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memory ” ( Hopfield , 1982 , p . 2554 ). In those systems it is possible to access information that is stored in the memory via their attributes .
Hopfield proposes a neural network in which the state of each neuron changes randomly in time and asynchronously . This model uses strong non-linearities to make choices , categorize , and regenerate information . Hopfield states that the analysis of collective emerging effects and of spontaneous computation should necessarily emphasize nonlinearities and the relationship of inputs and outputs .
From the collective behavior of these simple processors , new computational properties emerge and the system constitutes itself as a content-addressable memory . Those memories can be accessible given large enough fragments . Given its structure as a combination of parallel asynchronous processing elements , the system is robust to failure in individual devices and behaves in tandem with the concept of loose-coupling as defined by Simon ( 1973 ).
Wolfram ( 1984 ) discusses cellular automata ( CA ) and the insights that can be drawn from its use . First of all , Wolfram defines CA as simple discrete dynamic systems that have properties of self-organization . Fundamentally , CAs differ from traditional dynamic systems by the emphasis on spatially rigid rules , that is , the local influence of a given neighborhood . However , just as in the analysis of dynamic systems , the interest falls onto the trajectories of the CA system and on its attractors .
Given the definition and processes of CA , Wolfram identifies four typical classes of behavior . The first class allows predictions to be made with probability one , independently of initial conditions . In class 2 , the result of a specific cell can be given as long as its initial state is known . Class 3 leads to random states . However , from the initial states , it is possible to build an algorithm that leads to the correct prediction . Class 4 does not allow for predictions . The algorithm necessary to make such prediction would be as complex as the simulation of the evolution of the CA ’ s states . In this case , a model is not possible .
Wolfram affirms that the universality property — originally a contribution by Turing ( 1950 ) may very well be present in cellular automata :
Cellular automata may be viewed as computers , in which data represented by initial configurations is processed by time evolution . Computational universality implies that suitable initial configurations can specify arbitrary algorithms procedures . The system can thus serve as a general purpose computer , capable of evaluating a ( computable ) function . Given a suitable encoding , the system may therefore in principle simulate any other system , and in this sense may be considered capable of arbitrarily complicated behavior . ( Wolfram , 1984 , p . 31 )
The interest of studying CA , from the view of physicists , is that CAs are characterized as discrete dynamic systems in space-time , and were the starting point for all the following analysis about phase space ( Langton , 1986 ). In fact , this is how Langton comments von Neumann ’ s works : “ Von Neumann proved that cellular automata are capable of universal computation by showing that a universal Turing machine could be embedded in a cellular array ” ( Langton , 1986 , p . 129 ).
Langton ( 1986 ) makes a bold proposal in his paper discussing the “ possibility that life could emerge from the interaction of inanimate artificial molecules ” ( Langton , 1986 , p . 120 ). He does that using the prop-
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