MacCoil - Shell Coiling Visualization:
A Simplified Geometric Model of Shell Growth in Gastropods and Bivalves

INSTRUCTIONS:

Draw shells with this animation in two ways:

  • 1) Select pre-programmed models from the "Sample Shells" dropdown menu below the animation (parameter values for each shell model display in the yellow boxes).

  • 2) Draw your own:

        a) click on the red up/down buttons to increase/decrease parameter values, then

        b) click on the "Draw Shell" button (some parameter value combinations will force drawings outside the view box).

  • 3) Click on the "use defaults" button to return to the default shape.

NOTE: This very basic model by Illert (1983) was originally programmed by Rich Palmer in 1996(!) using Pascal to code a stand-alone application for Apple Macintosh computers. The code was converted to Javascript (in one pass!) in 2026, courtesy of: Code Convert AI.

Theory

CoilingParam drawing, 112K Diverse forms of bivalve and gastropod shells may be generated by a simple mathematical model of how the aperture (generating curve) ‘moves’ through space around and down the axis of coiling.

  • a = centroid offset- distance of the starting centroid (aperture centre) from axis of coiling
  • b = radius of the starting generating curve (aperture)
  • θ = coiling parameter, an angle that represents:
        - rate (per turn) the centroid moves down the axis relative to
        - rate (per turn) the centroid moves away from the axis
  • H/W = aperture shape- the ratio of height (H) to width (W) of the generating curve (aperture)

As a shell grows, the aperture centre (= centroid) traces out a logarithmic helicospiral.

This model of Illert (1983) is under-parameterized. For example:

  • It cannot draw a planispiral shell (because aperture expansion rate and centroid translation rate down the axis of coiling are not independent parameters, both are combined in the 'coiling parameter')
  • Aperture shape can only be a circle or oval (real shell apertures can have many shapes).
  • The long axis of the aperture can only be parallel or perpendicular to the axis of coiling (in many gastropods it lies at an intermediate angle relative to the axis of coiling).
Nonetheless, this model can approximate a surprisingly wide variety of gastropod and bivalve shell shapes.

  Shell coiling model references:

Other More Sophisticated Models to Visualize Shell Coiling

All three models below: a) allow coiling parameters to be specified and b) display full 3D-rendered images that may be rotated to view from any angle.

Wolfram2007 model, 57K Ramsden2007 model, 56K Resman2011 model, 57K
Wolfram 2007
(Mathematica)
  • Original 5-parameter model of Raup (1962)
Ramsden 2007
(Mathematica)
  • Simpler 3-parameter model
  • Strangely, only generates sinistral shells
Resman et al, 2011
(Mathematica)
  • A 7-parameter model that includes shell thickness

Return to Survey of Invertebrates (Zool 250) Legacy Home Page.

Copyright (c) 2026 by A. Richard Palmer. All rights reserved.
(revised Jan. 20, 2026)