(Ver 1.07b Dec. 9, 1996, © A.Richard Palmer; download)

*MacCoil *allows students to visualize the effects of changing different geometric coiling parameters on the shapes of mollusc shells. A 'point-and'click' interface allows parameters to be manipulated individually (see illustration below). Alternatively, pre-defined parameter combinations may be selected from the "Shells" menu to draw a variety of gastropod and bivalve shell forms.

The drawing algorithm also may help students better visualize how shells actually grow: 'new' shell is added progressively to previous apertures. *MacCoil * runs best on machines with a math coprocessor, but will still run on almost any version of Mac (including Plus and SE).

Unfortunately, *MacCoil * does not allow you to save new parameter combinations at present (a formal Macintosh interface for this ability involves more work than you might think). However, you may submit your favorite new parameter combitations (along with the taxon name and order/suborder membership) and I can easily add it to the list of items in the "shells" menu.

**Starting Centroid Offset:**Centroid refers to the center of the generating curve (=aperture). Increasing the value of this parameter, shifts the center of the initial generating curve further from the axis of coiling, one pixel at a time.**Starting Whorl Radius:**Sets the radius of the initial generating curve in pixels.**Coiling Parameter:**Determines the rate at which the center of the aperture moves down the axis of coiling relative to the rate at which it moves away from the axis of coiling (higher values yield taller shells).**Aperture Shape:**Sets the ratio of the vertical dimension of the generating curve over the horizontal dimension (higher values yield more vertically elongate apertures).**Number of Whorls:**Controls the number of whorls the program will draw for a given shell (in units of 0.5 whorls).**# Sections/Whorl:**Specifies the number of generating curves drawn per whorl. On a slow computer, reducing this value will increase the speed with which a shell is drawn.

The geometric model used by *MacCoil * (from Illert, 1982*) is under-parameterized (e.g., it cannot generate planispiral shells). Nonetheless it can reproduce a wide variety of shell shapes and allows students to see how small changes in geometric parameters can have rather large effects on overall shell shape.

Those interested in learning more about the variety of geometric models that have been developed to describe mollusc shell coiling should see the article by Stone (1996)**. Stone provides a comprehensive overview, and a discussion of the differences among models, in a nice historical framework.

* Illert, C. 1982. The mathematics of gnomonic seashells. Mathematical Bioscience 63:21-56.

** Stone, J.R. 1996. The evolution of ideas: A phylogeny of shell models American Naturalist 148:904-929.

*MacCoil * is a Freeware program. It may be distributed free of charge for non-commercial, educational use only.

*MacCoil * may not be sold or bundled with other software/hardware without expressed written consent of the copyright holder:

A. Richard Palmer

Department of Biological Sciences

University of Alberta

Edmonton, AB T6G 2E9

CANADA

You may download a fully functional freeware version of *MacCoil * (ver. 1.07b; Dec. 9, 1996; download size is 34K). This file is in a Macintosh self-extracting archive coded in BinHex 4.0 format. Mac web-browsers should automatically convert the BinHex file to the self-extracting archive. Please read the notes regarding SOFTWARE DISTRIBUTION.

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Program and WWW page copyright © 1997-2003 by A. Richard Palmer. All rights reserved.
*(revised May 26, 2003)*