The angle a sunflower found

Every dot is placed the same fraction of a turn around from the one before it, and a little further out. That single number is the only thing the slider changes. Drag it, or nudge it one hundredth of a degree at a time with the arrow keys.

The spiral arms you can count are never arbitrary: they are the denominators of the simple fractions that come closest to your angle. When a small denominator fits well — 120° is exactly a third of a turn — every seed lands on one of that many spokes, and the space between the spokes is wasted. The golden angle, near 137.508°, is the number that no simple fraction fits well. Nothing dominates, so nothing is wasted.

Sunflowers are not doing arithmetic. A bud that simply grows into the roomiest gap left by its neighbours arrives at this angle on its own, which is the more interesting fact: the packing is not a plan, it is what is left over when crowding runs its course.