Sponges and corals experience a type of growth, modular growth, that is more similar to the growth pattern of trees than that of animals. Modular growth, as the name implies, is the successive addition of identical or similar modular units to an existing organism. The structure these organisms take on as they grow is determined mainly by how fast and where new modules can be added. The process is easiest to illustrate with corals (Fig. 5.5). Each polyp secretes beneath it a layer of calcite, which accumulates as a roughly columnar zooid proliferation j I ^^ :|===i: :Ws iliiHi zooid proliferation
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arrays—rectangles, pentagons, hexagons—with the sponge's cells proliferating to fill in the spaces between the spicules (Fig. 5.6). The modular growth of sponges, therefore, involves the proliferation of the unit arrays formed by the spicules and their associated cells.
Modular growth results in body shapes that are much different from the typical shapes of higher organisms, which often are variants on simple geometrical solids, like spheres or cylinders. Modular organisms grow into more complicated shapes known as fractal objects, so called because the structures of their bodies exhibit fractal geometry. Fractal geometry is a very powerful way of describing the complex shapes frequently found in nature. Understanding the growth forms of sponges and corals requires that we come to grips with it. Like most powerful tools, fractal geometry is superficially intimidating, but it is in principle very simple.
The basics of fractal geometry are most easily appreciated by considering a common task: measuring the length of a curve. One might estimate a curve's length by "walking" a pair of dividers (or some other measuring device) along it and counting the number of steps required to span the curve (Fig. 5.7). The curve's estimated length is simply the product of the distance separating the divider's points and the number of steps. This procedure yields only a rough approximation of the curve's length, though, because dividing the curve into a series of straight-line segments leaves out the "curvy bits" that contribute some portion of its true length. To improve the approximation, one moves the points of the divider closer and repeats the measure-
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Figure 5.7 Estimating the length of a smooth curve. a: Dividing the curve into a series of straight-line segments. b: With shorter and shorter segment lengths, the estimated length of the curve asymptotically approaches the curve's true length.
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