For a long time I've been idly interested in how the shape of a complex organism gets determined during development at a microscopic level. Recently I've realized that plants could be a good place to start trying to understand that, because the structure of even a quite complex-looking plant can sometimes be described by a few simple behaviors. Here are some examples.
My radish plants have a single base where all foliage grows from. After it's first two seed leaves, it grows some number of large rough leaves which all descend to the same point. No other branching ever takes place.
My pea plants have only one long stalk, which grows symmetrical pairs of leaves at regular intervals. Occasionally, the base of a leaf pair spawns a mini-stalk, never more than 3 or 4 leaf-pairs long, ending in a "claw" of three tendrils. Most of the time, one of the three tendrils will split again in three (always the one aligned with the "top" of the stem, as determined by leaf orientation) .
My fennel plant has thick bases to its stems which each extend a few inches before branching starts. At that point, it branches at regular intervals in symmetric pairs of fronds, which in branch the same way. Those third-layer fronds branch at regular intervals but alternate sides, and there are always exactly four layers of branching no more and no less.
My basil plants seem roughly able to grow branches in any advantageous spot, with no rigid rules or geometric behaviors like the other examples.
My background is in mathematics, and all my knowledge of biology is dated to high school. I've always been confused by how DNA is presented as a "list of proteins", when it is clearly so dynamical and not static: each cell type only produces some of those proteins, and those proteins can in turn determine what proteins it's children produce, I guess, and this can create a rich (non-linear) hierarchy of tissue differentiation out of a linear list.
For a really complex organism like a mammal I guess that our understanding of how DNA gets actualized is phenomenological (i.e. we can tell that gene X correlates with macroscopic trait Y, even if we have no idea what the signalling mechanisms are behind it and which cell types produce a relevant protein and when.)
But is this true also for plants, or do we have a deeper understanding of what proteins differentiate, for instance, the four stalk types of a fennel plant, and why each type can only produce the next one? I think simple animals like sponges and nematodes and cnidaria probably would be as helpful as (or more than) plants, but as a gardener I see these plant geometries every day and am fascinated by them.
Does anyone know of a good reference, book or online, that discusses these topics? I'm okay with something a little out of my technical depth - I'd prefer a difficult answer to an incomplete one.
EDIT: Leaf architecture is also interesting, and probably inseparable from branch architecture on some level, but I focused on stalks and branches probably because I don't have the terminology to meaningfully describe leaf architectures.
