Control of gastropod shell form via apertural growth rates

This paper discusses and corrects ideas in Løvtrup and Løvtrup (J. Morphol. 197:53-62, '88) on how differential growth rates around the aperture cause the gastropod shell to coil at particular angles. The relationship between position relative to the shell apex and growth rate is derived. This lets us understand what information on relative growth rates around the aperture is sufficient to determine the shape of the logarithmic spiral that these growth rates generate. I argue that differential growth rates could not be physiologically controlled precisely enough to regulate apical angle; they passively follow, not actively direct, shell shape.