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

We introduce several concepts such as prime and composite rule, tools andmethods for causal composition and decomposition. We discover and prove newuniversality results in ECA, namely, that the Boolean composition of ECA rules51 and 118, and 170, 15 and 118 can emulate ECA rule 110 and are thusTuring-universal coupled systems. We construct the 4-colour Turing-universalcellular automaton that carries the Boolean composition of the 2 and 3 ECArules emulating ECA rule 110 under multi-scale coarse-graining. We find thatrules generating the ECA rulespace by Boolean composition are of low complexityand comprise prime rules implementing basic operations that when composedenable complex behaviour. We also found a candidate minimal set with only 38ECA prime rules---and several other small sets---capable of generating allother (non-trivially symmetric) 88 ECA rules under Boolean composition.

Rule Primality, Minimal Generating Sets, Turing-Universality and Causal Decomposition in Elementary Cellular Automata