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For although leaves typically expand significantly after they come out, the basic features of their shapes almost never seem to change.

There is some evidence that at least some aspects of the pattern of veins in a leaf are laid down before the main surface of the leaf is filled in, and perhaps the stems in the branching process I describe here correspond to precursors of structures related to veins. Indeed, the criss-crossing of veins in the leaves of higher plants may be not unrelated to the fact that stems in the pictures two pages ago often cross over—although certainly many of the veins in actual full-grown leaves are probably added long after the shapes of the leaves are determined.

One might at the outset have thought that leaves would get their shapes through some mechanism quite unrelated to other aspects of plant growth. But I strongly suspect that in fact the very same simple process of branching is ultimately responsible both for the overall forms of plants, and for the shapes of their leaves.

Quite possibly there will sometimes be at least some correspondence between the lengths and angles that appear in the rules for overall growth and for the growth of leaves. But in general the details of all these rules will no doubt depend on very specific characteristics of individual plants.

The distance before a new stem appears is, for example, probably determined by the rates of production and diffusion of plant hormones and related substances, and these rates will inevitably depend both on the thickness and mechanical structure of the stem, as well as on all kinds of biochemical properties of the plant. And when it comes to the angles between old and new stems I would not be surprised if these were governed by such microscopic details as individual shapes of cells and individual sequences of cell divisions.

The traditional intuition of biology would suggest that whenever one sees complexity—say in the shape of a leaf—it must have been generated for some particular purpose by some sophisticated process of natural selection. But what the pictures on the previous pages [400, 402] demonstrate is that in fact a high degree of complexity can arise in a sense quite effortlessly just as a consequence of following certain simple rules of growth.

No doubt some of the underlying properties of plants are indeed guided by natural selection. But what I strongly suspect is that in the

From Stephen Wolfram: A New Kind of Science [citation]