1. Modelagem Dinâmica com TerraME Aula 5 – Building simple models with TerraME Tiago Garcia de Senna Carneiro (UFOP) Gilberto Câmara (INPE)

2. Complex Adaptive Systems: Humans as Ants Cellular Automata:  Matrix,  Neighbourhood,  Set of discrete states,  Set of transition rules,  Discrete time. “CAs contain enough complexity to simulate surprising and novel change as reflected in emergent phenomena” (Mike Batty) Simple agents following simple rules can generate amazingly complex structures.

3. Complex adaptative systems How come that a city with many inhabitants functions and exhibits patterns of regularity? How come that an ecosystem with all its diverse species functions and exhibits patterns of regularity? How can we explain how similar exploration patterns appear on the Amazon rain forest?

4. What are complex adaptive systems? Systems composed of many interacting parts that evolve and adapt over time. Organized behavior emerges from the simultaneous interactions of parts without any global plan.

5. Characteristics of CA models (1) Spatially-dynamic model enabling extreme spatial detail; Simple and intuitive. Complexity without complication (Couclelis 1986); Bottom-up approach to spatial modelling: complex morphology as the result of simple morphogenetic principles; Self-organising systems with emergent properties: locally defined rules resulting in macroscopic ordered structures. Massive amounts of individual actions result in the spatial structures that we know and recognise;

6. Characteristics of CA models (1) Complexity is manifested as a set of fractal dimensions (radial, cluster rank size rule, etc.) Wolfram (1984): 4 classes of states: (1) homogeneous or single equilibrium (2) periodic states (3) chaotic states (4) edge-of-chaos: localised structures, with organized complexity.

7. An Example: The Majority Model for Segregation Start with a CA with “white” and “black” cells (random) The new cell state is the state of the majority of the cell’s Moore neighbours, or the cell’s previous state if the neighbours are equally divided between “white” and “black”  White cells change to black if there are five or more black neighbours  Black cells change to white if there are five or more black neighbours What is the result after 50 iterations? How long will it take for a stable state to occur?

8. The Modified Majority Model for Segregation Include random individual variation Some individuals are more susceptible to their neighbours than others In general, white cells with five neighbours change to black, but:  Some “white” cells change to black if there are only four “black” neighbours  Some “white” cells change to black only if there are six “black” neighbours Variation of individual difference What happens in this case after 50 iterations and 500 iterations?

9. Key property of cellular spaces: potential POTENTIAL

10. What is the potential of a cell? Potential refers to the capacity for change Higher potential means higher chance of change How can we compute potential? Potential People Nature

11. Different models for calculating potential Brian Arthur’s model of increasing returns Vicsek-Salay model: structure from randomness Schelling’’s model: segregation as self-organization

12. The Brian Arthur model of increasing returns Create a cell space and fill it with random values For example, take a 30 x 30 cell space and populate with random values (1..1000)

13. The Brian Arthur model of increasing returns Think of this cellular space as the starting point for a population What happens if the rich get richer? This model is called “increasing returns”  This effect is well-known in the software industry  Customer may become dependent on proprietary data formats  High switching costs might prevent the change to another product  Examples: QWERTY keyboard, and Microsoft Windows Arthur, B. (1994). “Increasing Returns and Path Dependence in the Economy”. Ann Arbor, MI: The University of Michigan Press.

14. The Brian Arthur model of increasing returns Consider a situation where the potential grows with a return factor  (  is a scale factor) O <  < 1 - decreasing returns (increased competition)  = 1 – linear growth  > 1 – increasing returns (rich get richer)

15. The Brian Arthur model of increasing returns Take the random 30 x 30 cell space and apply the increasing returns model  = 2 – What happens?

16. The Vicsek-Szaly Model: Structure from Randomness Consider a CA with a 4 x 4 neighbourhood Establish a random initial distribution  Historical accident that set the process in motion Pure averaging model