Sea Shells

math / code / curves

There are a large variety of sea-shells (and land shells) that can be simply described by rotating a ellipse around a log-spiral that has been projected onto a cone. The image below was generated using this approach:



The following images show the log-spiral, the spiral on the cone, a circle rotated about the spiral, and the resulting surface.



They were generated with the matlab function shells.m, which is hopefully self-explanitory if you read the comments.

You can generate many other shell shapes with the same code. Some examples calling shells in Matlab are given below.

clear
a = 0.8;
h = 2;
alpha = -0.1;
r1= 1.2;
r2 = 1.2;
shells

clear
a = 1;
h = 0;
alpha = -0.1;
r1 = 0.5;
r2 = 1.0;
shells

clear
a = 1;
h = 0;
alpha = -1;
r1 = 0.55;
r2 = 1;
N = 1/2;
shells

clear
a = 1;
h = 0;
alpha = -1;
r1 = 0.55;
r2 = 1;
N = 1/2;
f = 32*(1:2:15);
A = 0.05*2.^[0:-2:-14];
N_phi = 120;
shells