L-systems generate weevils, pizza toppings, and matriarchal lineages

# L-systems generate weevils, pizza toppings, and matriarchal lineages Source: [https://blog.plover.com/2026/09/25/](https://blog.plover.com/2026/09/25/) [L\-systems generate weevils, pizza toppings, and matriarchal lineages](https://blog.plover.com/misc/fibonacci-word-2.html) 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: ``` b → a a → ab ``` 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`a`s, or the total number of`b`s, 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*](https://blog.plover.com/math/ordinals/07-nested-shortlex.html), 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](https://blog.plover.com/math/fibonacci-word.html)\.  I tried to get Claude to help me with this article, but it said the premise was too stupid so I had to do it myself\. *\[[Other articles in category /misc](https://blog.plover.com/misc)\][permanent link](https://blog.plover.com/misc/fibonacci-word-2.html)*