05 July 2014

Fibonocci Coneflowers

Fibanocci patterns are found in the seeds of a sunflower head, and in the head of a coneflower. My sunflowers are not yet blooming, so come on and admire the coneflowers.

OK, it's time for your math class. Leonardo Pisano Fibonocci was an 11th century mathematician who brought the Arabic numbers we use today to the merchant world to replace the cumbersome Roman numerals. He also pondered (mathematically speaking) the successive reproductive growth of rabbit populations. (Only a mathematician...) He applied an old Indian Hindu numbering sequence to develop a formula calculating the count over time. The Hindu sequence is what we (our Western-centric society) now call the Fibonocci sequence. The sequence adds the previous two numbers in a series to arrive at the next one: 0,1,1,2,3,5,8,13,21,34...

But nature had already discovered this and was using it in all sorts of ways. The mathematical logarithmic spiral of a nautilus shell, the branching of certain trees, and the spiral seed arrangements of sunflowers and coneflowers all use this sequence or a formulation of it.

According to Innovation Factory, the image is a "Yellow Chamomile head showing the arrangement in 21 (blue) and 13 (aqua) spirals. Such arrangements involving consecutive Fibonacci numbers appear in a wide variety of plants. Plants produce their leaves and seeds from a growth tip that spirals around the plant or center of the seed head as it goes -- the most efficient way to pack seeds into the seed head... You get the closely packed Fibonacci spirals of seeds, with the number of clockwise and anticlockwise spirals at any point on the seed head a pair of successive Fibonacci numbers." Sure enough, my coneflower has 13 spirals in one direction, and 21 in the other.


Writing of coneflowers (Echinacea), I offer some observations on the three types in my garden: native Echinacea purpurea, Sundown of the Big Sky series, and Coconut Lime. The original echinacea purpurea are the most drough-tolerant, but the flower petals can droop, leaving a large prominent seed head. Bumblebees love them, and so do the goldfinches who perch on top and chow down. They are taller than the others with the largest flowers and largest seed cones -- making it easy for the finches to fly in for a snack.

The flowers can vary in their color intensity for no apparent reason -- some being a dark purple-pink, while others are light pink. They do have a distinct fragrance. Speaking of rabbits multiplying, they also easily seed themselves in my habitat.


Sundown, part of the Big Sky series, is what happens when breeders get involved. This coneflower puts out a riot of blooms early, then dies out before summer ends. The blooms start out with an beautiful orange color then fade in a few days into an dirty washed-out salmon. Deadheading does not seem to help the plant continue into the summer, as foliage turns a dark bronze like it has given up making chlorophyll. The plant goes ugly on me and slowly melts away until next year. The internet is full of stories of disappointments on this one.


Coconut Lime, another plant breeder introduction, looks different than the others. The blooms start out with petals and centers looking like the native, but the centers begin to increase into larger pompoms. The blooms last a long time, but bees never touch them. I suspect the thick pompoms prevent them from getting to the pollen, or the pollen is not to their liking. Height is much shorter than the other two coneflowers at about 16-inches (40 cm.)

For The Record:
  • Full sun
  • Small amount of fertilizer on the Sundown
  • Some early season pests eat bloom petals & leaves

Garden Calendar:
  • Blooming: coneflowers, liatris, rudbeckia, daisy, monarda,
     echinops, phlox, daylilies, bachelor button, zinnia, hydrangea
  • Harvested: 20 onions, green beans

7 comments:

Jean Campbell said...
So I grabbed my hat and went out in the hot afternoon sun to see this phenomenon in person on white Echinacea grown from seed by Susie-who-maintains-the-Jones-Lab-Butterfly-Gardens.

Then I checked blossoms like Shasta Daisies, Ratibida and even tiny Melampodium which required bringing in to a magifying light.

I'll never look at another coneflower without thinking of Swimray and Fibonocci.
Swimray said...
Jean,
I had to laugh but then checked my coneflower. 13 spirals in one direction, and 21 in the other. I added this to the blog post.
Ray
greggo said...
Interesting information. Purperea is very prevalent in my garden. I can't seem to remove a one. I'm adding palida and angustfolia.
John B. (DC Tropics) said...
I love Echinacea, especially the new ones in the red to orange range, but have had so little luck with them. I think my soil is simply too heavy, and I can't give them the blazing all-day sun they want.
Swimray said...
Greggo,
I had to look up the echinacea types you mentioned, not being familiar with them. Look like subtle variations, but also like they are native.

John,
I have not had good luck with the new orange Sundown - even though it IS growing in a good conditions!
Casa Mariposa said...
I think the Fibonacci sequence is fascinating! There is so much math in nature. :o) I avoid the newer coneflowers. They look like poodles to me. I prefer the tried and true varieties that the pollinators love.
Swimray said...
Casa,
You see poodles where I see pom poms.