Spatio-temporal information in society: cellular automata Gilberto Câmara Licence: Creative Commons ̶̶̶̶ By Attribution ̶̶̶̶ Non Commercial ̶̶̶̶ Share Alike http://creativecommons.org/licenses/by-nc-sa/2.5/

Computational Modelling with Cell Spaces Components Generalizes Proximity Matriz – GPM Hybrid Automata model Nested enviroment

Cell Spaces

Cellular Automata: Humans as Ants 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)

2-Dimensional Automata 2-dimensional cellular automaton consists of an infinite (or finite) grid of cells, each in one of a finite number of states. Time is discrete and the state of a cell at time t is a function of the states of its neighbors at time t-1.

Cellular Automata Neighbourhood Rules Space and Time t States t1

Most important neighborhoods Von Neumann Neighborhood Moore Neighborhood

Conway’s Game of Life At each step in time, the following effects occur: Any live cell with fewer than two neighbors dies, as if by loneliness. Any live cell with more than three neighbors dies, as if by overcrowding. Any live cell with two or three neighbors lives, unchanged, to the next generation. Any dead cell with exactly three neighbors comes to life.

Game of Life Static Life Oscillating Life Migrating Life

Conway’s Game of Life The universe of the Game of Life is an infinite two-dimensional grid of cells, each of which is either alive or dead. Cells interact with their eight neighbors.

Characteristics of CA models 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;

Which Cellular Automata? For realistic geographical models the basic CA principles too constrained to be useful Extending the basic CA paradigm From binary (active/inactive) values to a set of inhomogeneous local states From discrete to continuous values (30% cultivated land, 40% grassland and 30% forest) Transition rules: diverse combinations Neighborhood definitions from a stationary 8-cell to generalized neighbourhood From system closure to external events to external output during transitions