A "sunflower" means the set of points where Nth point has R=sqrt(N) and theta=g*2*pi*N in polar coordinates for some irrational number g. I CLAIM if g is a quadratic irrational and real P with 0<P<1/10 are fixed, then in the limit N-->infinity with D=N^P, that the set of sunflower points within distance D of the Nth sunflower point, all lie within epsilon of a set of points generated by translations and rotations of a fixed (g-dependent) finite set of 2-dimensional point lattices, where epsilon-->0 in the limit. FOURIER TRANSFORMS For a discrete point set, place unit-mass Dirac delta functions at each point, and then take the Fourier transform of the sum of those delta functions. Call that, for short, the "Fourier transform of the point set." So for the first 2048 points in a sunflower, the fourier transform "power spectrum" as a function of x and y is F(x,y) = sum(N=0..2047) [ cos(x*cos(N*2*pi*g)*sqrt(N))^2 + sin(y*sin(N*2*pi*g)*sqrt(N))^2 ] It seems to me that the lattice approximation theorem implies that the fourier transform of a an N-point sunflower will exhibit some kind of discrete structure in the N-->infinity limit, albeit it is not clear to me just what will happen. A greyscale picture of F(x,y), anyone?