Seashell surface

In mathematics, a seashell surface is a surface made by a circle which spirals up the z-axis while decreasing its own radius and distance from the z-axis.

\\ Various authors have suggested different models for the shape of shell.

David M. Raup proposed a model where there is one magnification for the x-y plane, and another for the x-z plane.

Chris Illert[1] proposed a model where the magnification is scalar, and the same for any sense or direction with an equation like which starts with an initial generating curve

and applies a rotation and exponential magnification.