Tracy Harms-3 wrote:
>
> A nice bit of illustrated commentary on a special number we don't tend
> to hear a lot about:
>
> http://maxwelldemon.wordpress.com/2009/05/20/unscheduled-post-the-silver-ratio/
>
Both golden (Fibonacci) and silver (octonacci) numbers can be obtained from
substitution rules applied to sequences of a two-letter alphabet. For
instance:
Fib=:(#~ 0&<)@(,/@:({&(>2;1 2)))&:<:^: NB. rule: 1->2, 2->12
7 Fib 1
2 1 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2
+/ 2 = 7 Fib 1
13
+/ 2 = 10 Fib 1
55
fib =: 3 : '+/2=(y-1)Fib 1'
I think that fib is not mentioned in the Roger's essay on
generating the Fibonacci's sequence.
Octonacci chains can be defined similarly as:
Oct=:(#~ 0&<)@(,/@:({&(>2;2 1 2)))&:<:^:
3 Oct 2 1
2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2
Such chains have many interesting properties...
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http://www.nabble.com/Silver-ratio%2C-geometrically-interpreted-tp23638554s24193p23644952.html
Sent from the J Chat mailing list archive at Nabble.com.
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