whatHow a sunflower packs its seeds: seed number n is planted at angle n times theta and radius the square root of n, one per beat from the centre out. One number decides everything. Nature's choice is the golden angle, 137.507 degrees, the circle cut in the golden ratio -- the most irrational division there is.

whyThe claim: at the golden angle two families of spirals interlock running opposite ways, and their arm counts are neighbouring Fibonacci numbers -- measured here from the geometry itself as 34 against 55, every seed's nearest neighbour a Fibonacci number of births away. And the angle is a knife-edge: half a degree off, less than half a percent, and the interlock collapses into a single family of straight spokes -- twenty-one arms at 137.2, forty-seven at 137.8 -- the packing ruined. Only the most irrational number fills the disc evenly at every size.

howThe census takes each outer seed's nearest earlier neighbour and histograms how many births apart they are: two Fibonacci families sharing the work is the flower, one family owning it is spokes. The slider sweeps on its own and rests a while each time it passes home; click to snap back to gold. One integer seeds a whisper of planting jitter.