Thispresentationdelvesintotheremarkablehistoryofaperiodictilingsandthedominoproblem.Aperiodictilesetsrefertocollectionsoftilesthatcanonlytiletheplaneinanon-repeating,ornon-periodic,manner.Suchsetswerenotbelievedtoexistuntil1964whenR.Bergerintroducedthefirstaperiodicsetconsistingofanastonishing20,426Wangtiles.Overtheyears,ongoingresearchledtosignificantadvancements,culminatingin2015withthediscoveryofamere11WangtilesbyE.JeandelandM.Rao,alongsideacomputer-assistedproofoftheirminimality.Simultaneously,researchersfoundevensmalleraperiodicsetscomposedofpolygon-shapedtiles.Notably,Penrose's kite and dart tiles emerged as early examples, and most recently, a groundbreaking discovery was made - a solitary aperiodic tile known as the "hat" that can tile the plane exclusively in a non-periodic manner. Aperiodic tile sets are intimately connected with the domino problem that asserts how certain tile sets can tile the plane without us ever being able to establish their tiling nature with absolute certainty. Moreover, aperiodic tilings hold a distinct visual aesthetic allure. In today'smusicalpresentation,theirartisticappealtranscendsthevisualdomainandextendsintotherealmofmusic.-JarkkoKari
Thispresentationdelvesintotheremarkablehistoryofaperiodictilingsandthedominoproblem.Aperiodictilesetsrefertocollectionsoftilesthatcanonlytiletheplaneinanon-repeating,ornon-periodic,manner.Suchsetswerenotbelievedtoexistuntil1964whenR.Bergerintroducedthefirstaperiodicsetconsistingofanastonishing20,426Wangtiles.Overtheyears,ongoingresearchledtosignificantadvancements,culminatingin2015withthediscoveryofamere11WangtilesbyE.JeandelandM.Rao,alongsideacomputer-assistedproofoftheirminimality.Simultaneously,researchersfoundevensmalleraperiodicsetscomposedofpolygon-shapedtiles.Notably,Penrose's kite and dart tiles emerged as early examples, and most recently, a groundbreaking discovery was made - a solitary aperiodic tile known as the "hat" that can tile the plane exclusively in a non-periodic manner. Aperiodic tile sets are intimately connected with the domino problem that asserts how certain tile sets can tile the plane without us ever being able to establish their tiling nature with absolute certainty. Moreover, aperiodic tilings hold a distinct visual aesthetic allure. In today'smusicalpresentation,theirartisticappealtranscendsthevisualdomainandextendsintotherealmofmusic.