=====Complexity & Emergence=====


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====Examples of Self-Organization (Emergence)====

|  Group Clapping  | Try this in class: Start clapping; aim for clapping at the same rate as everyone else in the room.  Self-organization without centralized control.   |
|  Conway's Game of Life  | [[https://academo.org/demos/conways-game-of-life/|Link to Applet]]   |

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====Belusov-Zhaboutinsky Reaction====

|  {{public:t-720-atai:250px-the_belousov-zhabotinsky_reaction.gif}}  | 
|  Simulated Belousov-Zhabotinsky Reaction. [[https://en.wikipedia.org/wiki/Belousov–Zhabotinsky_reaction|Source: Wikipedia]] |

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====Belusov-Zhaboutinsky Reaction====
|  What it is  | A chemical reaction discovered in 1950.   |
|  Why it's important  | Great visual example of the kind of emergent patterns can be created through auto-catalysis (chemical in this case). One of the first (the first?) scientifically published example of emergence identified as such.  |
|  Real version on Youtube  | https://www.youtube.com/watch?v=IBa4kgXI4Cg \\ https://www.youtube.com/watch?v=4y3uL5PRsZw&feature=related   |

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====How the Belusov-Zhaboutinsky Reaction Works====

|  {{public:t-720-atai:zhabotinsky-reaction-1.png?400|Belousov-Zhabotinsky Reaction}}  |
|  A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator. [[https://en.wikipedia.org/wiki/Belousov–Zhabotinsky_reaction|Wikipedia]]  |

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====Cellular Automata====
|  What it is  | An algorithmic way to program interaction between (large numbers of) rule-determined "agents" or cells.  [[https://en.wikipedia.org/wiki/Cellular_automaton|Wikipedia]]  |
|  Why it's important  | Powerful method to explore the concept of emergence. Also used for simulating the evolution of complex systems.    |
|  Explicates  | Interaction of rules.    |
|  Typical manifestation  | 1D or 2D grid with cell behavior governed by rules of interaction. Each cell has a scope of what it "sees" (its range of "causal ties").   |


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====CA Example 1====
| {{public:t-720-atai:emergence-fig.jpg}}  |
|  In this example   |
|  **Green --> Brown IF one or more are //true://** \\ * There are more than 20 green patches around and lifetime exceeds 30 \\ * There are less than 12 green patches around and lifetime exceeds 20 \\ * The number of surrounding green patches > 25 \\ * Lifetime > 60 ticks \\ **Brown --> Green IF both are //true//:** \\ * Number of surrounding green patches > 8 and heir lifetime combined > 80 \\ * Number of surrounding brown patches > 10  |


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==== Stephen Wolfram's CA Work====
|  CA  | http://mathworld.wolfram.com/CellularAutomaton.html   |
|  Book  | A New Kind of Science.   |
|  Why it's important  | Major analysis of rules for 1-D CAs. Most comprehensive work on CAs to date.    |
|  Rule 30   | [[https://en.wikipedia.org/wiki/Rule_30|Wikipedia]]    |

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