Life turns fifty

2021 ◽  
Vol 49 (3) ◽  
pp. 10-10
Author(s):  
SIGCAS Team

Mention to computer scientists, gliders, glider guns, birth and death rules and they smile remembering their efforts to study societal life. October marked the 50th anniversary of the publication of John Conway's game of Life in Martin Garner's Mathematical Games column [1], For the lay person with no knowledge of Life, it's difficulty to imagine how popular a single person game with only a single move (i.e. setting the initial conditions) could be.

1996 ◽  
Vol 06 (11) ◽  
pp. 2077-2086 ◽  
Author(s):  
GARY MAR ◽  
PAUL ST. DENIS

In Conway’s Game of Life every cell is either fully alive (has the value of 1) or completely dead (has the value 0). In Real Life this restriction to bivalence is lifted to countenance “real-valued” degrees of life and death. Real Life contains Conway’s Game of Life as a special case; however, Real Life, in contrast to Conway’s Game of Life, exhibits sensitive dependence on initial conditions which is characteristic of chaotic systems.


1999 ◽  
Vol 09 (10) ◽  
pp. 2105-2126 ◽  
Author(s):  
TAO YANG ◽  
LEON O. CHUA

Small-world phenomenon can occur in coupled dynamical systems which are highly clustered at a local level and yet strongly coupled at the global level. We show that cellular neural networks (CNN's) can exhibit "small-world phenomenon". We generalize the "characteristic path length" from previous works on "small-world phenomenon" into a "characteristic coupling strength" for measuring the average coupling strength of the outputs of CNN's. We also provide a simplified algorithm for calculating the "characteristic coupling strength" with a reasonable amount of computing time. We define a "clustering coefficient" and show how it can be calculated by a horizontal "hole detection" CNN, followed by a vertical "hole detection" CNN. Evolutions of the game-of-life CNN with different initial conditions are used to illustrate the emergence of a "small-world phenomenon". Our results show that the well-known game-of-life CNN is not a small-world network. However, generalized CNN life games whose individuals have strong mobility and high survival rate can exhibit small-world phenomenon in a robust way. Our simulations confirm the conjecture that a population with a strong mobility is more likely to qualify as a small world. CNN games whose individuals have weak mobility can also exhibit a small-world phenomenon under a proper choice of initial conditions. However, the resulting small worlds depend strongly on the initial conditions, and are therefore not robust.


2015 ◽  
Vol 21 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Randall D. Beer

Maturana and Varela's concept of autopoiesis defines the essential organization of living systems and serves as a foundation for their biology of cognition and the enactive approach to cognitive science. As an initial step toward a more formal analysis of autopoiesis, this article investigates its application to the compact, recurrent spatiotemporal patterns that arise in Conway's Game-of-Life cellular automaton. In particular, we demonstrate how such entities can be formulated as self-constructing networks of interdependent processes that maintain their own boundaries. We then characterize the specific organizations of several such entities, suggest a way to simplify the descriptions of these organizations, and briefly consider the transformation of such organizations over time.


2020 ◽  
Vol 26 (3) ◽  
pp. 338-365
Author(s):  
Peter D. Turney

We present a computational simulation of evolving entities that includes symbiosis with shifting levels of selection. Evolution by natural selection shifts from the level of the original entities to the level of the new symbiotic entity. In the simulation, the fitness of an entity is measured by a series of one-on-one competitions in the Immigration Game, a two-player variation of Conway's Game of Life. Mutation, reproduction, and symbiosis are implemented as operations that are external to the Immigration Game. Because these operations are external to the game, we can freely manipulate the operations and observe the effects of the manipulations. The simulation is composed of four layers, each layer building on the previous layer. The first layer implements a simple form of asexual reproduction, the second layer introduces a more sophisticated form of asexual reproduction, the third layer adds sexual reproduction, and the fourth layer adds symbiosis. The experiments show that a small amount of symbiosis, added to the other layers, significantly increases the fitness of the population. We suggest that the model may provide new insights into symbiosis in biological and cultural evolution.


1976 ◽  
Vol 23 (1) ◽  
pp. 56-60
Author(s):  
Lauren L. Meneghan

John Conway's game of “life” provides a delightful and fascinating game for students of junior high school. (The introduction to Mr. Conway's game can be found in an article by Martin Gardner in the October 1970 issue of Scientific American.) Mr. Conway intended that the game be played by one person, but it can easily be adapted so that two or three students can play the game at one time.


2016 ◽  
Vol 89 ◽  
pp. 348-352 ◽  
Author(s):  
Jinling Wei ◽  
Haiyan Zhou ◽  
Jun Meng ◽  
Fan Zhang ◽  
Yunmo Chen ◽  
...  

2009 ◽  
Vol 15 (3) ◽  
pp. 351-375 ◽  
Author(s):  
Nicholas M. Gotts

Small patterns of state 1 cells on an infinite, otherwise empty array of Conway's game of Life can produce sets of growing structures resembling in significant ways a population of spatially situated individuals in a nonuniform, highly structured environment. Ramifying feedback networks and cross-scale interactions play a central role in the emergence and subsequent dynamics of the quasi population. The implications are discussed: It is proposed that analogous networks and interactions may have been precursors to natural selection in the real world.


2008 ◽  
Vol 10 (04) ◽  
pp. 461-470 ◽  
Author(s):  
GUILLERMO OWEN

We develop a model of coalition formation based on personal proximities among the players of an n-person game. Several examples are worked out in detail, showing that certain coalitions are much more stable than others, and/or much more likely to form than others. We also consider the dynamics of such coalition-formation. By a numerical example, we show that small changes in the initial conditions can lead to very different results in the coalitions formed in a given game.


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