Matches in SemOpenAlex for { <https://semopenalex.org/work/W3007940085> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W3007940085 abstract "Cellular automata (CA) are fully discrete alternatives to partial differential equations (PDE). For PDEs, one often considers the Cauchy problem, or initial value problem: find the solution of the PDE satisfying a given initial condition. For many PDEs of the first order in time, it is possible to find explicit formulae for the solution at the time $t>0$ if the solution is known at $t=0$. Can something similar be achieved for CA? We demonstrate that this is indeed possible in some cases, using elementary CA rule 172 as an example. We derive an explicit expression for the state of a given cell after $n$ iteration of the rule 172, assuming that states of all cells are known at $n=0$. We then show that this expression (solution of the CA) can be used to obtain an expected value of a given cell after $n$ iterations, provided that the initial condition is drawn from a Bernoulli distribution. This can be done for both finite and infinite lattices, thus providing an interesting test case for investigating finite size effects in CA." @default.
- W3007940085 created "2020-03-06" @default.
- W3007940085 creator A5001901981 @default.
- W3007940085 date "2020-02-21" @default.
- W3007940085 modified "2023-09-27" @default.
- W3007940085 title "Explicit solution of the Cauchy problem for cellular automaton rule 172" @default.
- W3007940085 cites W1502875195 @default.
- W3007940085 cites W1513303009 @default.
- W3007940085 cites W1596857911 @default.
- W3007940085 cites W1973204073 @default.
- W3007940085 cites W199672743 @default.
- W3007940085 cites W2098134498 @default.
- W3007940085 cites W2133187798 @default.
- W3007940085 cites W2161420356 @default.
- W3007940085 cites W2502666551 @default.
- W3007940085 cites W2620849980 @default.
- W3007940085 cites W2725068886 @default.
- W3007940085 cites W2963907916 @default.
- W3007940085 cites W2963922713 @default.
- W3007940085 cites W350085919 @default.
- W3007940085 cites W604159441 @default.
- W3007940085 hasPublicationYear "2020" @default.
- W3007940085 type Work @default.
- W3007940085 sameAs 3007940085 @default.
- W3007940085 citedByCount "0" @default.
- W3007940085 crossrefType "posted-content" @default.
- W3007940085 hasAuthorship W3007940085A5001901981 @default.
- W3007940085 hasConcept C10138342 @default.
- W3007940085 hasConcept C105795698 @default.
- W3007940085 hasConcept C110121322 @default.
- W3007940085 hasConcept C11413529 @default.
- W3007940085 hasConcept C121332964 @default.
- W3007940085 hasConcept C134306372 @default.
- W3007940085 hasConcept C152361515 @default.
- W3007940085 hasConcept C153635880 @default.
- W3007940085 hasConcept C162324750 @default.
- W3007940085 hasConcept C182306322 @default.
- W3007940085 hasConcept C199360897 @default.
- W3007940085 hasConcept C26955809 @default.
- W3007940085 hasConcept C2776291640 @default.
- W3007940085 hasConcept C28826006 @default.
- W3007940085 hasConcept C33923547 @default.
- W3007940085 hasConcept C35527583 @default.
- W3007940085 hasConcept C41008148 @default.
- W3007940085 hasConcept C49344536 @default.
- W3007940085 hasConcept C51544822 @default.
- W3007940085 hasConcept C78045399 @default.
- W3007940085 hasConcept C90559484 @default.
- W3007940085 hasConcept C93779851 @default.
- W3007940085 hasConcept C97355855 @default.
- W3007940085 hasConceptScore W3007940085C10138342 @default.
- W3007940085 hasConceptScore W3007940085C105795698 @default.
- W3007940085 hasConceptScore W3007940085C110121322 @default.
- W3007940085 hasConceptScore W3007940085C11413529 @default.
- W3007940085 hasConceptScore W3007940085C121332964 @default.
- W3007940085 hasConceptScore W3007940085C134306372 @default.
- W3007940085 hasConceptScore W3007940085C152361515 @default.
- W3007940085 hasConceptScore W3007940085C153635880 @default.
- W3007940085 hasConceptScore W3007940085C162324750 @default.
- W3007940085 hasConceptScore W3007940085C182306322 @default.
- W3007940085 hasConceptScore W3007940085C199360897 @default.
- W3007940085 hasConceptScore W3007940085C26955809 @default.
- W3007940085 hasConceptScore W3007940085C2776291640 @default.
- W3007940085 hasConceptScore W3007940085C28826006 @default.
- W3007940085 hasConceptScore W3007940085C33923547 @default.
- W3007940085 hasConceptScore W3007940085C35527583 @default.
- W3007940085 hasConceptScore W3007940085C41008148 @default.
- W3007940085 hasConceptScore W3007940085C49344536 @default.
- W3007940085 hasConceptScore W3007940085C51544822 @default.
- W3007940085 hasConceptScore W3007940085C78045399 @default.
- W3007940085 hasConceptScore W3007940085C90559484 @default.
- W3007940085 hasConceptScore W3007940085C93779851 @default.
- W3007940085 hasConceptScore W3007940085C97355855 @default.
- W3007940085 hasLocation W30079400851 @default.
- W3007940085 hasOpenAccess W3007940085 @default.
- W3007940085 hasPrimaryLocation W30079400851 @default.
- W3007940085 hasRelatedWork W128120693 @default.
- W3007940085 hasRelatedWork W2033852181 @default.
- W3007940085 hasRelatedWork W2083156736 @default.
- W3007940085 hasRelatedWork W2112417391 @default.
- W3007940085 hasRelatedWork W2184149017 @default.
- W3007940085 hasRelatedWork W2188519877 @default.
- W3007940085 hasRelatedWork W2245394296 @default.
- W3007940085 hasRelatedWork W2299635917 @default.
- W3007940085 hasRelatedWork W2333342388 @default.
- W3007940085 hasRelatedWork W2583952405 @default.
- W3007940085 hasRelatedWork W2736606891 @default.
- W3007940085 hasRelatedWork W2782091266 @default.
- W3007940085 hasRelatedWork W2803584933 @default.
- W3007940085 hasRelatedWork W2949777296 @default.
- W3007940085 hasRelatedWork W3002302304 @default.
- W3007940085 hasRelatedWork W3025070896 @default.
- W3007940085 hasRelatedWork W3032652658 @default.
- W3007940085 hasRelatedWork W3101212039 @default.
- W3007940085 hasRelatedWork W72188416 @default.
- W3007940085 hasRelatedWork W3148198395 @default.
- W3007940085 isParatext "false" @default.
- W3007940085 isRetracted "false" @default.
- W3007940085 magId "3007940085" @default.
- W3007940085 workType "article" @default.