The Fibonacci sequence is so-called because in Western mathematics is
first appears in connection with a problem from Fibonacci's 1202 book
Liber Abaci. Fibonacci asks us to consider a rabbit farm where a
pair of baby rabits grows to adulthood in one month, and an adult pair
of rabbits gives birth to a new pair of babies after a month.
Representing an adult pair with a and a baby pair with b, we could
write this as:
Starting with one pair of baby rabbits, and performing the indicated substitutions month by month, we get:
b
a
ab
aba
abaab
abaababa
abaababaabaab
abaababaabaababaababa
abaababaabaababaababaabaababaabaab
abaababaabaababaababaabaababaabaababaababaabaababaababa
…
The total number of symbols (and pairs of rabbits) each month gives us
the Fibonacci sequence, as does the total number of as, or the total
number of bs, in each line.
A structure like this one, in which there are symbols, in this case
a and b, that are repeatedly replaced with strings of symbols, is
called an “L-system”, and this L-system in particular is the “Fibonacci L-system”.
Yesterday I happened to mention Zyzzyva, which is a genus
of weevils that I can only assume was named by a biologist who wanted
to be last in the dictionary. When I see a pattern like this I
instantly think of the Fibonacci L-system. We can use the Fibonacci L-system to generate a sequence
of increasingly long weevil names:
Yva
Zva
Zyva
Zyzva
Zyzzyva
Zyzzyzyzva
Zyzzyzyzzyzzyva
Zyzzyzyzzyzzyzyzzyzyzva
Zyzzyzyzzyzzyzyzzyzyzzyzzyzyzzyzzyva
Zyzzyzyzzyzzyzyzzyzyzzyzzyzyzzyzzyzyzzyzyzzyzzyzyzzyzyzva
Or pizza toppings:
eroni
proni
peroni
peproni
pepperoni
peppepeproni
peppepeppepperoni
peppepeppeppepeppepeproni
peppepeppeppepeppepeppeppepeppepperoni
peppepeppeppepeppepeppeppepeppeppepeppepeppeppepeppepeproni
Or family matriarchs:
Grandma
Grandmam
Grandmamma
Grandmammamam
Grandmammamammamma
Grandmammamammammamammamam
Grandmammamammammamammamammammamammamma
Grandmammamammammamammamammammamammammamammamammammamammamam
I had to cheat a little here because there's an a in the middle that
I didn't substitute. If we don't skip that we get the unpronounceable
“Grmammandmammamammamma”.
A quick computer search suggests several other variations, including both “mammaries” and “titties”, but to prevent this article from devolving into juvenile sniggering, I'm going to cut the scroll here.
Amazingly, there was a previous article on a closely related topic.
*[Other articles in category /misc]
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