Fibinocci

[Voyager2MnM]

fibonacci'd

Hmmmm, will just have to take a closer look at all of those lovely shots on your EarthGoddess thread, while waiting... (not so) patiently for a closer peek.

7778742049 & 12586269025

Just an example of what can be seen in the flowers of a few common flowers

Iris - 3 petals
Primrose - 5 petals
Ragwort - 13 petals
Daisy - 34 petals
michaelmas daisy - 55 petals
michaelmas daisy - 89 petals

 

[Earthgoddess]

hmmmm

12586269025, 20365011074


peek or peak? hmmm

all those flowers just a meadow full of numerically perfect yet sporadically random spirals...yet even in the desert there are spirals upon spirals of life.

 

[Voyager2MnM]

peek's have it

So sorry. Have noted and changed the perilously poor usage of peak instead of peek, in the previously posted passage of mine.

32951280099, 53316291173 (52nd & 53rd terms in the sequence)

It should also be noted that there is a great amount of mis-information concerning this series of numbers and the related golden ratio. Looking around at the retoric it would appear artists and architects were running around with this golden spiral creating works according to the ratio. As well as an almost mystical assumption that all of nature is linked to it, in some segments of the population. Amoung many other things. It is prudent to look carefully at the "report linkages" and judge carefully what is really going on.

 

[Earthgoddess]

86267571272, 139583862445

I do apologize if my pagan bent on the world has taken from the truest beauty of this equation...way too Da Vinci Code I suppose.
The element of beauty and simplicity is simply within the mathematics.
All of nature, perhaps I over reach in some posts, but there is order within the apparent chaos, even in a riotous meadow.
Sometimes there is safety in an assumption that there is more order, and less chaos.
I,for one, tend to seek out the chaos and yet am irresistibly drawn to the order-the refuge that it provides.
The bad boys of the universe appeal and break hearts while the orderly, controlled nice guys stand off to the side. And I have found myself more and more drawn to that precise safety, that order, because truly I know that beneath that control often is a more perfect chaos, a more intense wildness.
But that might just be the dark dreams of a woman in lust.
That riptide warning that is repeatedly ignored, just to experience it.
The almost romance of whispers, the soft play of skin that might be more than passion-all of it chaotic, all of it so uncontrolled yet so tightly reined in after, awkward phrases, uncomfortable moments. Chaos.Riptide. Life.

 

[Voyager2MnM]

56 & 57

225851433717 & 365435296162

We as humans have a tendancy to try to make order and organization to things that are chaotic and disordered. And even make associations were coincidence occur. These are easy traps everyone has a tendancy to do. I for one have often fallen prey to such things. It is reassuring and comfortable to see order and symmetry even were none truely exists. I have probably tried to over copensate for these tendancies at times. But within the natural world can be found true examples of this interesting sequence and the golden ratio it defines. And even when this ratio cannot be found there are other equations that define what is happening. Often providing order in what may otherwise appear chaotic.

 

[Earthgoddess]

58,59,60

591286729879
956722026041
1548008755920

Order within chaos, and hands rising from the foam of a riptide. The only trouble is when the hands are pulling you into the churning water, to join in a dance of chaotic pleasures and there below in the water floats a shell, a perfect Fibonacci spiral inhabited by a creature of slime and tentacles,mucous laden and simple minded.
So within order there is living chaos, within chaos perfect linear order and within the heart of most of mankind a perfect/imperfect balance of emotions and ethics.

And now I up the ante, trios of numbers, since the energy of three is transcendent, and again magickal.

 

[Voyager2MnM]

61, 62, 63

Meeting your challenge...

2504730781961
4052739537881
6557470319842

Even within the living chaos of that creature of slime and tentacles, mucous laden and simple minded, there is order. It hunts for food, evades predation and seeks to procreate. And even in the chaos of the riptide, you can find it has scowered the bottom revealing new treasures of order. And in a sense the emotions and ethics of humans add the greatest amount of chaos to our world as we all bring differing diesires hopes and focus.

 

[Earthgoddess]

chowder

10610209857723, 17167680177565, 27777890035288

All humanity seeks the same as that simple mollusk-eat,procreate, avoid predators-we are no more simple or more complex except for our capacity to love. Love beyond measure, romance beyond memory,and lust beyond want, all of which are utter chaos. Humans have screwed up the most simple order of life for centuries with those emotions. Mating for life has practicality, many animals follow this prescription for success. Its we humans who attach these romantic notions to biological imperatives.

Yet within my own sardonic view is a heart that flutters, a soul that yearns and a desire to remove myself from the mollusks. No chowder for me thanks, that might have been a couple in love.

 

[Voyager2MnM]

New England style...

44945570212853
72723460248141
117669030460994

Mmmm, it is hard for me to pass up a good New England style chowder.With so many emotions running rampant in my feeble mind, I find myself feeling compassionate for the the little mollusk, thinking it might be a part of a loving coupe. But hunting for a way to enjoy a good cup of chowder, while avoiding succumbing to starvation.

 

[Earthgoddess]

70,71,72

190392490709135
308061521170129
498454011879264

Pity the mollusk, I think not, again just another dot on the spiral-eat or be eaten.
Starvation has many forms, cats starve even with full bowls of crunchy goodness at their feet waiting saintly for a small morsel of wet food. People starve as touch withers to nothing, whispers of passion fall silent and needs overcome wants. Starvation is so slow in these realms, almost like freezing to death.
Personally, regarding chowder, I prefer mollusks steamed, again that heat and flame aspect,the chaos of the boiling whirlpool. But I adore them raw-elemental, briny, sweet.The sea's own ultimate essence, the salty swirl. But I do know others find them to be dangerous balls of slimy bacteria laden mucus. And yet others enjoy them until later after a peaceful initial consumption they take quiet and purging revenge.

But for me, like a good pinniped, I like my shellfish raw, kissed by the tang of salt, freed from the confines of their shells with a scoop and a twist.

 

[Voyager2MnM]

73, 74, 75

806515533049393
1304969544928657
2111485077978050

H S M Coxeter, in his Introduction to Geometry (1961, Wiley, page 172) - see the references at the foot of this page - has the following important quote:

it should be frankly admitted that in some plants the numbers do not belong to the sequence of f's [Fibonacci numbers] but to the sequence of g's [Lucas numbers] or even to the still more anomalous sequences

3,1,4,5,9,... or 5,2,7,9,16,...

Thus we must face the fact that phyllotaxis is really not a universal law but only a fascinatingly prevalent tendency.

But the tendency has behind it a universal number, the golden section,which we will explore on the next page.
Article: He cites A H Church's The relation of phyllotaxis to mechanical laws, Williams and Norgate, London, 1904, plates XXV and IX as examples of the Lucas numbers and plates V, VII, XIII and VI as examples of the Fibonacci numbers on sunflowers.


In this Cactus there are 4 spirals in one direction and 7 spirals in the other direction

 

[Kylan]

I know I could 'Google' in an attempt to follow the sequence, but I shan't insult those posting by doing so.

I ask you to please consider this as merely an obscene interruption in the flow of wonderful phraseology to clumsily express gratitude.

 

[fire_breeze]

Fibonaccis!!

It just a shame that I discovered this thread so late... *sigh*

 

[Earthgoddess]

join us

Oh come now, the sequence is always open to new comers...and so simple.

3416454622906707 ,5527939700884757, 8944394323791464

Again the celtic inspired spirals caught my eyes as yesterday as again I wandered wenchily among the dappled shade of the Renn fest. I was blessed with wonderful company, and that made the day flow sweetly to its conclusion, as fingers wound spirals, wants wound wishes,yearning wound itself.

 

[fire_breeze]

What, and destroy the beautiful, almost perfect, flow?

Oh, very well, if you insist.

14472334024676221
23416728348467685
37889062373143906

 

[Voyager2MnM]

82, 83, 84

A pleasant welcome...

61305790721611591
99194853094755497
160500643816367088

My minds eye sees cool breezes among the throngs congregating beneath the shimmering shade of the trees. The scents of foods from various lands and times wafting in the air, mixing with the smoke of the smiths furnace and glass blowers kiln. The sounds of children playing with shield and wooden sword or rams horn. And to share this in good company must have been as special a treat for you as for the company that was kept

 

[Earthgoddess]

A welcoming wave

Ah another player in the game, or dancer in the dance, twisting and turning.
My mind revels in the rhythms of the fair. The clang of words, well handled. The ringing tones of swords deftly clashing. The sense of timelessness, and the scents of oils rich and spicy on sweet skin. So deliciously exposed and offered by bodices. Like fall's own favored fruit the pomegranate, skin opened to revel jewels.
85 86 87
259695496911122585,420196140727489673, 679891637638612258

 

[fire_breeze]

Thank you...

And I can only hope that I can keep up with the weaving and threading of this exquisite dance...

88, 89, 90:

1100087778366101931
1779979416004714189
2880067194370816120


I'm beginning to realise that the truest voyage is to uncover the spirals of secrets hidden in the very depth of my psyche.

 

[Voyager2MnM]

Voyages

With spirals going this way and that, the journey of self discovery is a life long challenge and as well as a joy. Around each curve a new discovery, around each bend a new realization. With each realization, a revelation about who we are.

The fair offers many things to many people. From the small child blowing large multi colored soap bubbles in the afternoon sunlight, ribald humor performed cleverly, old trades rediscovered by the new generations, archaic tools and sports performed, the curls of hair highlighted in the rays of the sun. The discovery of new jewels of sweet fruit. The allure of a bodice so nicely filled and demanding attention by its very existence.

91, 92, 93
4660046610375530309
7540113804746346429
12200160415121876738

http://www.youtube.com/watch?v=5Xgw84Kwrh8

 

[Earthgoddess]

wanderers welcomed

94,95,96
19740274219868223167, 31940434634990099905, 51680708854858323072

Learning to spiral through life is a skill that will serve the practitioner well. For every ancient smithy manning the fiery forge there is a new apprentice fresh from the age of the computer's calling. Nothing is new, all is new, all is ancient, all is ever all. The portions of the journey that are often most revealing are when we assume its a major revelation, and in making that assumption reveal a piece of ourselves. These tiny reveals or shows, are us being caught in a parlor trick. The magicians slight of hand, now tipping the trick, the cards so carefully stacked, the coins rolled faster... all a simple trick beautifully performed. There are those among us who claim no magic at all but within the twists of a curl kissed by sun, a heart beats faster for the shy smiles, and warms a pale rosebud.
And what exists for that bubble instant, that fragile sphere suspended by magic and yearning alone is magic. What more dare we dream of, that suspension of simple soap and water sustains our very breath, captured and floating. Yet we dream on, watching the wishes spin upward into yet another spiral. Is it our yearnings for more, more answers,more revelations that make us wander the paths of long ago. Is it not a simple thing to want to fill a bodice, a costume, a prop. Or has it moved deeper into who we might have once been, released by the past to return again and walk a new level of the spiral. Alchemy now in sterile laboratories, medicine no longer the realm of a wise woman,and astronomy reaching into ever further places beyond the dreams of even Tycho Brahe's supernova.

 

[fire_breeze]

I shall do my best...

97, 98, 99

83621143489848422977
135301852344706746049
218922995834555169026


And I have come to realise that we are all students, in one way or another.

 

[Voyager2MnM]

Waxing Philosophical

100, 101, 102

354224848179261915075
573147844013817084101
927372692193078999176

If we loose the desire to learn and explore, like the student, we lose the chance of self discovery and understanding. The inquisitive nature provides the opportunity to explore those spirals of life and find the clues to ourselves at the centers. Rather than just having life happen... we actively seek a richer more fullfilling life. It is always a precious thing to find someone willing to explore the world around them as well as themselves.

 

[Earthgoddess]

103, 104, 105

1500520536206896083277
2427893228399975082453
3928413764606871165730

Waxing and waning like the moon, we control our wants and fulfill our dreams. Thus we are absolutely the captains of our destiny whether we opt for that or not, the ship sails on despite our struggle to grasp the rudder. Wiser than I have pondered escapes from the mundane, plotted overthrowing what suffocates and finally chosen to remain snuggled against the mediocre safety of the known.
I find myself looking to the skies for navigation clues, seeking outside of self, outside of that warm den. Now and again the den of iniquity seems to call me, louder each cry.

 

[Voyager2MnM]

deserted... or distracted!

It has been pointed out that my absence could be construed as desertion! I take umbrage at this suggestion And hasten to point out that real life often intervenes requiring one to take a short hiatus, or even withdraw from a desired activity long before the much anticipated successful completion of that activity. While this could lead to frustration and/or mis-understanding in some, it may actually be perceived as a long protracted foreplay, building the anticipation to a new levels for the patient sort. So that when there is a return to the favored activity, there is a very heightened sense of enjoyment and relief in it

106, 107, 108
6356306993006846248183
10284720757613717413913
16641027750620563662096

Much has been said about the curves and ratio seen with this series. I have a mathmatical curiosity...

Take any four adjacent members of the series. Multiply the largest of the four by the smallest of the four. Then take the second largest and multiply by the second smallest. The two products are always 1 larger or 1 smaller than the other. As an example...

series members:
F(10) = 55
F(11) = 89
F(12) = 144
F(13) = 233

F(10) x F(13) = 55 x 233 = 12815
F(11) x F(12) = 89 x 144 = 12816

or

F(18) = 2584
F(19) = 4181
F(20) = 6765
F(21) = 10946

F(18) x F(21) = 2584 x 10946 = 28284464
F(19) x F(20) = 4181 x 6765 = 28284465

 

[Earthgoddess]

110,111,112

43566776258854844738105
70492524767089125814114
114059301025943970552219

Desertion was a strong word, I apologize profusely. I should have said neglected, oh alright, maybe neglect is too strong as well. Sometimes perhaps I am a tad high maintenance, more like a bon-bon than a regular confection, not soft, sweet and compliant. I am fully aware that withdrawing from an activity often makes the outcome, the eventual outcome,much more appreciated.
Happiness should be like that, even if you defer the pleasures for a time, say maybe placing them on hold. Perhaps we miss opportunities to be truly happy because all that lies in our pathway is the struggle and we miss the outcome's potential. Too often we do not see the forest for the trees, missing happiness and fulfillment that had we exercised patience and not always sought the pitfalls we might have enjoyed. So easy to become engrossed in the possibilities, the myriad of potentials, and miss the simplicity of the present moment. The enjoyment and pleasures at our fingertips, it is like missing the dewy softness of a baby's cheek as we worry about paying for college.

Simple things, simple solutions, living only in today, not casting our nets further ahead than we can see. Enjoying the journey as much as the anticipated arrival.