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COMPUTING SCIENCE

In Search of the Optimal Scumsucking Bottomfeeder

Brian Hayes

Ichnology for the Ichnorant

When I first saw the photographs in Trace Fossils and Problematica, I assumed that the meandering paths had been inscribed by animals browsing on the surface of the seafloor, like snails leaving a slime trail on the glass of an aquarium. My assumption was mistaken; most of the fossils are actually burrows formed by worms living below the sediment surface. This was my first clue that understanding the nature of the trails might require some actual knowledge of fossils, rather than merely treating them as an exercise in abstract pattern formation.

The study of trace fossils—as distinct from body fossils—is the discipline known as ichnology (from the Greek ichnos, footprint). It is practiced by a small but thriving community, which has its own journals, conferences, traditions and vocabulary. Lots of vocabulary. Ichnology lives in a kind of parallel universe set apart from the rest of paleontology, identifying and naming "ichnospecies," which often have no known correlates among conventional biological species. In other words, ichnologists may conclude that various trace specimens were all made by the same kind of organism (thus constituting an ichnospecies), but they can rarely associate the ichnospecies with an animal known from body fossils.

Figure 1. Fossilized scribbles in stoneClick to Enlarge Image

The traces that resemble self-avoiding walks have been classified in ichnospecies such as Nereites cambrensis (from the Paleozoic era) and Helminthoida labyrinthica (found in Cretaceous and Eocene strata). None of these ichnospecies have been matched with known organisms, but most authors suggest they were worms of one kind or another. Expert opinion on the structure of the fossils is that they are tunnels rather than surficial grooves. Some tunnels are hollow, with walls consolidated by a mucous secretion; others are packed with fecal pellets, indicating that the animal was eating its way through the sediment.

Even though the animals lived in rather than on the seafloor, their trails are remarkably planar. This is mildly curious—what constrained their movements to two dimensions?—and also important in the context of self-avoiding walks. When confined to a plane, a self-avoiding walker is in constant peril of becoming trapped in a cul de sac of its own creation, surrounded by previously occupied sites. Although such one-way dead ends are also possible in higher dimensions, they are rarer. In two-dimensional space, trapping is so common that a random self-avoiding walker almost never gets far; constructing a long walk takes careful planning. The walk usually has a repetitive pattern—as seen in the ichnofossils.

Anyone who has ever mowed a lawn will recognize two of the most common motifs in the fossils. The first is the back-and-forth meandering pattern known as boustrophedon. (The original sense of this word is always given as "going as the ox plows," although I suspect the ox has little choice in the matter.) The worm follows a straight track for a certain distance, then makes a hairpin turn and proceeds parallel to the first track, then another 180-degree turn the other way. Thus the pattern grows as a series of alternating left and right hairpin turns, connected by straight segments traversed in opposite directions.

The second common motif is a spiral, which is even simpler. A left-handed worm follows the rule: Always turn left as sharply as you can without crossing your own path. The result is an Archimedean spiral, with the radius increasing by equal increments on each revolution. Note that the spiral is an outward one, formed of ever-larger loops. When I mow my lawn, I start at the perimeter and spiral inward, so that the last patch of grass to be mown is near the middle. As research for this article, I decided to try it the other way, beginning where I usually end. The experiment was not a success; I ran out of lawn on one edge while there was still a wide swath to mow elsewhere. I'll have more to say on this point below.








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