Technique · Geometry
Nautilus and sprig
A chambered nautilus shell in single-weight line art, a logarithmic spiral with bowed chamber walls, beside a leafy sprig.
Nautilus and sprig is drawn geometry, rebuilt as it changes. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- Nautiloids are survivors of a group of shelled cephalopods about 500 million years old; their relatives the ammonites died out with the dinosaurs.
- The tube that runs through a nautilus shell, the siphuncle, lets the animal pump fluid out of its chambers and so rise or sink.
- A chambered nautilus builds a new, larger chamber as it grows and seals off the old one; a thin tube pumps fluid in and out of the older chambers so that the animal can control its buoyancy.
- A real nautilus shell widens by a factor of roughly three with each turn.
- The chambered nautilus (Nautilus pompilius) lives in the deep waters of the Indo-Pacific and rises toward the surface at night to feed; it lives in the last, outermost chamber, and the older chambers behind it are sealed off and joined to it only by the thin siphuncle.
- The outside of a nautilus shell is striped on top and pale underneath, so that from above it blends with dark water and from below with the bright surface: a camouflage called countershading; the inside is lined with pearly nacre.
- A nautilus has dozens of sticky tentacles (about ninety) and no suckers, and it moves by squirting water from a funnel, a gentle jet propulsion.
- Oliver Wendell Holmes wrote his poem The Chambered Nautilus in 1858, ending with the call to build more stately mansions, as the animal does when it outgrows a chamber.
The mathematics
- In polar form the spiral is r = a e^(b theta); here one full turn multiplies r by 3.00, so b = ln(3.00) / 2 pi = 0.175.
- The 14 walls in each turn are 25.71 degrees apart, and each is the one before it scaled by 1.082.
- A logarithmic spiral crosses every ray from its centre at the same angle, so each whorl is a scaled copy of the one inside it: growth without change of shape.
- The golden spiral grows by the golden ratio every quarter turn, about 6.9 times per full turn; measured nautilus shells grow by about three, so the popular claim that the nautilus is a golden spiral is not true.
In art
- Polished nautilus shells were mounted by goldsmiths as drinking cups in sixteenth- and seventeenth-century Europe.
- One weight of ink is enough to show structure, which is why botanical and shell studies have long been drawn in clean line.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes