I find recursive acronyms fun and poetic.
Recursive acronyms are acronyms that refer to themselves, just like functions that would call themselves. I don't want to get too mathy, but let's just show an example of recursive functions:
factorial(n) = if (n = 0) then 1 else n * factorial(n-1)
Used to calculate the factorial of a number, this function calls itself on the third line.
Recursive acronyms are mostly used in computer science and mathematics, but Visa (the company which operate eponym credit card) is an example of a recursive company name. It indeed stands for Visa International Service Association, in which Visa stands for Visa International Service Association, in which Visa stands for Visa International Service Association and so on.
On Wikipedia's page dedicated to recursion, one can find a section concerning "Recursive humor" (a very geeky humor, you might rightly think). You can read there that "putative recursive step does not get closer to a base case, but instead leads to an infinite regress". In other words, there is no way to end a recursive acronym: it just calls itself on and on. To go back to the Visa example, we could have written that "Visa International Service Association contains Visa which stands for Visa International Service Association, which contains Visa, which stands for Visa International Service Association" forever.
If we go back to the factorial function:
factorial(n) = if (n = 0) then 1 else n * factorial(n-1)
we can see that when n = 0, the function stops calling itself: there is an ending condition to the recursion.
In recursive acronyms, there is none, that's where it gets funny. Wikipedia quotes a joke that can be found in a book's glossary: "Recursion, see Recursion.".
Alllllright. This being said, how can a recursive acronym destroy itself?
Well, when an acronym is recursive on its last letter, you just get stuck in an infinite loop. You could spend your whole life trying to find what YOPY stands for (Your own personal YOPY), the acronym would survive you.
But most recursive acronyms are recursive on other letters than the last (usually the first one). Here are some examples:
Small aside, note that some recursive acronyms (ZWEI) call other recursive acronyms. Another example: GNU stands for "GNU's Not Unix" and CYGNUS for: "CYGNUS, Your GNU Solutions".
Let's try to find out what BIRD means. The first letter stands for BIRD. Let's find out what the B of that BIRD stands for then. BIRD. Let's find out what the B of that BIRD stands for then. BIRD. We get stuck on the first letter. But an acronym is formed by the initial letters (or syllables) of other words, right? Since you cannot know what the letters after the B in BIRD mean, can we still say that BIRD is an acronym? Do the other letters even exist, if we get stuck on the first one? They could live somewhere out of our reach. Should we keep those letters if we can never reach them? Shouldn't BIRD just be reduced to B? The acronym has just destroyed itself. Except if you consider that B stands for B...