Explore Cliff Pickover's Virtual Seashells (VRML)

(Select image at left to see detail of a computer graphical simulation of the fossil seashell, Nipponites.)

The following VRML (Virtual Reality Markup Language) files will allow you to explore various 3-D models using a VRML Browser. The files run best with "GLVIEW" a browser available at http://www.inx.de/~hg/ for Windows 95 and Windows NT. If you use this browser, you can see the forms grow by selecting Options->Config->Draw Directly. (Other VRML browsers are easily obtainable on the web. For example, see http://www.vrml.org/. Depending on your machine and browser, some of these may take a minute to render. I use hardware acceleration to render these quickly. MIME type is x-world/x-vrml.)

Iteration procedures for biological pattern generation are particularly useful for bizarre varieties of seashells on the borderline between deterministic classical equiangular spirals on the one hand and unstable oscillations on the other.

Phylum Mollusca is the second largest phylum of the animal kingdom, and is made up of such forms as clams, snails, slugs and octopuses. The group has enormous diversity, both in shape and size, ranging from the twisted, wormlike solenogastrids to the baglike octopuses. Cephalopods represent the most specialized of the molluscan group and include octopuses, cuttlefish, squids and nautiluses. One group of cephalopods, the ammonoids reached their peak in the Mesozoic era and became extinct at the end of the Cretaceous period. It is known that ammonoids avoided the extensive shallows in which large dinosaurs sometimes swam and their sizes ranged from tiny shells of 1/2 inch diameter to some with a diameter of 6 to 7 feet.

For software and background on the mathematics of these seashell forms, see Pickover, C. (1994) Computers and the Imagination (St. Martin's Press).

VRML files:

Explore Generic snail-like form.
Explore Generic snail-like form. This is a high-resolution version of the previous and is slower to render.
Explore Fossil of Nipponites mirabilis . This form, like the following form, lived during the time of the dinosaurs. Comparison of the computer graphics with the actual fossil validates the growth formulas. Notice the irregular oscillations within and perpendicular to the coiling plane.
Explore Fossil of Madagascalites ryu . This creature begins life linearly and then spirals back down around itself.
Explore Artistic coral .
Explore Buckyball molecule .

Acknowledgment: The seashell growth research is a collaboration with theoretical chonchcologist, Christ Illert.

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