Did I miss a follow up article? Was there every a WPNM Part 2?

An analogy to IFS as a model of fern growth is the golden-ratio model of spiral phylotaxis, the process that makes the spirals of seeds in daisies and sunflowers, for instance. Each seed in the spiral is a certain exact angle, the golden ratio times 360 degrees, from the previous seed. If that angle is only slightly off, the spiral doesn’t look nearly the same. So do the genes code for this magic number? It turns out they don’t; there’s a much simpler model: each new beginning seed in the center of the spiral takes the biggest gap between recently-created seeds. That simple dynamic in turn produces the golden ratio angle between successive seeds.

Similarly for ferns. There is some growth process, and the IFS-fern-like shape is just a result of that process. The IFS parameters aren’t coded in the genes, except in a very indirect way.
IFS is top-down and growth is bottom-up.

I think the author got IFS and L-System models’ place in the world reversed. IFS’s only reproduce pictures. L-Systems go a little more toward describing the way plants–at least their branch structures–grow. There are definite parallels between IFS’s and L-Systems. But L-Systems still only describe the physical growth process, they don’t say why the branches branch at the times and angles they do.

There is a more detailed model of tissues of dividing cells called Map L-Systems. As far as I know these only work for fairly small clumps of cells so far. They get even closer to describing how tissue shapes end up the way they do. But Map L-Systems are still deterministic: each cell of a given type divides into cells of two programmed types. The process doesn’t involve communication or feedback between cells, except for a simple kind of mechanical pushing.

So, in my spare time I work on two different approaches to algorithmic leaves: IFS’s with non-linear functions, and Map L-System-like setups with more stuff. Nothing great to report.

But to me, the most intersting question is about mathematics that is developed many years before anything in the real wolrd is found that it describes. It is one thing to set out to describe something with math. It is another thing to develop math in the academic cloister, with nary a care in the world to ‘applicability,’ and then one day find that said mathematics perfectly describes something new that we run across (eg, riemannian geometry and general relativity).

So while I think your caution here is extremely valid, I also think there is still something to pursue as well.

BTW: Lindenmeyer while a joint auther of TABoP you should really have mentioned Prusinkiewicz and Hanan with him.

Here’s another thing to think about. Is our symbol pi (sorry, don’t know if I can generate in html) fundamental? No it’s just a symbol. There might be a better language where we don’t need some symbol. We use it because our language fails to exactly describe it. So we invented the abstraction. Obviously the same goes for our other symbolic constants as well.