I see the golden ratio part .... what I don't see is any reference to the Archimedes Spiral. You can ignore me, or lead me by the nose.
The spiral growth of sea shells provide a simple,
but beautiful, example . . . Bottom of page
http://goldennumber.net/animals1.htm
Sorry that link should be
http://goldennumber.net/nature.htm
or
http://goldennumber.net/spirals.htm
At the bottom of the page