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
.
