Monday, December 17, 2012

Real Sunflowers.

We all know that the sunflower spirals are skewed one way eg 13 and the other way eg 21,  or whatever Fibonacci number is displayed.  Next I will  study the Fibonacci angles. eg 137.5 degrees. 


This is a real Artwork.  It shows real Joy. 
 It shows how accurate is the eye of the artist, Abby Heathcote.


Wednesday, December 12, 2012

Geometry of a Theoretical Sunflower

Everyone knows that there are spirals with Fibonacci series relationships in the Sunflower.

I wish to explore the basic geometry and try to work out how it really might be so.

Here is a circle divided into 6, simply, with a compass.  Then each section is divided into 3 then 3 again.  This makes 54  which is close to 55, a Fibonacci number.  I was delighted to find that there are 54 in each circular row from inside to outside.  The base of the flower is like a huge placenta holding all those ovaries which will be fertilised to become mature seeds.

I've drawn simply diagrams for a range of numbers with bias to those close to Fibonacci numbers:-


It was interesting to find online as I searched New Scientist a video
"3D Vortex Illusion in a 100 Year Old American Quilt"
Instead of compass curves dividing concentric circles as in my diagram 1, there were straight lines radiating out from centre, and alternate "squares" were red and white.
See Friday Illusion, in  of 7 Dec 2012.

Powers of Further Phi.

I have calculated quite a few numbers.  One can see Correlations.  If one were to calculate the whole bang lot then we could create a grid pattern and see multiple correlations;  almost exact.

I tried to add these tables to the previous post, but errors occurred, so this is posted separately.

I also made an error in posting Powers of Pi too early;  it would have been more orderly to connect the Ouroboros post with the Zero post.  Too hurried.  Better late than never,  they say.

Powers of Phi

Curiosity impels me to study the Powers of Phi.

I am trying to discover for myself any more Equations and Correlations.
And here is one.  It is already known,
for I  saw it on Wikipedia after I had figured it out for myself.
Dr Ron Knott's Fibonacci website is famous.
You can find there "what's new" to do with powers of Phi.
He also distinguishes between Phi and phi ( 1.61803 and 0.61803, respectively.)

Here might be something new.
Imagine there are more Golden Means, not only Fn / Fn-1
There is Fn / Fn-2,  Fn /Fn-3, ........Fn / Fn-20,    etc.
I like to call them Phi One,  Phi two,  Phi three,  .... Phi Twenty.......etc.

Compare both Tables.  There are Correlations.
The numbers might be different if taken to 4 decimal places only.
.  I have published back in  "Fibonacci Equations", post Nov 21, 2010  part 8.
The ratio results use many Fibonacci numbers, 
showing how amazingly exact and consistent the values are, especially for larger numbers!

.eg  For Fn / Fn-10         F26 / F16 = 75025 / 610 = 122.9918
F36 / F26 = 9227465 / 75022 = 122.99186

I have to check my  numbers because there were errors in my early calculations for The Fibonacci Series.  We can check with Dr Knott's website-  he has published the first 500 numbers in the series.

Mending Mistake #1.

I mentioned a huge mistake in a graph I drew in  2010:-

10 to the power of  minus any number is not equal to minus 10 to a power,
 as I plotted the negative Y axis wrongly!

All Powers of 10 with a minus should be located between zero and one.

The negative Y axis should be -10,  -10 squared, etc

The second graph here is an amended one;  just imaginary
and most maybe somewhere wrong too!
Zero is the singularity,  the black hole....

****Dr Ron Knott has a famous Fibonacci site and he does use minus fibonacci numbers.

This table of Fibonacci numbers is simplified for easy plotting on a graph.
Observe the elegant regularity of the iterations  with regard to Powers of 10.

What is going on between 0 and 1? 
I tried to figure it out,
imagining mini-fibonacci series ie 0, 0.1, 0.2, 0.3, 0.5 etc.
Then mini mini f. series ie 0, 0.001, 0.002, 0.003, 0.005 etc.
Then continuing up to millionth.

I did draw graphs but it would take many sheets of paper up.
This is just simple playing.

For between 0.000001 and 1.0 the  " ultra fibonacci series"   might be
.000001,  .000002, .000003, .000013 near .00001 on vertical axis.
then .000144 near .0001 on axis, then .001597 near .001 on axis,
then .010946 near .01 on axis, then .121393 near .1 on axis
and .83204030 near 1.0 on axis1   If it were true it would be a miracle!
Just guessing.  The last mini fib no  relates to F30 which is 83204030.
Or F31 / 1000000  is next -  ie  1.3462931.
All squashed into the space near zero, the singularity.
And it goes on forever!

 Ten to the power  minus 33 cm.   
The Planck length;  you can see it on the Cosmic Ouroboros Diagram.
Said to have been chosen as our bearable limit to space in our known universe.
(Named after Max Planck who also has an Institute outside Munich named after him.)

It could go to 10 to the power minus infinity.  I am guessing forever.
Enormous Power between us and Vacuum.
Nassim Haramein has given much thought to all of this.  Worth a hearing on YouTube.

I once found the Vedic OM on a site
This has great creative drawing etc, sanskrit,  but no longer vedic om.
So, looking further,  one finds much on Internet on this subject. has t shirts etc for sale with the symbol on it.
Especially interesting is one with layers of AUM/OM,  as if floating in space.

The symbol reminds me of 0, 1, 1, 2, 3-  did the Ancients Know something?
Something going on around zero.....
I search google for "Vedic";  it is just fascinating;  an enormous realm to study..

What does Aum sound like?
See Jill Purce's YouTube video, "Just One More Breath".
Overtone chanting in a tower in Middleburg, Holland, in 1984.
Find more on
It is" based on harmonic series-  makes our own biology/geometry audible,
allowing us to hear in a sonorous way our own structure.
We are hearing what we are."
Jill is married to biologist Dr Rupert Sheldrake and there is more on YouTube
of great interest-  Look for Bruce Lipton also.
eg try "A Morphic Resonance of Love." Oct 25, 2009,  London.
A fine rendition of Hava Nagila is a real treat, with young
Merlin Sheldrake on accordion, with musicians in a group of four.
There are a great many people alive today and they are already helping save the world.

Powers of Pi

There is an unusual book, "Co-Evolution" by Alec Newald;  one can buy it from Nexus Magazine.  Alec's story is of "aliens" or "Other Visitors" taking him to the planet Haven where he met many friendly Beings and he learnt their ways.  I was interested that they used 12, and Pi squared.  They built houses that looked like snails!  There were buildings like pyramids.  Even the space craft were shaped like pyramids, spinning as they travel time and dimensions.

To me the lesson could be that these folk might be our future ancestors.  Their sun is dying and they are looking for another planet to call home.  In fact our Moon was their Home until a terrible dimensional mistake by their too clever scientists made it  a dead place.  Old beyond time!  A few of them managed to escape and go to Planet Earth in early Ages not quite habitable then, and not many survived.  Accomplished survival somehow.  To time travel backwards to try  to mend mistakes and change history is deemed to be useless because it might happen that they would have no familiar future to return to.  They are unable to reproduce like humans do,  their mouths are tiny holes to suck up nutrient (no smiles),  their heads are huge and eyes are huge,  etc.  You know the image.

The question to me is-- do we want to look like them in our future incarnations?

My feeling is That is what might happen if we continue to love technology without caring how it affects our health and humanity.  Of course I could be greatly mistaken-  or it could be true.....
The German techno wizards are making robots so real almost human even capable of deceit (Ref is a ABC Radio National "Future Tense" program.  What if these humanoid robots were to be the only ones to survive in future?  It makes their creation now to be a problem morally and ethically.  Humans and robots both deserve love.  It is a question of values beyond money and convenience.

The time is NOW and it is a singularity between past and future.
What we do now or what we decide not to do now will affect the possible future and it can mend the past.   What we do now could fix the sun on Haven, with Love, and bring back Life to our future Selves!
An Enlightened Person can achieve much through Love,  the strongest Power in the Universe.  If one person can do it, then potentially every one of us could be able to do so too. 
One might stress out thinking it impossible.
However there are a myriad possibilities and realities.  We choose what we are able to do,  and there is said to be a lot of help out there if we need it.  A Quantum Leap in Consciousness on the part of humanity and miracles might happen!   There might be a happy aspect to the End of the Mayan Calendar!  December 21,  only  2 weeks away,  and counting......

What kind of world could you imagine in which you could be happy and creative-  forever?

Anyway,  here are the Powers of Pi:-

Our Place in the Universe

In a recent post I mentioned The Cosmic Ouroboros.  
The Maya knew it as a symbol for the imminent closing of an age.
We are said to be facing the end of a 26,000 year cycle!
I feel it is an important image for us to see our place = in
the very centre of this Universe:-

I was worried about copyright laws, so I searched Google.
An Australian artist has also painted the Ouroboros.
and post of Thursday November 1, 2012
She writes that a similar diagram(as used by Nancy Abrams and
and printed in a recent Resurgence Magazine)
is in "Just Six Numbers" by Astronomer Royal Lord Martin Rees.
Thus I feel it is ok for me to draw my own version.

Ant and Human live in the yellow mid section of 1 cm.
I forgot to draw in the mountains and the Earth in relative size position
to the righ of humanst.  So this is how we fit in!

Most amazing is the microcosm,  with smaller and smaller particles.
I believe that the world of spirit lives in the minutest size realm.
The Ancients knew it!  In Shinto the prayer says
"Gokubi jissoo gengen shikai...."  which means
 "in the realm of infinitesimal particles"...
which are gen gen.....
I learned the Amatsu Norigoto Prayer while I was 20 years a member
of Sukyo Mahikari.  The Holy Founder received revelations  and I treasure
these Teachings which even touch on quantum science, eg neutrons , and high energy particles.
Anyway the revelations showed that many ideas had become wrong, back to front, over the ages.
eg it should be Taka Ama Hara ,  ie ama not maga.  The latter denotes evil gods...

Most fortuitously, last night I found some YouTube videos which are entirely apt!
One is from Nexus Conference, 2010.
Presented by Nassim Haramein, a self taught man,
with "The Schwarzschild Proton"  - all 1 hour and 30 minutes was fascinating.
Nassim even explained the Planck length!  Most unexpected were many of his insights.
Every proton is a mini black hole.  Two protons spin around each other at
the speed of light, according to his maths.  Much more, as you can imagine.
Space.  The Vacuum.  The Universe.  The Multiverse.  And the MicroCosm.
We are MADE of Light.  We can find out much more on
Nassim has a Youtube video,  Nibiru has come and gone.  We are floating in Grace.  Good.

I found this and related videos via   This is a most unusual and confronting website.
 It pays to persevere with it and look up Fibonacci and spirals and vortexes, Phi,  Fractals,  Mandelbrot;
  Jain or Vedic sacred geometry and mathematics.  Yes there are videos on Vedic Maths.

Responding Literally **

Mindful of the end of the Mayan Calendar December 21,  I decided to take literally Mother Nature's challenge quoted in the last post-  "to learn to follow the designs of her nature."

So I planted brown rice seeds in a pattern according to Fibonacci, as follows:-

**Please click on images, to enlarge them


Insert 3/4/2015   Nothing grew from the rice seeds!  Only couch grass and oats.  At least I found out some design in the numbers.

We are awaiting rain,  and there is hardly any, for the last two months only 8mm has fallen!
I only have rainwater in a tank from my shed 4 m x 4 m roof.  The tank is full but might be needed.
Here is photo of area planted, with containers weighted with dirt to mark the spot.

To the left is a clump of rye 5 ft tall from last  year's seeds.

This Pattern has shown me a larger bilateral symmetrical Pattern with Fibonacci numbers.
Every third number is even and the two numbers in between are both odd.
This means there is a central rib,  all the way up,  like so:-

fairy grass  22/10/2012  6 AM

a delight to see in my garden

Radiance indicates left edge of a fogbow
or white rainbow.  22/9/2012  6:27 AM

One can see such a sight once or twice a year;
sometimes the bow is more evident than this.

Pink Peach tree in blossom
to cheer us up.
16/9/2012  9 AM