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. [br]The colorzones are marked with circles through P[sub]40[/sub], P[sub]125[/sub], P[sub]263[/sub] and P[sub]1473[/sub] (source: Chris Impens).

Chris Impens summarizes: [i]"[br]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."[/i].[br]PS: the [url=https://en.wikipedia.org/wiki/Lucas_number]sequence of Lucas[/url] uses the same formula but starts from 1 and 3 instead of 0 en 1.