Cellular automata (CA) are pretty straight forward mixers can simulate complex processes both in space and time. A CA includes six defining components: a framework, cells, an area, rules, initial conditions, as well as an update sequence. CA models are pretty straight forward, nominally deterministic yet able to showing phase changes and emergence, map easily to the data structures utilized in geographic computer, and are simple to implement and understand. It has led to their recognition for applications for example calculating land use changes and monitoring disease spread, among many more.

**cellular automata**: A regular framework of cells, each in a single of the finite quantity of states. America of cells within the framework are updated concurrently in discrete time steps where the condition of every cell is altered based on some rules that rely on the condition from the cell and individuals of their neighbors in the previous time step.

Cellular automata (CA) are computational abstractions that permit simulations of spatially distributed phenomena as well as their dynamics with time. CA are some of the simplest ways that complex systems behavior could be shown, and therefore happen to be famous modeling geographic systems that demonstrate complexity, including land use change, urban growth, human and vehicle movement, multiplication of disease, sand dune formation, and plant life change. Benefits of CA models are that they're simple, nominally deterministic yet able to showing phase changes and emergence, map easily to the data structures utilized in geographic computer, and are simple to implement and understand.

A CA includes six defining components: a framework, cells, an area, rules, initial conditions as well as an update sequence. The framework sets the restrictions and limits from the system, for instance constraining a CA to a couple of dimensions, and deciding what goes on in a region’s edges. Geographical examples usually select a study area or region, and mask the level so the CA cannot apply beyond them. Cells are similar spatial units, frequently squares or pixels, which cover the geographic extent in a selected resolution. Geographical data for CA are frequently selected to coincide with satellite image pixels or geographic grids, which are already partitioned into tessellations. The area may be the region of interaction one of the cells. In classical CA, this is actually the immediately adjacent two cells in a single dimension and also the Moore (8) or Von Neumann (4) neighbors in 2 dimensions. Changes inside a cell are created by making use of the guidelines inside the neighborhood, and altering the cell when the situation warrants it. Cells will also be understood to be getting mutually exclusive states, some classes that the cell can belong. For instance, the group of states for any land use cell might be . All cells within the CA should be in one of these simple states at each period of time. The guidelines would be the determinants from the conditions to which the active cell can change states. Simple CA designs include couple of rules, for instance in Conway’s classic 1970 CA bet on Existence (Adamatzky, 2010), cells are only able to possess the states alive (1) or dead () on the square grid by having an 8 cell neighborhood. Each and every part of time, two rules are applied according to the number of from the neighbors are alive: an active cell will die whether it has less that several than three live neighbors a defunct cell can come to existence whether it has exactly three live neighbors otherwise it remains unchanged (Gardner, 1970 1972). Figure 1 shows a preliminary distribution of live cells, and also the configuration after sequences of your time steps. In the style of geographical CA models, the guidelines set and it is construction, or derivation from actual change data, is frequently a main issue with the CA model design task.

*Figure 1. The first conditions and additional time steps for that Bet on Existence. White-colored cells are “;dead”, and black “;alive.”*

The first the weather is the beginning set or seed generation for that model, usually a real spatial configuration or map from the phenomenon in the beginning period for that modeling, like a land use map of the city this year, once the goal would be to simulate changes to 2030. The option of initial conditions is essential. For instance in Conway’s bet on Existence described above, setting all cells to dead will produce no change, while setting all cells to alive can make all cells die in only one iteration, a phase change. Lastly, cells should be updated. Usually during one model period of time all rules are put on each cell to ensure that all rows and posts of cells within the framework, using the new states entering a duplicate buffer grid, then your replica replaces the initial. Many models use discrete time steps, for example ten minutes, 30 days, or perhaps a year for every time step. Updates continue before the target time is arrived at, or perhaps a given quantity of change has had place.

CA’s origins lie within the 1940s at Los Alamos National Laboratory, where Stanislaw Ulam was analyzing very growth on the lattice network while John von Neumann ran the issue of self-replicating systems. Ulam recommended that the self-replicating system might be simulated like a mathematical abstraction, a 2-dimensional cellular automata with a lot of states. Von Neumann demonstrated in past statistics that the CA pattern could indeed make endless copies of itself, showing that the self-replicating machine was possible, an essential advance in solving the halting problem (von Neumann, 1951: von Neumann & Burks, 1966). However, CA continued to be in the margins of mathematics until twenty five years later. Throughout the 1970s, the sport of Existence was devised by John Conway and popularized by Martin Gardner in the column in Scientific American. Analysis of Conway’s game demonstrated that entire systems of cellular automata could grow, extinguish themselves, or jump between chaos and organization. Starting in 1983, Stephen Wolfram started a complete systematic analysis from the behavior of 1-dimensional CA, formalizing the kinds of patterns that may be derived (Wolfram, 1983).

That complex systems behavior could be simulated in the simplest of CAs brought Wolfram to write A New Type of Science (Wolfram 2002). Wolfram noted that cellular automata have importance to all scientific discipline, including biology and geography. Only using a 1 dimensional CA, Wolfram demonstrated that any mathematical function could be simulated, implying that any phenomenon and then any dynamic might be modeled by CA. He suggested four possible classes of CA. At School 1, patterns rapidly evolve right into a stable pattern and randomness disappears. At School 2, patterns rapidly evolve into an oscillating structure, with a few randomness remaining. At School 3, patterns evolve into pseudo-random or chaotic structures by which regular structures are rapidly eliminated by dissipating randomness. At School 4, any initial pattern evolves into complex structures with unpredictable interactions. The proven fact that CA has been shown to duplicate system behavior from extinction to stability and from chaos to complexity means they are especially appropriate for geographical problems as well as their dynamics.

The majority of the concepts of CA could be learned by simple experiments with Conway’s bet on existence. Some online software packages that to experiment are: Golly, a wide open-source simulation system for Existence along with other cellular automata which includes very fast generation, and Python scripts for editing and simulation Mirek's Cellebration, a totally free 1-D and a pair of-D cellular automata viewer, explorer and editor for Home windows and Xlife, the conventional UNIX X11 Existence simulation application now ported to Home windows, with as many as eight possible states per cell. Experiments will disclose that no matter initial conditions, with time 1 of 3 outcomes will result: (1) all cells will die (2) certain stable and constant geometrical configurations will emerge or (3) stable but altering patterns that oscillate, move, or perhaps replicate leaves the CA under constant change. Named emergent patterns that don't change range from the Block, Beehive, Loaf, Boat and Tub. Individuals that survive by oscillation over different length periods of time range from the Blinker, Toad, Beacon, Pulsar and Pentadecathlon. Patterns that survive by movements would be the Glider and light-weight Spaceship. Meta structures include glider guns, rakes and puffer breeders, which sometimes take very lengthy periods of time to construct after which stabilize as generators of gliders along with other patterns. Types of each receive around the Wiki entry for “;Conway's Bet on Existence.” It's these more complicated structures, Wolfram’s class 4, which are of finest interest for types of complex spatial phenomena, since stability isn't involved with urban growth, land use change, or traffic movement.

In geography, early factors of cellular automata were by Tobler (1979) and then Couclelis (1985). The emergence of GIS and remote sensing as causes of gridded geographic data appropriate for cellular modeling, and enhancements in structured programming languages to control grids elevated the amount of curiosity about CA throughout the 1990s. Much research was centered in the Santa Fe Institute, and transported in to the geographic information science community following the 1996 Santa Fe GIS and Ecological Modeling conference. A host of CA designs include been accustomed to simulate urban growth and it is effects, reviewed by Sante et al. (2010). CA designs include proven very popular in modeling land use change, and are generally used through the spatial sciences.

*Figure 2. Cellular Automaton Model (SLEUTH) Forecast for 2050 of Land Use within the Eastern U . s . States for that Mid-Atlantic Integrated Assessment through the U.S. Ecological Protection Agency. Source: Candau, J., Rasmussen, S. and Clarke, K. C. (2000) A coupled cellular automaton model for land use/land cover dynamics. fourth Worldwide Conference on Integrating GIS and Ecological Modeling (GIS/EM4): Problems, Prospects and Research Needs. Banff, Alberta, Canada, September2 – 8, 2000. [Public Domain image Environmental protection agency/USGS].*

Reserach has investigated restricted CA models, where CA processes are restricted by weighted potentials, geographic distributions or economic constraints. CA methods have highly effective in modeling traffic flow, human movement, natural systems for example erosion and streams, wildfire, and lots of other locations. CA have proven helpful in aiding the classification process for remotely thought images. Many applications use geocomputation and performance computing with CA models, because the simple operations are often parallelized. Since about 2010, there's been a brand new curiosity about CA model rule selection and model calibration using machine learning methods, for example support vector machines, genetic algorithms and artificial neural systems. They make an effort to automate the guidelines for any CA by utilizing actual change information, by research into the classes from the surrounding pixels. For instance, a 2000 along with a 2010 land use map could be differenced, and also the cells that altered states isolated and accustomed to extract the modification conditions like a purpose of contributory factors, for example distance or topographic slope.

There's a obvious match between geographical regions and CA. GIS and remote sensing allow data to become quickly formatted, resampled and selected to supply layers of geographic information for CA modeling. Indeed, some GIS packages include CA tools inside the software. Additionally they set the first conditions, i.e. the land configuration before the period of time utilized by the CA, and may be used to display and evaluate future conditions by map comparison. When multiple time slices of information exist, the model could be calibrated using hind-casting, i.e. the model map distribution anytime could be evaluated from the actual data to check model precision. In calibration, the guidelines from the CA and frequently the weights provided to individuals input layers that influence the CA could be adjusted before the model offers the best simulation from the “;present”, or at best the timeframe most abundant in recent data. The calibrated model may then be run to return to create forecasts. It's the easy data set up, combined with the simple nature of CA models, which are the method’s chief advantages.

An essential element of CA models is they are “;bottom-up” models. All change happens at specific locations, and aggregate behavior emerges in the coalescence from the local. Thus all interactions in CA are independent and native, without any influence-at-a-distance effects. At high spatial resolutions, these influence distances can be quite small, just meters on the floor. Obviously many have contended this makes CA unacceptable for modeling systems with increased complicated and longer range interactions, for example social, demographic and economic models. Others have noticed that CA models also absorb immense levels of computer time, and may take several weeks or many years of try to yield accurate forecasts. Elevated computing power, lower computing costs and performance computing have countered this claim. Lastly, in CA models the same time step is assumed (say twelve months) that could vary from the right time resolution of the particular city or data, in which a census might be available only decadally.

Overall, CA have enjoyed a long duration of very frequently applied spatial models, specifically for spatially distributed dynamical systems. They're flexible enough to integrate well along with other types of modeling, for example Agent-Based models and Multi-Qualifying criterion Evaluation, and could be evaluated and calibrated with lots of geostatistical and machine learning methods. Refinements and enhancements in CA methods continue unchecked, and also the spread from the models with other disciplines and applications will make sure this status for that immediate future.

Adamatzky, A., (erectile dysfunction.) (2010). *Bet on Existence Cellular Automata*. Springer.

Couclelis, H. (1985). Cellular worlds: a framework for modelling micro–macro dynamics. *Atmosphere and Planning For A,* *17*, 585-596.

Gardner, M. (1972). Mathematical Games. *Scientific American,* *226*, 114-118.

Gardner, M. (1970). Mathematical Games: The great mixtures of John Conway's new solitaire game "existence". *Scientific American,* *223*, 120-123.

Sante, I., Garcia, A. M., Miranda, D., & Crecente, R. (2010). Cellular automata models for that simulation of real-world urban processes: An evaluation and analysis. *Landscape and concrete Planning,* *96*, 108-122. DOI: 10.1016/j.landurbplan.2010.03.001

Tobler, W. (1979). Cellular geography. In S. Gale and G. Olsson (Eds.) *Philosophy in Geography*, 379-86. Dortrecht: Riedel.

von Neumann, J. (1951). "The overall and logical theory of automata," in L.A. Jeffress, (erectile dysfunction.) Cerebral Mechanisms in Behavior – The Hixon Symposium, John Wiley & Sons, New You are able to, 1-31.

von Neumann, J., & Burks, A. W. (1966). *Theory of Self-Reproducing Automata*. College of Illinois Press.

Wolfram, S. (1983). Record Mechanics of Cellular Automata. *Reviews of contemporary Physics,* *55*(3), 601-644.

Wolfram, S. (2002). *A Brand New Type of Science*. Wolfram Media.

- Describe exactly what a cellular automaton is and just what its critical factors are.
- Discuss how CA evolved through its rise in mathematics, information technology, and geography.
- Identify CA concepts and patterns while using bet on Existence and straightforward software.
- Summarize how CA continues to be adapted for modeling in geography using GIS.
- Critique CA for modeling geographical systems.
- Demonstrate how you can check out the CA research literature.

- Check out the Wikipedia entry for Conway’s Bet on Existence. What exactly are types of a few of the static forms that may emerge hanging around of Existence?
- Do you know the six factors that form a CA? That are areas of the geographic input data, and that are areas of the CA model itself?
- Define an intricate system and what's meant by emergence. How come CA’s good tools for understanding complexity?
- So how exactly does a CA integrate both space and time?
- How quickly can alter propagate across an area when modeled by CA? Do you know the implications of the rate of dynamics for modeling geographical systems?
- How did CA change from information technology and physics into geography, and why?
- Research five papers written within the last five years which use CA models in geography.

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