Design Principles for Achieving High-Performance Submicron Digital Technologies

Emergence, Complexity and Computation

Adamatzky

McIntosh

2016

Section: Discussionsupporting

confidence: 59%

A Computation in a Cellular Automaton Collider Rule 110

Emergence, Complexity and Computation

Adamatzky

McIntosh

2016

“…Designs for computing these tubes follow a principle based on an unconventional computing representation paradigm (Mills, 2008). In this way, Fredkin and Toffoli have developed a concept of a general-purpose computation based on ballistic interactions between quanta of information that are represented by abstract particles (Fredkin and Toffoli, 2002). The Boolean states of logical variables are represented by balls or atoms, which preserve their identity when they collide with each other.…”

Section: Plasmodial Tube and Circular Computationmentioning

confidence: 99%

Majority Gates and Circular Computation in Slime Mould

Adamatzky

Mayne

et al. 2015

07/20/2015-07/24/2015

Slime mould has been proven to be a fruitful living substrate for implementing a wide range of computing circuits from computational geometry to collision-based logical circuits to robot control. It is apparent, however, that constructing working real-time universal processors from the slime mould is non-trivial task. We explore here similarities between development of slime mould protoplasmic tubes, transportation of cytoplasm inside the tubes and dynamics of propagating patterns in cellular automata. Based on these analogies we will propose computing devices realisable in the living slime mould.

“…CA as super computer models are developed extensively in [104,20,16,59,82,99,111,92,44,98,33,3,4,5,1,115,45,66].…”

Section: Final Remarksmentioning

confidence: 99%

Wolfram’s Classification and Computation in Cellular Automata Classes III and IV

Emergence, Complexity and Computation

Seck-Tuoh-Mora

Zenil

2013

We conduct a brief survey on Wolfram's classification, in particular related to the computing capabilities of Cellular Automata (CA) in Wolfram's classes III and IV. We formulate and shed light on the question of whether Class III systems are capable of Turing universality or may turn out to be "too hot" in practice to be controlled and programmed. We show that systems in Class III are indeed capable of computation and that there is no reason to believe that they are unable, in principle, to reach Turing-completness.Keywords: cellular automata, universality, unconventional computing, complexity, gliders, attractors, Mean field theory, information theory, compressibility. Wolfram's classification of Cellular AutomataA comment in Wolfram's A New Kind of Science gestures toward the first difficult problem we will tackle (ANKOS) (page 235): trying to predict detailed properties of a particular cellular automaton, it was often enough just to know what class the cellular automaton was in. The second problem we will take on concerns the possible relation between complexity of Cellular Automata and Turing universal computation, also highlighted by Wolfram in his ANKOS (page 691-on Class 4 behaviour and Universality): I strongly suspect that it is true in 1 arXiv:1208.2456v2 [nlin.CG] 29 Aug 2012 general that any cellular automaton which shows overall class 4 behaviour will turn out-like Rule 110-to be universal. The classification and identification of cellular automata (CA) has become a central focus of research in the field. In [108], Stephen Wolfram presented his now well-known classes. Wolfram's analysis included a thorough study of one-dimensional (1D) CA, order (k = 2, r = 2) (where k ∈ Z + is the cardinality of the finite alphabet and r ∈ Z + the number of neighbours), and also found the same classes of behaviour in other CA rule spaces. This allowed Wolfram to generalise his classification to all sorts of systems in [114].An Elementary Cellular Automaton (ECA) is a finite automaton defined in a 1D array. The automaton assumes two states, and updates its state in discrete time according to its own state and the state of its two closest neighbours, all cells updating their states synchronously.Wolfram's classes can be characterised as follows:• Class I. CA evolving to a homogeneous state • Class II. CA evolving periodically • Class III. CA evolving chaotically • Class IV. Includes all previous cases, known as a class of complex rules Otherwise explained, in the case of a given CA,:• If the evolution is dominated by a unique state of its alphabet for any random initial condition, then it belongs to Class I.• If the evolution is dominated by blocks of cells which are periodically repeated for any random initial condition, then it belongs to Class II.• If for a long time and for any random initial condition, the evolution is dominated by sets of cells without any defined pattern, then it belongs to Class III.• If the evolution is dominated by non-trivial structures emerging and travelling along the evolution...