2,755 research outputs found
Reproducing the cyclic tag system developed by Matthew Cook with Rule 110 using the phases f1_1
This paper implements the cyclic tag system (CTS) in Rule 110 developed by Cook in [1, 2] using regular expressions denominated phases fi_1 [3]. The main problem in CTS is coding the initial condition based in a system of gliders. In this way, we develop a method to control the periodic phases of the strings representing all gliders until now known in Rule 110, including glider guns. These strings form a subset of regular expressions implemented in a computational system to facilitate the construction of CTS. Thus, these phases are useful to establish distances and positions for every glider and then to delineate more sophisticated components or packages of gliders. In this manuscript, it is possible to find differences with the results exposed in Wolfram's book [2], inclusively some mistakes which avoid to obtain an appropriated realization of CTS in Rule 110; fortunately, these irregularities were discussed and clarified by Cook
Production of gliders by collisions in Rule 110
We investigate the construction of all the periodic structures or “gliders” up to now known in the evolution space of the one-dimensional cellular automaton Rule 110. The production of these periodic structures is developed and presented by means of glider collisions. We provide a methodology based on the phases of each glider to establish the necessary conditions for controlling and displaying the collisions of gliders from the initial configuration
Determining a regular language by glider-based structures called phases fi_1 in Rule 110
Rule 110 is a complex elementary cellular automaton able of supporting universal computation and complicated collision-based reactions between gliders. We propose a representation for coding initial conditions by means of a finite subset of regular expressions. The sequences are extracted both from de Bruijn diagrams and tiles specifying a set of phases fi_1 for each glider in Rule 110. The subset of regular expressions is explained in detail
Rule 110 objects and other constructions based-collisions
The one-dimensional cellular automaton Rule 110 shows a very ample and diversified glider dynamics. The huge number of collision-based reactions presented in its evolution space are useful to implement some specific (conventional and unconventional) computable process, hence Rule 110 may be used to implement any desired simulation. Therefore there is necessity of defining some interesting objects as: solitons, eaters, black holes, flip-flops, fuses and more. For example, this work explains the construction of meta-gliders; for these constructions, we specify a regular language in Rule 110 to code in detail initial conditions with a required behavior. The paper depicts as well several experimental collision-based constructions
Complex dynamics emerging in Rule 30 with majority memory
In cellular automata with memory, the unchanged maps of the conventional
cellular automata are applied to cells endowed with memory of their past states
in some specified interval. We implement Rule 30 automata with a majority
memory and show that using the memory function we can transform quasi-chaotic
dynamics of classical Rule 30 into domains of travelling structures with
predictable behaviour. We analyse morphological complexity of the automata and
classify dynamics of gliders (particles, self-localizations) in memory-enriched
Rule 30. We provide formal ways of encoding and classifying glider dynamics
using de Bruijn diagrams, soliton reactions and quasi-chemical representations
Local information transfer as a spatiotemporal filter for complex systems
We present a measure of local information transfer, derived from an existing
averaged information-theoretical measure, namely transfer entropy. Local
transfer entropy is used to produce profiles of the information transfer into
each spatiotemporal point in a complex system. These spatiotemporal profiles
are useful not only as an analytical tool, but also allow explicit
investigation of different parameter settings and forms of the transfer entropy
metric itself. As an example, local transfer entropy is applied to cellular
automata, where it is demonstrated to be a novel method of filtering for
coherent structure. More importantly, local transfer entropy provides the first
quantitative evidence for the long-held conjecture that the emergent traveling
coherent structures known as particles (both gliders and domain walls, which
have analogues in many physical processes) are the dominant information
transfer agents in cellular automata.Comment: 12 page
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
Localization dynamics in a binary two-dimensional cellular automaton: the Diffusion Rule
We study a two-dimensional cellular automaton (CA), called Diffusion Rule
(DR), which exhibits diffusion-like dynamics of propagating patterns. In
computational experiments we discover a wide range of mobile and stationary
localizations (gliders, oscillators, glider guns, puffer trains, etc), analyze
spatio-temporal dynamics of collisions between localizations, and discuss
possible applications in unconventional computing.Comment: Accepted to Journal of Cellular Automat
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