▁t + 1 . ▁▁ 3 . ▁ ▁If ▁a ▁given ▁cell ▁is ▁in ▁the ▁rest ing ▁state ▁at ▁time ▁t ▁and ▁at ▁least ▁one ▁of ▁its ▁neighb ors ▁is ▁in ▁the ▁excited ▁state ▁at ▁time ▁t , ▁then ▁the ▁given ▁cell ▁is ▁in ▁the ▁excited ▁state ▁at ▁time ▁t + 1 , ▁otherwise ▁( no ▁neighbor ▁is ▁excited ▁at ▁time ▁t ) ▁it ▁remains ▁in ▁the ▁rest ing ▁state ▁at ▁time ▁t + 1 . ▁ ▁In ▁this ▁way ▁the ▁whole ▁grid ▁of ▁cells ▁adv ances ▁from ▁their ▁initial ▁states ▁at ▁t ▁= ▁ 0 ▁to ▁their ▁states ▁at ▁t ▁= ▁ 1 , ▁then ▁to ▁their ▁states ▁at ▁t ▁= ▁ 2 , 3 , 4 , ▁etc ., ▁producing ▁a ▁pattern ▁of ▁cells ▁in ▁the ▁various ▁states ▁for ▁each ▁time . ▁ ▁See ▁the ▁first ▁animation ▁in ▁Bel ou so v – Z hab ot in sky ▁reaction ▁for ▁a ▁striking ▁example ▁of ▁behavior ▁that ▁can ▁be ▁exhib ited ▁by ▁this ▁model . ▁The ▁three ▁states ▁are ▁indicated ▁by ▁different ▁colors . ▁ ▁Mathemat ical ▁description ▁▁ ▁To ▁describe ▁the ▁G H ▁model ▁more ▁mathemat ically , ▁consider ▁the ▁simplest ▁case ▁of ▁a ▁grid ▁of ▁square ▁cells ▁ ▁. ▁At ▁each ▁time ▁ ▁the ▁cell ▁ ▁has ▁a ▁state ▁▁ ▁The ▁type ▁of ▁neighborhood ▁is ▁not ▁important , ▁so ▁long ▁as ▁each ▁cell ▁has ▁some ▁neighb ors . ▁In ▁a ▁square ▁grid ▁( as ▁opposed ▁to ▁hex ag onal ), ▁either ▁four ▁or ▁eight ▁cell ▁neighborhood s ▁work ▁fine .