This post contains what purports to be a fractal poem. It’s not a bad poem in its own right, but the link to fractal geometry was too subjective for my taste. However, it got me thinking about what else a “fractal poem” might mean, and I was up till two that morning bringing my idea into fruition. I shared the poem I came up with in the comments, but a fuller explanation appears below.
I based my poem on a simple L-system. An L-system contains a set of rules, applied iteratively, for replacing one symbol with a sequence of symbols. For example, suppose we agree to replace “A” with “ABBA” and “B”, with “BA”. Then, starting with “A”, the first iteration gives “ABBA”, the second iteration gives “ABBABABAABBA”, the third “ABBABABAABBABAABBABAABBAABBABABAABBA” and so on. The connection to fractal geometry is that if we interpret the symbols graphically (e.g. “A” for “go forward” and “B” for “turn left”), we get a squiggly line whose squiggliness depends upon the number of iterations.
I used an L-system where “A” becomes “ABBA”, “B” becomes “BCCB”, and so on. (Using numbers rather than letters, this is: “n → n, n+1, n+1, n”.) After two iterations, we have “ABBABCCBBCCBABBA”, which is the structure I used for my poem, interpreting each letter as representing a line and requiring all lines assigned the same letter to rhyme. In other words, it had to be a 16-line poem in which lines 1, 4, 13 & 16 rhyme, lines 2, 3, 5, 8, 9, 12, 14 & 15 rhyme, and lines 6, 7, 10 & 11 rhyme.
Here is the result. It has, I think, an interesting aesthetic quality when read aloud.
This doggerel does not intend
To satisfy the reader’s would
For art that is remotely good;
It will not serve to meet that end,
So don’t imagine that it could.
But in its rhyming structure you
Might find, if you are able to,
A pattern to be understood
That’s relevant to trees of wood
And clouds of water vapour, too -
The applications are not few -
For it possesses fractalhood.
Look closely, and you’ll comprehend
The secret pattern, bad or good,
Which, if this text were longer, could
By iterative means extend.
After a third iteration, the structure would be a challenging ABBA BCCB BCCB ABBA BCCB CDDC CDDC BCCB BCCB CDDC CDDC BCCB ABBA BCCB BCCB ABBA. Four iterations would give you an epic poem of 256 lines. You’re welcome to give that a go, or maybe you’d prefer to write your own variation on a shorter poem like mine.
Here are some more links that I found over the Christmas holidays:
- The development of a foetus, animated.
- Strong Language is a new linguistics blog about swearing. Mostly. Along the way it covers a variety of topics and is worth a look.
- A well-presented and informative video on placenames ending in -stan.
- A curious difference between the Andromeda Galaxy and our own.
- All of the best arguments against vaccination together on one page. (No, it’s not blank, but you’ve got the right idea.)
As for the holidays themselves, I don’t feel like writing a report, but rest assured I had an excellent time. Here are two photographs that capture some special moments.
The photo on the left shows my niece and her parents (my sister on the left, pregnant with her second child) at the Christmas table as it is being prepared. Of note are the origami mangers, complete with jelly baby and paper straw, alternating with paper trees. The brown paper bags are what we used instead of crackers.
On the right is a framed photo set showing miscellaneous moments in Elke’s life so far. This was Rebecca’s Christmas present to me, and it is now hanging above the light switch in my bedroom.