English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Cellular automata (CA) have been utilized for decades as discrete models ofmany physical, mathematical, chemical, biological, and computing systems. Themost widely known form of CA, the elementary cellular automaton (ECA), has beenstudied in particular due to its simple form and versatility. However, thesedynamic computation systems possess evolutionary rules dependent on aneighborhood of adjacent cells, which limits their sampling radius and theenvironments that they can be used in.  The purpose of this study was to explore the complex nature ofone-dimensional CA in configurations other than that of the standard ECA.Namely, "long-distance cellular automata" (LDCA), a construct that had beendescribed in the past, but never studied. I experimented with a class of LDCAthat used spaced sample cells unlike ECA, and were described by the notationLDCA-x-y-n, where x and y represented the amount of spacing between the celland its left and right neighbors, and n denoted the length of the initial tapefor tapes of finite size. Some basic characteristics of ECA are explored inthis paper, such as seemingly universal behavior, the prevalence of complexitywith varying neighborhoods, and qualitative behavior as a function of x and yspacing.  Focusing mainly on purely Class 4 behavior in LDCA-1-2, I found that Rule 73could potentially be Turing universal through the emulation of a cyclic tagsystem, and revealed a connection between the mathematics of binary trees andEulerian numbers that might provide insight into unsolved problems in bothfields.

Investigation of Rule 73 as Case Study of Class 4 Long-Distance Cellular Automata