▁is ▁at ▁least ▁one ▁square ▁of ▁four ▁neighbor ing ▁cells ▁with ▁one ▁of ▁the ▁following ▁patterns : ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁▁▁▁▁▁▁ 1 ▁ 2 ▁▁▁▁▁▁▁ 2 ▁ 0 ▁▁▁▁▁▁▁ 0 ▁ 1 ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▁▁▁▁▁▁ 0 ▁ 0 ▁▁▁▁▁▁▁ 1 ▁ 1 ▁▁▁▁▁▁▁ 2 ▁ 2 ▁ ▁or ▁some ▁reflection ▁or ▁rotation ▁of ▁one ▁of ▁these . ▁These ▁patterns ▁cannot ▁be ▁killed ▁off ▁by ▁their ▁surr ound ings . ▁It ▁is ▁the ▁" only ▁if " ▁part ▁of ▁this ▁result ▁which ▁is ▁most ▁interesting . ▁If ▁none ▁of ▁these ▁patterns ▁is ▁present ▁at ▁t ▁= ▁ 0 , ▁then ▁in ▁any ▁bounded ▁region ▁the ▁pattern ▁eventually ▁sett les ▁down ▁to ▁all ▁zeros . ▁ ▁The ▁key ▁tool ▁in ▁the ▁proof ▁in ▁▁ ▁is ▁a ▁" w inding ▁number " ▁which ▁is ▁shown ▁to ▁be ▁invariant ▁for ▁this ▁model . ▁ ▁One ▁easy ▁consequence ▁of ▁the ▁theorem ▁stated ▁above ▁is ▁that ▁if ▁there ▁are ▁no ▁" ref ract ory " ▁cells ▁ ▁initially ▁then ▁the ▁pattern ▁will ▁die ▁out ▁in ▁any ▁bounded ▁region ▁( wh ether ▁the ▁total ▁grid ▁is ▁finite ▁or ▁infinite ▁in ▁extent ). ▁This ▁property ▁of ▁an ▁exc itable ▁medium ▁was ▁found ▁earlier , ▁in ▁the ▁paper ▁of ▁Wiener ▁and ▁Rosen bl u eth , ▁and ▁does ▁not ▁hold ▁if ▁there ▁are ▁" hol es " ▁in ▁the ▁region . ▁ ▁Notes ▁ ▁References ▁▁▁ ▁R . ▁F isch , ▁J . ▁Gra v ner , ▁D . ▁Gr iffe ath , ▁Met ast ability ▁in ▁the ▁Green berg – H ast ings ▁model