Theoretical Fibonacci Vortex Christmas Tree

Crocheted in dark green cotton.
Begin with 1, then 2, then 3, then 5, then 6, then 7, then 8.........just increase 1 at the end of each row, then work in a spiral.
Mark the end of each row with a different colour yarn.
So the 21st row has 21 stitches (shown by adding yellow);  the 34th row has 34 stitches (yellow), the 55th row has 55 stitches (yellow), The 72nd row has 72 stitches (light green colour).

You could go on forever and make a really big vortex.

It is a tradition of mine to do some kind of Christmas tree maths  on this blog  every year since 2012...  in 2014, 2015.
In 2013 there were photos of ---angels.  Recently I counted how many angels I now have in my caravan.  It is 14-   in sculptures, models, paintings, cards and tapestries!

In August and November 2013 there was good work on Pythagoras Fibonacci triangles and the square root of Fibonacci numbers, in cascades, resulting in a brand new value for another kind of "Phi" derived from the relationship definition equation having the square root of 5....!  = 1.793 604........


Usually the join goes vertically up, though sometimes it spirals around and up-  I don't know why, or which one is right. I only know it is tricky to keep the work exactly right at the very ends of a row.

I bought this lovely Christmas card
and present it here, on this Christmas Dayl

Happy wishes to all,  now and forevermore.

My aunt in Austria found this card in a shop in Linz, 20 years ago.  She recognised it as a sculpture made by her sister, my mother.  "Trudi's Engel 1942".

Truly a spirit of Christmas.

I have earlier published my mother's sculptures on this blog at "Tribute to Trudy"  19/4/2012
Also "A Better Photo" 6/6/2012.

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Christmas Baubles

My plan is to write up all the info for these asap.
this one is crocheted in 8 ply two colour wool.
Begin with 6 stitches....to 12, 18, 24, 30, 34.

The mauve cotton sphere is to 34, in 5 ply cotton.
The top blue one is to 34 in 4 ply equiv cotton yarn.
The white one is to 48, in 5 ply wool.
Size 2 crochet hook.


****Back in -July 2014- I published posts on making Spheres-  mathematical models and all.  I still need to write up better Instructions for How to make them.....

Please click on image to enlarge it.
right click to save or print.

This is how to make the 36 diameter sphere.
Make 6 chains into a loop. Single crochet 6 loops, then continue spiral with1 row 12, then 1 row 18, then 2 rows 24, then 2 rows of 30, then 4  rows of 36 around middle.
Then decrease stitches symmetrically until 6 are left  BUT  fill padding into shape at 18 stitches.
You can keep front of crochet work inside (as in the 8 ply blue and green ball),  or keep front side of work outside the ball.  Nice either way.

Here are instructions mind map for making 48 diameter ball.  12 rows each hemisphere.

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This one is made to 72 stitches, knitted, with pattern in green, using 4 double pointed No 13 knitting needles.  Quite intricate .    4 ply equivalent cotton yarn.

Please click on image to enlarge it.  For 60 and 72 around middle of ball.

Design is to make 6 repeats around the middle of the ball.
Empty squares are for you to make your own design.

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The above image is from
 http://theknitbitch.blogspot.com.au/2011/09/knitting-christmas-baubles.html
We can find a lot of exquisite crochet models of all kinds, including amigurumi, on the above blog.

The red and white balls are made by Arne and Carlos,  of http://www.kerstballenbreien.nl -   Norwegian patterns.
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Theoretical Fibonacci Ripples IAW the Protocols.

Insert 22/12 2016  here is the 377 model!



















Here is 2015 post....
The completed model has just been made, to 233.
The crochet rows segue perfectly with the recently published Eternal Protocols, all along the Fibonacci Series.  I have calculated up to 610 and it seems that the method continues further.  It would take too many hours of sitting crocheting to do more than the 233.
Work here is done with 3 ply baby wool and number 2 crochet hook.

More:-
27/12/2015
Please click on images to see more clearly.  You can scroll along images one after the other.
 Right click to save or print.
The numbers segue along beautifully.  That is how I made the model of the "ripples".
It is a bit tricky at the end of each row.  I do mark the spot with a different colour yarn.

Calculations for Concentric Circles (Ripples)

Iaw the Fibonacci Series.  Circumf = 2 x Pi x  r = 6.283 x r
Fn                    radius              r1 – r2             rows              
10946              1742.2 =r1       665.5               666                  
6765                1076.7=r2        411.3               411                  
4181                665.4               254.2               254                  
2584                411.3               157.1               157                  
1597                254.2               97.1                 97                    
987                  157.1               60                    60                    
610                  97.1                 37.1                 37                    
377                  60                    22.9                 23                    
233                  37.1                 14.2                 14                    
144                  22.9                 8.7                   9                      
5 5                    8.8                   3.4                   3                      
34                    5.4                   2.1                   2                     
21                    3.3                   1.2                   1                     
13                    2.1                   0.8                   1                      
8                      1.3                   0.5                                          
5                      0.8                                                                                                                                                                  

                                                                                        

Yellow marks the end of the row.  Note the first loop of next row is white, due to the nature of crochet the loop carries over to the next stitch.  One needs to be assiduous in counting.  Even a mistake of one stitch can put the work out.  It is gratifying when one comes to the end of each row with the correct number of stitches!

Here is diagram with each of the 6 segments being about 50 degrees from centre.  The half (7th) segment varies and seems to form a curve.  Does this have the effect of pulling the rest of the circumference into a spiral direction?  I wonder about the dynamics of real ripples and vortexes.

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 ok     - more work for anyone inclined to be interested......
I am keeping the images on this page small because you really do have to click on them to enlarge them and so see better.

Calculations for Concentric Circles (Ripples)

Iaw the Fibonacci Series.  Circumf = 2 x Pi x  r = 6.283 x r

Fn                    radius              r1– r2              rows             

10946              1742.2 =r1       665.5               666                 

6765                1076.7=r2        411.3               411                  

4181                665.4               254.2               254                  

2584                411.3               157.1               157                  

1597                254.2               97.1                 97                    

987                  157.1               60                    60                   

610                  97.1                 37.1                 37                    

377                  60                    22.9                 23                    

233                  37.1                 14.2                 14                    

144                  22.9                 8.7                   9                      

89                    14.2                 5.4                   5                      

55                    8.8                   3.4                   3                      

34                    5.4                   2.1                   2                      

21                    3.3                   1.2                   1                      

13                    2.1                   0.8                   1                      

8                      1.3                   0.5                                          

                                                                                                                                                                                       

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I hope someone likes this work!  There are almost never any comments.......It can't all be referrer spam in those pageview numbers!

 Happy 2016.  It may be a difficult year.....See UK Councillor Simon Parkes' YouTube videos.
It is up to every single human to imagine our world into its true Being.  Don't let aliens dictate to us. We have sovereignty tho we have some handicaps due to problems from past traumas.  Aliens deserve respect just like we deserve respect.  They might do to us the same things "in our best interests" as if we are dumdums, just the same as "western" invaders have done to indigenous peoples....
 Let's help each other. Conversation.  Find out the Truth.
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Eternal Protocol for Building Numbers. Summary!

Please click on images to see them more clearly.

Of what Use is this?
Well, one can crochet a whole cascade of Ripples,
and one might  knit or crochet seashells in a new and different way.
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PS  28/12/2015
These are not hard and fast rules.  The action of rounding off decimalled numbers to full numbers does create discrepancies.  In the interests of crochet of knit we have to use whole numbers.
We can see this in the next post where the Fibonacci Ripples are made.  For three rows we use 5 to 8 rather than 4 to 7,  and for 9 rows we use 13 to 22 rather than 14 to 23.
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Eternal Protocol, Part 5. Prime Numbers.

Please click on images to see them more clearly

Notice the reiterating Fibonacci numbers.....
Series within series.
Divide a Fibonacci number by 29 and you get 13 exactly for 377,  and almost exactly for the others.





















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Next = Not Fibonacci Numbers.

Any old numbers !

Please click on images, to enlarge.











Notice that prime numbers follow certain diagonals.
Within these are composite primes eg  3 x 7.  or powers of prime numbers.  
Squares of prime numbers lower rhs.
Squares of even numbers,  2, 4, 16, etc top lhs  inner diagonal
See Wikipedia for info on Ulam Spirals.  I found this in Nexus magazine.
More info to follow, as soon as I find it....

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Eternal Protocol, Part 4. The 3, 6, 9, etc

Please click on images to see them more clearly.

Please click to enlarge.  This came from Nassim Haramein Facebook page.

This is a 3 number.  Some might call it a "composite prime"  ie 7 x 3....next post.




















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The "6" series  links in with degrees in a circle, 360,  so is useful.
Note these are not Fibonacci numbers.  It is a part of the "3" Story.

*** I used this array when I crocheted the red Hyperbolic Crochet Apple  (Torus)....26 Sept 2014.
only to 72 circumference.















More interesting info to follow eg     http://www.trinfinity8.com    
and quote from Nicola Tesla...

30/1/2016  I have permission from Dr Kathy J Forti to quote:-

 ******* Excerpts from “Fractals of God” by Kathy J. Forti E book location 1272 etc Nikola Tesla said “If you only knew the magnificence of the numbers 3, 6 and 9, you would have the keys to the universe. He believed that somehow these numbers served as portals to other dimensions and expanded consciousnesses.

My quest led me to the…..Fibonacci Sequence…0,1,1,2,3,5,8,13,21,34, 55….. But I discovered if we start with 0+3, 3, 6, 9, 15, 24, 39, 63, 102, 165, 267, 432……., each of these numbers……(runsum)…comes to 3, 6, 9. Eg 165 to 12 to 3 Solfeggio tones intended to be music to the Soul or “inner ear”……396Hz, 417Hz, 528Hz, 639Hz, 741Hz, 852Hz, “I learned that when these tones are coupled with the Algorithmic Codes I was given…(by the Founders, 8th dimension Beings of 12 strand even 24 strand DNA)….and played with fractals…a powerful force for transformation…..stimulate healing potential…..it led to quartz crystals….lattice power…piezoelectric charge…..the Hadron super Collider also uses crystals – 60,000 rod like crystals……the King’s Chamber in Giza Pyramid is lined with hundreds of tons of silicon quartz crystals embedded in granite…chamber resonates at 438Hz = the note A……The human body ….is one big transmitting and receiving station……………..stream the Algorithms right into a crystal…..the crystals hold on to the information….nanoseconds only…..self cleaning…….this led to the Trinfinity8 device….based on Atlantean technology this is a spiritual device…..lifting vibrations to a higher level…..debut 2009….a 15 minute session, even a 12 minute protocol, works wonders with people, things, places, countries……will help to change the landscape of energy medicine…..the Rod of Ra into the 21st century…….crystals and multi- layered algorithms. …..Tokujin Yoshioka…grew a large slab of crystals over a 6 month period…..to music of Tchaikovsky’s “Swan Lake”…..echoes the work of Dr Masaru Emoto with water ice crystals…….Our Planet’s immune system….even Planetary and Group Healing, eg Syria…..alchemy, even magical….The Sacred 3. The 3 symbols in her dream = the Ankh, the Was Sceptre, the Djed Pillar……..also…”don’t rule out “computer intelligence”…I ask my computer to show or tell me what it needs… we are both growing and evolving……” See www.Trifinity8.com Australian distributor of devices is Rasunath Alston. 

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