Sunflower Spirals

Sunflower Spirals

Place each new seed a fixed angle around from the last one, a little farther out, and see what grows.

1Turn per seed

2Settings

1000
Try nudging the angle by a hundredth of a degree.

3Why the golden angle

Simple fractions close to your turn

4About the pattern

This arrangement is called phyllotaxis, Greek for “leaf arrangement.” It shows up in sunflowers, daisies, pine cones, pineapples and the leaves around many stems. Count the spirals on a real sunflower and you usually get two neighboring Fibonacci numbers, such as 34 one way and 55 the other.

The drawing uses a model published by Helmut Vogel in 1979: seed number k sits at an angle of k × (the turn), at a distance from the center proportional to √k, so every seed gets about the same amount of room.