A Computation in a Cellular Automaton Collider Rule 110

Mart́ınez, Genaro J.; Adamatzky, Andrew; McIntosh, Harold V.

doi:10.1007/978-3-319-33924-5_15

Cited by 9 publications

(4 citation statements)

References 43 publications

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“…But, although this can be confined in a physical computing device several limitations should be improved: avoid the use of mirrors and the use of flags. An option is that they could be manipulated into in a ring (or virtual CA collider [32,27]).…”

Section: Discussionmentioning

confidence: 99%

Logical Gates via Gliders Collisions

Mart́ınez

Adamatzky

Morita

2018

Reversibility and Universality

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An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours and a certain number of its own past states. Some cellstate transition rules support gliders, compact patterns of non-quiescent states translating along the chain. We present designs of logical gates, including reversible Fredkin gate and controlled not gate, implemented via collisions between gliders.

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Section: Discussionmentioning

confidence: 99%

Logical Gates via Gliders Collisions

Mart́ınez

Adamatzky

Morita

2018

Reversibility and Universality

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“…Glider collisions and interactions can produce other particles such as socalled 'blocks', 'beehives', 'blinkers', 'traffic lights', and a less common pattern known as the 'eater'. Particle collisions in cellular automata, as in high particle physics supercolliders, have been studied before [16], demonstrating the computational capabilities of such interactions where both annihilation and new particle production is key. Particle collision and interaction profiling may thus be key in controlling the way in which computation can happen within the cellular automaton.…”

Section: Emergent Patterns In the Game Of Lifementioning

confidence: 99%

Algorithmic Information Dynamics of Emergent, Persistent, and Colliding Particles in the Game of Life *

Zenil¹,

Kiani²,

Tegnér³

2019

From Parallel to Emergent Computing

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Without loss of generalisation to other systems, including possibly non-deterministic ones, we demonstrate the application of methods drawn from algorithmic information dynamics to the characterisation and classification of emergent and persistent patterns, motifs and colliding particles in Conway's Game of Life (GoL), a cellular automaton serving as a case study illustrating the way in which such ideas can be applied to a typical discrete dynamical system. We explore the issue of local observations of closed systems whose orbits may appear open because of inaccessibility to the global rules governing the overall system. We also investigate aspects of symmetry related to complexity in the distribution of patterns that occur with high frequency in GoL (which we thus call motifs) and analyse the distribution of these motifs with a view to tracking the changes in their algorithmic probability over time. We demonstrate how the tools introduced are an alternative to other computable measures that are unable to capture changes in emergent structures in evolving complex systems that are often too small or too subtle to be properly characterised by methods such as lossless compression and Shannon entropy.

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“…Rule 110 can simulate a cyclic tag system [12], cyclic tag systems can simulate tag systems [12,14], tag systems can simulate Turing machines [7], and a Turing machine (developed by Eppstein and published by Cook [12]) can simulate Rule 110 and therefore such a Turing machine is universal. The CULET can simulate the universal Turing machine which simulates the behaviour of Rule 110, complex behaviour, and collisions of particles [15,16].…”

Section: Universal Eca: Rule 110mentioning

confidence: 99%

A Turing Machine Constructed with Cubelets Robots

Figueroa¹,

Zamorano²,

Mart́ınez³

et al. 2019

JRNAL

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We describe the design and implementation of a modular and distributed robot that physically simulates functioning of a 2-symbols Turing machine. The robot is constructed with Cubelets (small autonomous robot-cubes used for teaching basic robotics and programming for kids) and Lego® bricks (thus the robot is called CULET). The Cubelets robotic blocks allow for a high level programming: instead of a traditional code, the robots are programmed by assembling various elementary blocks of robots together. We illustrate how read and write operations are physically implemented by the CULET.

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A Computation in a Cellular Automaton Collider Rule 110

Cited by 9 publications

References 43 publications

Logical Gates via Gliders Collisions

Logical Gates via Gliders Collisions

Algorithmic Information Dynamics of Emergent, Persistent, and Colliding Particles in the Game of Life *

A Turing Machine Constructed with Cubelets Robots

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