Bittorio revisited: structural coupling in the Game of Life

2019 ◽  
Vol 28 (4) ◽  
pp. 197-212 ◽  
Author(s):  
Randall D Beer
Keyword(s):  
Cellular Automaton ◽  
State Transition ◽  
The State ◽  
Theoretical Frameworks ◽  
Transition Graph ◽  
Structural Coupling ◽  
Game Of Life ◽  
Interaction Graphs ◽  
State Transition Graph ◽  
Autopoietic System

The notion of structural coupling plays a central role in Maturana and Varela’s biology of cognition framework and strongly influenced Varela’s subsequent enactive elaboration of this framework. Building upon previous work using a glider in the Game of Life (GoL) cellular automaton as a toy model of a minimal autopoietic system with which to concretely explore these theoretical frameworks, this article presents an analysis of structural coupling between a glider and its environment. Specifically, for sufficiently small GoL universes, we completely characterize the nonautonomous dynamics of both a glider and its environment in terms of interaction graphs, derive the set of possible glider lives determined by the mutual constraints between these interaction graphs, and show how such lives are embedded in the state transition graph of the entire GoL universe.

scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.

1A1-L10 Contact-State Transition Graph for Complex Shaped Objects(New Control Theory and Motion Control)

2011 ◽  
Vol 2011 (0) ◽  
pp. _1A1-L10_1-_1A1-L10_3
Author(s):  
Kensuke HARADA ◽  
Hiromu ONDA ◽  
Natsuki YAMANOBE ◽  
Eiichi YOSHIDA ◽  
Tokuo TSUJI ◽  
...  
Keyword(s):  
Control Theory ◽  
Motion Control ◽  
State Transition ◽  
Transition Graph ◽  
Contact State ◽  
State Transition Graph
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