The ‘Game of Life’- alternate method to Earth’s climate modeling

by Paulina Ćwik

With all the technological advancements of the 21st century, unveiling the future of climate change and its impacts on societies and the environment remains difficult. This is especially true because anthropogenic climate change involves a multitude of complex interactions and feedback between climate system components, such as atmosphere, land, surface, sea-ice, etc., and biological, geophysical, social, and economic systems. Additional complexity to the dynamics of climate change is also resulting from a myriad of processes in coupled sub-systems that are nested at various spatiotemporal scales, such as, for example, interactions between a single cell, a plant, and an entire forest [1]. The interplay between components within the climate system is therefore complex, but the understanding of these dynamics is of essential value for assessment of potential impacts of climate change and future planning on suitable adaptation strategies. But how to do that? One of the most promising methods to study the mechanisms by which the dynamic system components interact is cellular automata.

The concept of a cellular automaton (singular form of cellular automata) isn’t new.  It originated in the 1940s with work of two scientists of Los Alamos National Laboratory: Stanislaw Ulam and John von Neumann [2]. A cellular automaton is a computer model of a system represented on a regular grid with cells [3, 4]. Each cell is in a one of finite states and it evolves at each time step of a simulation. The evolution itself depends on the states of the neighboring cells and set of adopted rules describing the behavior of a cell. The grid of cells is arranged without gaps or overlapping and is usually representing one or two dimensions, although a cellular automaton can operate in many dimensions.

Fig.1. Examples of patterns generated by a sequence of two-dimensional cellular automaton rules. Figure adopted from: “Wolfram, S. A new kind of science. Wolfram Media, Inc., 2002. Section 5.2 Cellular Automata, pp.174.”

One of the first scientists who actively contributed to an expansion of cellular automata interest beyond academia was British mathematician John Horton Conway [5]. In 1970 Conway invented ‘Game of Live’, a game that simulates real-life processes using a two-dimensional cellular automaton (Fig. 2). Conway’s game can be envisioned as a ‘Go’ board, where each cell has a state such as “on” and “off”, or “alive” and “dead”. The number of state possibilities can vary but is always finite. Each cell has its neighborhood – a set of cells, typically directly adjacent to the specific cell, that can be defined in a number of ways. There are many types of neighborhood configurations possible to use in the game. According to relatively simple transition rules established at the beginning of the modeling process, a state of a cell will change. It will happen with each time step, and the change will depend on the state of the cell itself and the state of its neighborhood. The change in a state applies to the whole grid at the same time. Depending on the modeler’s decision on neighborhood type, the local or global interaction between the cells in the model can be expressed.

Fig.2 Conway’s Game of Life. Adopted from https://www.jpytr.com/post/game_of_life/

The discovery of the ‘Game of Life’ was published by Martin Gardner in Scientific American’s Mathematical Games [6] and became instantly very famous. But why? The goal of the game is to identify patterns that evolve in interesting ways. The reason why the game has attracted this much interest is because of its ability to generate complex patterns of behavior that no one could predict. In a complicated system with many interactions between elements, such as in Earth’s climate system, abstraction of the system’s connections to a network, like in the ‘Game of Life’, helps us to find underlying patterns and simplicity that can be translated to mathematical rules. And this is due to one of the most astonishing properties of the game, namely, that it is governed by a set of very simple transition rules. The game capture unpredictability and other features of self-organizing behaviors that are observed in real life, proving that it is possible to simulate real-life processes using computer modeling.

The “Game of Life” and cellular automata have been proven to be extremely powerful conceptual tool to explore pattern formation and to simulate a complex behavior of the analyzed system. It shows that complex phenomena do not have to result from a set of complex rules or interactions. Complexity may, in fact, result from the evolution of interactions based on simple set of rules iterated over time. Perhaps, the same can be applied to climate system?

Thanks to the simplicity of underlying transition rules and the ability of efficient computational implementation of many concurrent processes, cellular automata can serve as an alternative method to climate modeling [7-9]. Non-equilibrium phenomena, meaning the ones that are constantly evolving (like in the dynamic Earth’s system), are not well modeled by static mathematical equations but are best described by evolutionary dynamics that shape them. Cellular automata are well designed to capture these patterns and allow studying new dynamical approaches to better understand the phenomenon that occurs on a scale of a whole Earth’s climate system.

Bibliography:

1. Snyder, C.W., Mastrandrea, M.D. and Schneider, S.H., (2011). “The Complex Dyanmics of the Climate System: Constraints on our Knowledge, Policy Implications and the Necessity of Systems Thinking”. In Philosophy of complex systems (pp. 467-505). North-Holland.
2. Sarkar, P. (2000).”A brief history of cellular automata”. Acm computing surveys (csur). 32(1): 80-107.
3. Wolfram, S. (1984).”Universality and complexity in cellular automata”. Physica D: Nonlinear Phenomena.10(1-2): 1-35.
4. Wolfram, S. (1984). “Cellular automata as models of complexity”. Nature. 311(5985). 419.
5. Adamatzky, A. (2010). “Game of life cellular automata”. Vol. 1. London, Springer.
6. Gardner, M. (1970). “Mathematical Games – The fantastic combinations of John Conway’s new solitaire game “life””. Scientific American223: 120-123.
7. Gaudreau, J., Perez, L. and Drapeau, P., (2016). BorealFireSim: A GIS-based cellular automata model of wildfires for the boreal forest of Quebec in a climate change paradigm. Ecological Informatics, 32, pp.12-27.
8. Lu, Q., Chang, N.B., Joyce, J., Chen, A.S., Savic, D.A., Djordjevic, S. and Fu, G.,(2018). Exploring the potential climate change impact on urban growth in London by a cellular automata-based Markov chain model. Computers, Environment and Urban Systems, 68, pp.121-132.
9. Kassogué, H., Bernoussi, A.S., Amharref, M. and Ouardouz, M., (2019). Cellular automata approach for modelling climate change impact on water resources. International Journal of Parallel, Emergent and Distributed Systems, 34(1), pp.21-36.