Autoacronyms

What is an autoacronym?

Consider the phrase nine inch nails. The initial letters n i n of the three words in the phrase are also the first three letters of the first word nine. Since the phrase is three words long, the fourth letter e and all the rest of the letters in the phrase remain unaccounted for. Here is a longer example (the last letter accounted for is the second o in took):

At that time he also tearfully took in many elegant heirlooms, even a lilac sofa of the elderly Aunt Rose from Ulster, long lost, yes, too often overlooked, kindly, indulgent. Not many Aunts…

An autoacronym is a phrase such that the n th letter in the phrase is also the initial letter of the n th word in the phrase.

Generating autoacronyms

Any autoacronym that does not consist simply of one-letter words must be infinite. Suppose, for example, that an autoacronym has for its first word oz. It has to have at least two words -- one for each letter of oz -- and the second word has to start with z. Even if you take the shortest way and make that second word just z, you now have three letters, and so you need another word. So the best you (or rather God) can do is the infinite string oz z z z z...

Autoacronyms like that are like rational numbers in decimal form -- rather boring after a while:

It is actually quite easy to generate autoacronyms like the last one. Take a set of letters x(1), x(2),..., x(n). For each letter x(i) choose a word w(i) starting with that letter and containing only letters from the set. To generate your autoacronym, use the following procedure:

1. Make a phrase containing words from those just chosen.
2. Replace each occurrence of x(i) in the phrase with the corresponding word w(i).
3. Repeat step 2 infinitely many times.

For the example above, the rules are:

1. Find “a” and replace with “a”
2. Find “e” and replace with “eat”
3. Find “i” and replace with “I”
4. Find “t” and replace with “tie”

It’s unlikely that your autoacronym will make much sense, or at least much more than the example above. But it is guaranteed to be an autoacronym.

Production rules

You can use the find/replace command in a word processor to generate autoacronyms. Although the following commands can be carried out one-by-one manually, it is much easier, if you can do so, to include them all in a macro:

1. For each letter x(i), find and replace the letter with the string “#i" (the term string denotes any sequence of characters):

   For the example above, the rules are:

   Find “a” and replace with “#1”

   Find “e” and replace with “#2”

   Find “i” and replace with “#3”

   Find “t” and replace with “#4”

2. For each string "#i”, find and replace it with the word w(i) followed by a space (the spaces delimit the words, and thus determine the initial letters that form the acronym).

   For the example above, the rules are:

   Find “#1” and replace with “a ”

   Find “#2” and replace with “eat ”

   Find “#3” and replace with “I ”

   Find “#4” and replace with “tie ”

The rules may seem roundabout: why not just replace x(i) with w(i) instead of using “#i” as an intermediary? The answer is that if the rules are applied in sequence (rather than all at once, which a word processor can’t do), then the intermediaries are necessary to avoid having the replacement strings themselves replaced (as would happen if “e” were replaced by “eat” and “t” were then replaced by “tie”). The effect of the intermediaries is to make it as if the rules were applied all at once.

Once you've written the macro, choose a word from among the w(i), or a phrase consisting of such words. Apply the macro as many times as you want or have time for (in the example, the rules produce a string roughly 3 times as long as the input string, so applying them 5 times yields a string roughly 243 times as long).

Textures

If you substitute colored dingbats or images for the letters (and eliminate spaces) you can create interesting textures like this:

(The second and third have been blurred a little.) Indeed production systems (i.e. systems of rules like the above, applied recursively to their own output) would seem to be a convenient rapid means to produce non-periodic textures for web-page backgrounds and the like, without stored images.

Related Patterns

The Aronson sequence is given by the rule

1. ‘t’ is the first, fourth, eleventh, ... letter of this sentence

The first few numbers in the sequence are:

For more information and some related sequences, see the Online Encyclopedia of Integer Sequences.

References

OULIPO. La littérature potentielle.