Seed n sits at angle n × θ and at a distance √n from the center. With θ set to the golden angle the seeds pack evenly. Nudge it by a tenth of a degree and the pattern collapses into spokes.
Why 137.5°
The golden angle is 360° × (1 − 1/φ), where φ ≈ 1.618.
φ is the hardest number to approximate with fractions, so no two
seeds ever line up on the same ray and gaps get filled as they
appear.
Counting spirals
The spirals you see are parastichies: seeds whose index differs by a Fibonacci number. Near the center 21 and 34 dominate, farther out 34 and 55, then 55 and 89. Try highlighting each one.
Not a fractal
Every seed is the same size and density is uniform across the disc, so there is no detail at smaller scales. The self-similarity is in the spiral counts, which climb the Fibonacci sequence as you move outward.