What it is
Phyllotaxis is the botanists' word for how a plant arranges its leaves or seeds. The sunflower rule is short. Seed number i sits at a distance proportional to the square root of i from the centre, and is turned round by i times a fixed angle. The square root spreads the seeds evenly over a disc.
The plates
Five plates of 1,000 seeds each. The dial is the turn angle. At 100 degrees the packing breaks into about 18 spokes. At 121 degrees it gives a double spiral. At 137.3 and 137.8 degrees spiral arms are visible. At 137.508 degrees, the golden angle, the seeds pack evenly. Dots whose centre falls inside the letters are drawn a little larger.
100°
121°
137.3°
137.508°
137.8°
The plates are drawn by mosaic, a small Python library of our own, built on numpy, scipy, shapely and contourpy. No image model is involved, and each plate is a flat-colour SVG under 45 KB. The word Ciao is the safari's constant: it sits in the same place on every plate.
What we did and found
The two plates nearest the golden angle are 0.208 and 0.292 of a degree away from it, and both show spiral arms. About a fifth of a degree is enough to lose the even packing.
The Voronoi cell uses these same seeds: there, each seed of a sunflower spiral is given the part of the canvas nearest to it. See the Voronoi cell →
What is open
Only the angle has been turned. The spacing rule, the square root, is the same on every plate.
mosaic is not yet part of Platypus, our visuals engine. That is why this cell is marked as working and not as shipped: the page is our notebook on the element.