Technique · Geometry
Phyllotaxis
Seeds placed at the golden angle, as in a sunflower head; the angle swings slowly so the spirals form, thicken and give way again.
Phyllotaxis 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 golden angle, about 137.5078 degrees, is 360 degrees divided by the golden ratio squared; seeds placed at that turn never line up on spokes, so the head fills evenly.
- Alan Turing spent part of the last years of his life on why plants show Fibonacci numbers, in unfinished work on phyllotaxis.
- Plants make each new seed or leaf where there is most room at the growing tip, pushed away by the ones before; models and experiments of that rule produce the golden angle as the stable pattern.
- Helmut Vogel published this seed model in 1979; large sunflower heads typically show 34 and 55, or 55 and 89, spirals in opposite directions, neighbouring Fibonacci numbers.
- In 1992 Stephane Douady and Yves Couder reproduced the pattern with drops of ferrofluid falling at a steady rhythm onto a dish in a magnetic field, each drop pushed away by the ones before it.
The mathematics
- Seed n sits at radius c sqrt(n) and angle n times 137.508 degrees; the square root gives every seed the same area, pi c squared, so the head is evenly filled however many seeds there are.
- An angle that is a simple fraction of a turn puts seeds on straight spokes with wide gaps between them; the golden ratio is the number hardest to approximate by fractions, which is why it is the best angle to avoid spokes.
- At 137.508 degrees the seeds are 0.000 degrees from the golden angle: a tenth of a degree or two can be enough to break the Fibonacci spirals into a few wide arms.
In art
- The Core, the education building at the Eden Project in Cornwall (2005), has a roof whose panels are laid out in sunflower spirals.
- Spirals of seeds and scales are among the most copied patterns in design, from jewellery to ceiling domes, because they combine order with an even spread.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes