Additive cellular automata and algebraic series
Theoretical Computer Science
Hierarchy of fuzzy cellular automata
Fuzzy Sets and Systems
Cellular automata in fuzzy backgrounds
Physica D
Number-conserving cellular automaton rules
Fundamenta Informaticae - Special issue on cellular automata
Universality and decidability of number-conserving cellular automata
Theoretical Computer Science - Algorithms,automata, complexity and games
Number-conserving cellular automata I: decidability
Theoretical Computer Science
Number conserving cellular automata II: dynamics
Theoretical Computer Science
On conservative and monotone one-dimensional cellular automata and their particle representation
Theoretical Computer Science - Special issue: Theoretical aspects of cellular automata
Fuzzy Cellular Automata for Modeling Pattern Classifier
IEICE - Transactions on Information and Systems
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
RBFFCA: A Hybrid Pattern Classifier Using Radial Basis Function and Fuzzy Cellular Automata
Fundamenta Informaticae - Special issue on DLT'04
Radial View of Continuous Cellular Automata
Fundamenta Informaticae - Membrane Computing
Cellular automata based on artificial neural network for simulating land use changes
Proceedings of the 45th Annual Simulation Symposium
Cellular automata model based on machine learning methods for simulating land use change
Proceedings of the Winter Simulation Conference
Solving the parity problem in one-dimensional cellular automata
Natural Computing: an international journal
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Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the ''fuzzification'' of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper, we are interested in the relationship between Boolean and fuzzy models and, for the first time, we analytically show the existence of a strong connection between them by focusing on two properties: density conservation and additivity. We begin by showing that the density conservation property, extensively studied in the Boolean domain, is preserved in the fuzzy domain: a Boolean CA is density conserving if and only if the corresponding FCA is sum preserving. A similar result is established for another novel ''spatial'' density conservation property. Second, we prove an interesting parallel between the additivity of Boolean CA and oscillations of the corresponding fuzzy CA around its fixed point. In fact, we show that a Boolean CA is additive if and only if the behaviour of the corresponding fuzzy CA around its fixed point coincides with the Boolean behaviour. Finally, we give a probabilistic interpretation of our fuzzification which establishes an equivalence between convergent fuzzy CA and the mean field approximation on Boolean CA, an estimation of their asymptotic density. These connections between the Boolean and the fuzzy models are the first formal proofs of a relationship between them.