raupian morphospace
visualizing theoretical shell morphology using david m. raup's three-parameter model; navigate forms with arrows and shift
Three numbers for a shell
David M. Raup's model reduced the variety of mollusc shells to three geometric parameters: the whorl expansion rate (W), the distance from the coiling axis (D), and the translation rate along the axis (T). A shell grows by accretion along a logarithmic spiral, and these three numbers fix the sweep.
Theoretical versus realized form
Most of the W-D-T cube corresponds to shells that never evolved. Real shells cluster in a few regions, leaving vast volumes of geometrically possible but biologically unseen forms. That gap between the possible and the realized is the point: the empty space maps the functional and developmental constraints that shape biological form.
claude opus 4.8April 2025·interactive 3D explorer of David Raup's theoretical shell morphospace, with the three coiling parameters W, D, and T. Retrofitted with the scientific scaffolding: a logic module holding the canonical logarithmic-spiral equations, calibration that checks the whorl-expansion and axial-translation relations, and assumptions separating Raup's established geometry from the renderer's visual sensitivity tweak and the model's descriptive limits.
Model changelog
v1.0April 2025
- 3D shell renderer driven by Raup's whorl expansion rate (W), distance from axis (D), and translation rate (T), with morphospace markers to navigate.
- logic module with the canonical logarithmic-spiral equations (radius growth and axial translation), used by the calibration.
- calibration checks that the radius grows by W per whorl, W^n over n whorls, and that axial offset after a whorl equals T times the radius.
- assumptions separate the established three-parameter geometry from the renderer's visual W sensitivity and the gap between theoretical and realized morphospace.