June 14, 2021:  Here we see the revised fencing system.  The pole is now
inside with the seedling for easier attachment.



June 19, 2021: Looks kind of lonely down there!   



July 1, 2021:  About two weeks later I removed the string which helped
to keep the cage in place.



Growth was getting more rapid by the day.  Not long after this day
there was a "flock" of some kind of leaf chewing insects which
required some periodic spraying with liquid Sevin (by Bonide).  It
seemed to do the trick. It may have been Japanese beetles, but I could
never see them.  Some leaves were entirely eaten!



July 11, 2021:  Ten days later, the seedling made it up another foot
or so to the duct tape.  The first string ties were done after it left
the protective cage.



Another shot showing the entire plant.  It began to take more water
with the oncoming heat wave(s).



July 25, 2021:  Two weeks later (Day 54) -- Virtually NO problems with
this sunflower.  I began to expect great results on each visit to the
garden.  As with all sunflowers though, it isn't until the final few
weeks when any evidence of a flower comes.  This was a waiting game,
and the weather was cooperating.  Some good, steady rains came as
well.



August 4, 2021: (Day 64) Much thicker stem now.  Just reaching the last row of
pole duct tape today! 



August 21, 2021; (Day 81) The final push!  "Something" seemed to be
happening up top at this time, but It was not clear since I had no
ladder.  (I never did rent one, so all these pictures were from a
standing [on] ground position). It did look as if the terminal shoot
was forming a small spherical bud.



September 6, 2021:  (Day 97) Wow!  This was what greeted me to the
garden on Labor Day at 8:20 AM.  Sure enough!  Just about 100 days as
promised on the small seed packet! Following the taking of this
picture (without a tripod) I notices there seemed to be some good
definition to the flower's whorl patterns.  I zoomed in on them as one
does on a cell phone, to see if it was true i could see the fine
detail!  Sure enough!  It was there!


  

The image below is actually the same image as the one above at its
full 100% magnification.  I thought it would be interesting to
hand-draw fine white lines to see how many whorls (spiralling
counter-clockwise to the left) there were.  As you can see from the
white number 55 in the center, I counted exactly this many whorl
pathways! 55 is the 10th Fibbinacci number! I was amazed by this
because I was expecting to count 34 whorles (as indicated in The New
Path Drawing.  I concluded that THAT research I had done was for other
composite flower structures and/or that the level of drawing detail
was too much for book illustrator to render clearly.  Whatever the
case, I was now sure the sunflower had more golden ratio detail than
previously thought.  But if THIS counter-clockwise whorl pattern had a
count of 55, what do you suppose the clockwise whorl count would be?




To my amazement, it most certainly turned out to be 89.  Exactly! 
This is the 11th Fibbinaci number!  Carrying this one step further, we
find the Golden Ratio of Phi comes up when we divide 89 by 55.  This
equals 1.61818181812...




More could certainly be written about this fascinating ratio and how
it occurs again and again in nature.  Instead, I leave you with an
image of my now framed drawing depicting various aspect of sunflower
seeds and their "Golden Ratio Connection" with one another.  Not only
is this a story about mathematical patterns, but also one of 
simple beauty we find in a nurtured sunflower seed.  I
suppose we could see my sunflower also as a living proof!