David Raup proposes a simple three-parameter "shell space," the parameters being

(the rate of growth of the spiral),

(the "tightness" of the shell cavity), and

(the rate of creep parallel to the spiral axis).

This simplified model of "shell space" was later adopted by Dawkins, who coined the terms "flare," "verm," and "spire" for the parameters

,

and

, respectively, as an illustration of the notion of "design space" in the book

*Climbing Mount Improbable*.

Here are precise definitions of the parameters.

1. If

is the distance between a point

on the generating spiral and that spiral's axis, and

the distance from the corresponding point

one turn later, then

, which is strictly greater than 1.

2. If

is the distance between the spiral axis and the inner edge of the shell cavity, and

the distance between the spiral axis and the outer edge on the same turn, then

, which is greater than or equal to 0 and strictly less than 1.

3. If the acute angle between the line

and the horizontal is

, then

.