Phyllotaxis and sunflower spiral generator

Why sunflowers spiral

Phyllotaxis is the arrangement of leaves, seeds and petals on a plant. In a sunflower head, each new seed appears at a fixed angle from the previous one. If that angle is the golden angle, about 137.5°, the seeds spread so evenly that no gaps open up, however many there are, and they line up in two sets of spirals that run in opposite directions.

The numbers of spirals in the two sets are neighboring Fibonacci numbers, for example 34 and 55. Pine cones, pineapples and daisies follow the same rule. A formula of this kind was proposed by Helmut Vogel in 1979: the point number n sits at a distance proportional to the square root of n, and at the angle n times the golden angle.

How the generator builds them

Ornamatic places the points by this formula, then draws a motif on each: a dot, a petal turned along its spiral, a square or a diamond. The motifs can grow towards the rim of the head, as real seeds do. Heads are placed on a square or a hexagonal grid and repeat exactly across the edges of the tile.

A small change of angle changes the picture completely. Away from the golden angle, the points gather into rays, fans and rings, the more so the further the angle is from 137.5°. Colors go around the spirals or by rings.

What you can adjust

• Motif — dots, petals, squares or diamonds.
• Points — from 20 to 900 in one head.
• Angle — the turn between successive points; 137.51° is the golden angle.
• Motif size and growth — how large the motifs are, and how much larger towards the rim.
• Head size and grid — the radius in lattice spacings, on a square or hexagonal grid.
• Colors — by spiral, by ring or one color; any palette.

Export and use

Download the seamless tile as PNG or SVG, or copy a ready CSS background. The patterns you create are free to use, personally or commercially.