We have now got a collection of sequences of M's and N's which begins: 0: N =N 1: M =M 2: M N =MN 3: M N M =MNM 4: M N M M N =MNMMN 5: MNM MN MNM =MNMMNMNM. The general rule is replacing every M in one month by MN in the next and similarly replace every N by M. The M of month 2 become MN again and the N of month 2 has become M, so month 3 is: "MNM" Month 0: 1: 2: 3: N - M - M - M \ \ N N - M The following month, the M becomes "MN" since they have produced a new pair (and the original pair also survives). Next month, the pair become Mature, denoted by "M". Lining up the RabbitsIf we return to Fibonacci's original problem - about the rabbits (see the Fibonacci home page if you want to remind yourself) then we start with a single New pair of rabbits in the field. įirst we re-examine Fibonacci's original Rabbit problem and see how it can generatean infinite sequence of two symbols and in a later sectionwe see how the same sequence is very simply related to Phi also. The Golden String contains a copy of itselfįibonacci Numbers and the Rabbit sequenceThis page is all about a remarkable sequence of 0s and 1s which is intimately related tothe Fibonacci numbers and to Phi:ġ 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1.Now you can hear the Golden sequence too.The first 2000 bits of the Rabbit Sequence.The rabbit sequence and the "spectrum" of Phi.The rabbit sequence defined using the fractional parts of Phi multiples.The rabbit sequence defined using the whole part of Phi multiples.The number of additions when computing f(n).Another way to generate The Rabbit sequence.Fibonacci Numbers and the Rabbit sequence.Contents The icon means there is a Things to do investigation at the end of the section. The Fibonacci Rabbit sequence - the Golden String The Golden String of 0s and 1sOther names for the Rabbit Sequence are the Golden Sequence because, as we shall see, it isclosely related to the golden section numbers Phi (=1♶180339.) and phi=(0♶180339.).
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