the growth of sunflowers
differente zones
For a large number of points you don't see anymore the whole as one spiral but as a whole of spirals. Sometimes you can even distinguish different zones. In the applet below they are delineated and colored differently, when clicking the checkboxes.
The colorzones are marked with circles through P40, P125, P263 and P1473 (source: Chris Impens).
growth of a sunflower
Chris Impens summarizes: "
Very simplified, one could imagine the actual botanical process to be as follows. The seeds are arranged, one after the other, in a roughly circular way and, continuously competing for space against each other, they end up in the best arrangement: a FIDIPAS with small partial quotients and a number of points that stops growing before the outer rays start building up. Such a FIDIPAS is bound to display spiral families counting a Fibonacci or Lucas number of members, or other numbers arising from similar arrangements with a different offset.".
PS: the sequence of Lucas uses the same formula but starts from 1 and 3 instead of 0 en 1.