Technique · Geometry
Seed heads
A dandelion clock or a sea urchin: seeds spread over a sphere by the golden angle, each with a bright node and a fan of fine hairs or tapering spines, the head turning slowly.
Seed heads 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
- The pattern of seeds on a sphere is called the Fibonacci lattice; it is also used to place sample points evenly over a globe or an image in computer graphics, because it spreads points very evenly with a single simple rule.
- Each dandelion seed hangs from a ring of fine hairs called a pappus, and in 2018 a team led by Cathal Cummins showed in Nature that the ring holds a separate ring of spinning air above it, a vortex that lets the seed stay aloft far longer than a solid parachute of that size.
- A dandelion head is not one flower but a hundred or more tiny flowers packed together, and each one becomes one seed; the "clock" is the whole head of seeds, each with its own parachute, waiting for a breath of wind.
- Dandelion seeds can travel kilometres on the wind, and far greater distances have been reported; the plant needs no insects to make a seed.
- The golden angle, about 137.5 degrees, is the turn that leaves the most even spacing however many seeds there are, because it is the angle that is hardest to approximate by a fraction: it is why sunflower seeds, pine cones and these heads show spirals in two directions at once.
The mathematics
- Seed i of n is put at height z = 1 - (2i + 1) / n, turned by i times the golden angle, 2 pi (1 - 1 / phi) = about 137.5 degrees, about the axis; each seed then covers an equal share of the sphere's area (150 seeds, each about 0.67 percent).
- Seen from one side the sphere is a disc, and the seeds near its rim are seen edge-on, so their hairs lie along the rim; that is why the edge of a head looks soft and hairy while its middle looks like a bed of separate tufts.
In art
- A sphere of radiating lines is one of the oldest shapes in decoration: sunbursts, haloes, fireworks and spiny shells all show it, and a seed head or a sea urchin is that shape made by growth.
- The sunburst, a disc with rays, was a favourite ornament of the Baroque and of Art Deco, from monstrances and clocks to cinema ceilings, and a head of seeds or spines is the same shape made by growth.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes