tree-growing procedure. The computer starts by drawing a single vertical line. Then the line branches into two. Then each of the branches splits into two subbranches. Then each of the subbranches splits into sub-sub-branches, and so on. It is ‘recursive’ because the same rule (in this case a branching rule) is applied locally all over the growing tree. No matter how big the tree may grow, the same branching rule goes on being applied at the tips of all its twigs.
The ‘depth’ of recursion, means the number of sub-sub-. .. branches that are allowed to grow, before the process is brought to a halt. Figure 2 shows what happens when you tell the computer to obey exactly the same drawing rule, but going on to various depths of recursion. At high levels of recursion the pattern becomes quite elaborate, but you can easily see in Figure 2 that it is still produced by the same very simple branching rule. This is, of course, just what happens in a real tree. The branching pattern of an oak tree or an apple free looks complex, but it really isn’t. The basic branching rule is very simple. It is because it is applied recursively at the growing tips all over the tree - branches make subbranches, then each subbranch makes sub-sub-branches, and so on - that the whole tree ends up large and bushy.
Recursive branching is also a good metaphor for the embryonic development of plants and animals generally. I don’t mean that animal embryos look like branching trees. They don’t. But all embryos grow by cell division. Cells always split into two daughter cells. And genes always exert their final effects on bodies by means of local influences on cells, and on the two-way branching patterns of cell division. An animal’s genes are never a grand design, a blueprint for the whole body. The genes, as we shall see, are more like a recipe than like a blueprint; and a recipe, moreover, that is obeyed not by the developing embryo as a whole, but by each cell or each local cluster of dividing cells. I’m not denying that the embryo, and later the adult, has a largescale form. But this largescale form emerges because of lots of little local cellular effects all over the developing body, and these local effects consist primarily of two-way branchings, in the form of two-way cell splittings. It is by influencing these local events that genes ultimately exert influences on the adult body.
The simple branching rule for drawing trees, then, looks like a promising analogue for embryonic development. Accordingly, we wrap it up in a little computer procedure, label it DEVELOPMENT, and prepare to embed it in a larger program labelled EVOLUTION. As a first step towards writing this larger program, we now turn our attention to genes. How shall we represent ‘genes’ in our computer model? Genes in real life do two things. They influence development, and they get passed on to future generations. In real animals and plants there are tens of thousands of genes, but we shall modestly limit our computer model to nine. Each of the nine genes is simply represented by a number in the computer, which will be called its value . The value of a particular gene might be, say 4, or -7.
How shall we make these genes influence development? There are lots of things they could do. The basic idea is that they should exert some minor quantitative influence on the drawing rule that is DEVELOPMENT. For instance, one gene might influence the angle of branching, another might influence the length of some particular branch. Another obvious thing for a gene to do is to influence the depth of the recursion, the number of successive branchings. I made Gene 9 have this effect. You can regard Figure 2, therefore, as a picture of seven related organisms, identical to each other except with respect to Gene 9. I shan’t spell out in detail what each one of the other eight genes does. You can get a general idea of the kinds of things they do by studying Figure 3. In the middle of the
The ‘depth’ of recursion, means the number of sub-sub-. .. branches that are allowed to grow, before the process is brought to a halt. Figure 2 shows what happens when you tell the computer to obey exactly the same drawing rule, but going on to various depths of recursion. At high levels of recursion the pattern becomes quite elaborate, but you can easily see in Figure 2 that it is still produced by the same very simple branching rule. This is, of course, just what happens in a real tree. The branching pattern of an oak tree or an apple free looks complex, but it really isn’t. The basic branching rule is very simple. It is because it is applied recursively at the growing tips all over the tree - branches make subbranches, then each subbranch makes sub-sub-branches, and so on - that the whole tree ends up large and bushy.
Recursive branching is also a good metaphor for the embryonic development of plants and animals generally. I don’t mean that animal embryos look like branching trees. They don’t. But all embryos grow by cell division. Cells always split into two daughter cells. And genes always exert their final effects on bodies by means of local influences on cells, and on the two-way branching patterns of cell division. An animal’s genes are never a grand design, a blueprint for the whole body. The genes, as we shall see, are more like a recipe than like a blueprint; and a recipe, moreover, that is obeyed not by the developing embryo as a whole, but by each cell or each local cluster of dividing cells. I’m not denying that the embryo, and later the adult, has a largescale form. But this largescale form emerges because of lots of little local cellular effects all over the developing body, and these local effects consist primarily of two-way branchings, in the form of two-way cell splittings. It is by influencing these local events that genes ultimately exert influences on the adult body.
The simple branching rule for drawing trees, then, looks like a promising analogue for embryonic development. Accordingly, we wrap it up in a little computer procedure, label it DEVELOPMENT, and prepare to embed it in a larger program labelled EVOLUTION. As a first step towards writing this larger program, we now turn our attention to genes. How shall we represent ‘genes’ in our computer model? Genes in real life do two things. They influence development, and they get passed on to future generations. In real animals and plants there are tens of thousands of genes, but we shall modestly limit our computer model to nine. Each of the nine genes is simply represented by a number in the computer, which will be called its value . The value of a particular gene might be, say 4, or -7.
How shall we make these genes influence development? There are lots of things they could do. The basic idea is that they should exert some minor quantitative influence on the drawing rule that is DEVELOPMENT. For instance, one gene might influence the angle of branching, another might influence the length of some particular branch. Another obvious thing for a gene to do is to influence the depth of the recursion, the number of successive branchings. I made Gene 9 have this effect. You can regard Figure 2, therefore, as a picture of seven related organisms, identical to each other except with respect to Gene 9. I shan’t spell out in detail what each one of the other eight genes does. You can get a general idea of the kinds of things they do by studying Figure 3. In the middle of the
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