life

30. Conway’s “Game of Life” • Experiment to determine if a simple system of rules could create a universal computer. • “Universal computer" denotes a machine that is capable of emulating any kind of information processing by implementing a small set of simple operations. • To find self-reproducing organisms within the life system

31. Artificial Life • Boids • Floys • Game of life • Life exists in computer?

32. Artificial Life • What is life? • Can we study and research life in other media instead of proteins? Selfproducing Evolutionary ...

33. Artificial Life • Artificial life study and research human-made systems that possess some of the essential properties of life. • There are many such systems that meet this criterion—digital ( boids, floys, game of life, …), and mechanical (robots)

34. Artificial Life • Life “as we know it”;生命如我所知 • Life "as it could be“;生命如其所能 • .

35. Artificial Life • Cellullar Automata • Genetic Algorithms -evolutionary computation • Societies and Collective Behavior • Virtual Worlds • Artificial brain • Robots

36. Societies and Collective Behavior • Attempting to understand high-level behavior from low-level rules; • Artificial populations which posses the behavior of life. - How the simple rules of Darwinian evolution lead to high-level structure, - Or the way in which the simple interactions between ants and their environment lead to complex trail-following behavior.

37. Societies and Collective Behavior -boids -floys -artificial socialty -artificial ecology -artificial fishes

38. Artificial Life- Societies and Collective Behavior • Understanding this relationship in particular systems promises to provide novel solutions to complex real-world problems, such as disease prevention, stock-market prediction, and data-mining on the internet

39. Robots • Construction of adaptive autonomous robots; -The robotic agent interacts with its environment and learns from this interaction, leading to emergent robotic behavior;

40. Virtual Worlds • Artificial trees • Artificial fishes

41. Artificial Life Neuroscience economics Artificial Life Biology and medicines Ecology Engineering Socialogy and psycology

42. Artificial Life Evolutionary computing Artificial Intelligence Artificial Life Neural networks Graphics and computer animation Engineering

43. Artificial Life • The way to study and research the complex systems. • Truly interdisciplinary fields: biology, chemistry and physics to computer science and engineering.

44. Open problems • 生命是如何从非生命的物质中产生的？ • 生命系统的潜能和极限是什么？ • 生命与心灵（意识）、机器和文化之间有什么联系？

45. Open problems • 在试管中生成一个大分子原型生命组织（molecular proto-organism） • 在基于硅的人工化学中完成向生命的转变 • 确定最基本的生命组织的存在性 • 模拟一个单细胞生物的生命周期 • 解释在生命系统中，规则和符号是如何从物理动力学中产生的

46. Open problems • 确定在无穷尽的生命进化过程中什么是不可避免的 • 确定从特定系统向一般系统进化所必需的条件 • 建立在任何尺度下合成动态结构（dynamical hierarchy）的形式框架 • 确定我们对于生物和生态系统的影响带来的结果的可预测性

47. Open problems • 发展一套进化系统的信息处理、信息流和信息生成的理论 • 在人工生命系统中演示智能和意识的涌现 • 预测机器在下一次生物进化时代的影响 • 提供一个量化的文化与生物进化之间联系的模型 • 建立一个关于人工生命的伦理原则

48. L system • 同时使用产生式规则： • 如： a→ab, b→a b a ab aba abaab abaababa

49. 龟几何 • (x,y,α)表示龟的状态。(x,y)表示位置，α表示龟爬行的方向。 • 步长：d; 角度增量: δ • 用下面命令控制龟的运动:

50. 龟几何 F: 向前移动步长d, 新状态:(x 1, y1, α) X1 = x + cosα * d Y1 = y + sinα* d 在点(x,y)与(x 1, y1)之间画一条线。 (x1,y1) α (x,y)