„FLOCK‟ OF BIRDS Harmony reigns- flocking. Not predictable from knowing all there is to know about any single bird. “Emerges" from simple rules instinctively followed by each bird: 1) Keep a precise distance away from and stay aligned with your nearest neighbours. 2) Avoid predators.
TERMITE MOUNDS “Intelligent" cooperation-elaborate galleries and chimneys control air flow to manage temperature and humidity inside the nest! Individual termites-no notion, no perception(the workers are blind!) Respond to very local chemical cues left behind by other termites Temperature/humidity and airflow cues
What We‟re Looking At: (D) DEPENDENT: ”Rise” out of more fundamental properties or substances => depend on those properties or substances (I) INDEPENDENT: “Novel” or “irreducible” => in a certain sense independent from, the more fundamental properties or substances.
Emergence- Complexity From SimplicityThe way complex systems and patterns arise out ofa multiplicity of relatively simple interactions.
What makes Emergent Phenomena interesting?“BORN” from a class of fundamental properties YET,Add something entirely NEW to these more fundamental properties
What Is Life?Living beings- 1)Organized in complex and functional ways. 2)Ability to adapt.Vitalism and Mechanism-Contradict D and I!
Perspectives Of Emergence1) STRONG EMERGENCESystem components-do not determine new propertiesProperties- UNEXPECTED developments during interactions between components New properties IRREDUCIBLE!
2) WEAK EMERGENCEInteractions between system components-determine propertiesNew properties- Difficult to explain given current scientific knowledge and methods of prediction.Emergence-A MODEL to describe a system‟s behavior INDUCTIVE BUT NOT THEORITICAL PREDICTABILITY!
Weak Emergence And SimulationObserve Emergence States Emergence Law Emergence Law Initial Conditions Predict States!
The Good Side Of The StoryModern Science‟s problems-weak emergence.Computer Modeling!
Are discrete, abstract computational systems that are useful as general models of complexity.
Features Of Cellular Automata Discrete time generation (the temporal unit) Discrete space(Universe) a regular grid of cells (the spatial unit) any finite dimensions Finite number of states each cell has one state at a certain time Local evolution-Creation of a Generation The state of a cell at time t is a function (the rule) of the states of a finite number of selected cells (its neighbours) at time t-1
Features Of Cellular Automata(Contd.) UPDATE RULE –invoke the states of a cell‟s neighbouring cells at tn – is applied to each and every cell in the universe. Deterministic evolution Each time the rules are applied to the whole grid, a certain new generation is created based on the states of previous generation.
An Example of CA Space: 1-D States: black(B) and white(W) Neighborhood: two adjacent cells Rules: A white cell becomes black if any of its neighbors are black, and remains white otherwise. A black cell remains black.
Another ExampleCURRENT PATTERN NEW STATE FOR CENTER CELLN1 Centre N21 1 1 01 1 0 01 0 1 01 0 0 10 1 1 10 1 0 10 0 1 10 0 0 0
Approach To Biological Modeling Very Mathematical---Discretized and Simplified, but still! Physical systems using physical laws--Integro Differential equations (NON LINEAR!) with complex boundary conditions AIM: To discretize them--simpler rules!
The UNIVERSE and its CELLS : 1) The grid that constitutes the universe is rectilinear so that each cell is a square with 2 spatial dimensions and1 temporal dimension. 2)The Universe in the Game of Life is infinite, both spatially and temporally. Possible STATES a cell might be in : Alive and dead. NEIGHBOURHOOD : The 8 cells immediately surrounding it, above and below, to each side, and at the four corners.
Lifes Transition Rules At each time step t exactly one of three things can happen to a cell:1) BIRTH: If the cell state at t − 1 was 0 (dead), the cell state becomes 1 (alive) if exactly three neighbours were 1 (alive) at t − 1;2) SURVIVIAL : If the cell state at t − 1 was 1 (alive), the cell state is still 1 if either two or three neighbours were 1(alive) at t − 1;3) DEATH: If the cell state at t − 1 was 1 (alive), the cell state becomes 0 (dead) if either fewer than two or more than three neighbors were 1 (alive) at t − 1 (cells can die of “loneliness” or “overpopulation”).
Glider Guns Conway‟s 50 Dollar Prize---Any initial configuration with a finite number of living cells, the population cannot grow beyond some finite upper limit. To disprove -discover patterns that keep adding counters to the field. Gosper‟s Glider Gun-produces its first glider on the 15th generation, and another glider every 30th generation from then on