A Green Kelp Shell. Knitted.

Green seashell, 

For these you must use steel  knitting needles, size 12 or 14, to allow 366 stitches.
Plastic knit needles will snap.  use thinner yarn ie not more than 4 ply;  best is 2 or 3 ply cotton or wool.

Cast on 235 + 10 for lip.  You can omit these 10 stitches for lip if you wish to make it simpler.

Row 1.                  Cast off 5 stitches.  Knit 75, leave other stitches on needle, turn.

Row 2.                  Slip 1, purl 75, purl 2 together.

Row 3.                  Cast off 2, knit 95…..

Row 4.                  Slip 1, purl 92, knit 2 together.

Row 5.                  Cast off 1, knit all along needle, increase on every 4^th stitch.  Snip yarn leaving end to secure later.       235 stitches become 293.

The beginning of the work makes a lip at the mouth of shell shape.

Row 6.                  Slip 120 stitches onto needle,   introduce yarn again, purl 172, knit 1.

At the end of every purl row now I make an indent of 3 stitches to make a flare at the mouth of shell.  Ie the next knit row, knit 3, turn.   Slip 1, purl 1, knit 1. Then begin the knit row…..some people might just like to purl 3 on one row and knit 3 on other row to make indent.

Row 7.                  Knit 173 + 30 ie 203, turn,  leave the 90  on needle.

Row 8.                  Slip 1, purl 201, knit 1.

Row 9.                  Knit 203 + 40 ie 243, turn.  (Leave 50 on needle.)

Row 10.                Slip 1, purl 241, knit 1.    

Row 11.                Use new colour eg dk green,  Knit 3 increase in every 4^th stitch.
Makes 293 to 366 stitches.

This all makes upper part of seashell.

Do 3 more rows of 366 stitches.
Every knit row make 4 stitches into 5.   Knit 3, knit 2 together. Until 1 stitch remains.

Pearl the alternate rows.

Please see diagram of maths numbers.   Click on images of diagrams or tables to see more clearly.

***  to keep a copy of pattern,  highlight text, press control and c together to copy.  Bring up new Word page, press control and v for paste.  Or,   for diagrams, click image,  right click and download image to computer, save and print out later.

(To crochet this model, work backwards.  I begin with 1 stitch and make the hyperbolic fan and then the shoulder.  I use size 2 crochet hook.  Thick wool might be too hard to configure.

There will be more shell models with crocheted pattern in these posts.)

Please click on diagram to see it better.

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Another variation for shoulder of seashell model.

Omitting lip 10 stitches.

Cast on 235

Row 1.                  Knit 75, slip 20 stitches onto right hand knitting needle,  leave others on first needle.

Row 2.                  Pull yarn across back of work, and purl the 95 stitches.

Row 3.                  Knit 95 + 20 ie 115, slip 20 stitches on to needle, turn.

Row 4.                  Pull yarn across work and purl the 135 stitches.  There are 100 stitches from before.

Row5.                   On these 235 stitches, increase once every 4^th stitch, making 293 in all at row’s end.  Snip yarn leaving end to secure later.

Row 6.                  Slip 70 stitches onto right hand needle.  Introduce yarn again and purl 223 stitches.

Row 7.                  Knit 203 stitches, turn.   20 stitches remain on first needle,plus the 70.

Row 8.                  Slip 30 on to right hand needle  (makes 120), take yarn across work,  purl 173.

Row 9.                  Knit 133,   40 + 120 stitches remain on first needle.  Turn.

Row 10.                Slip 30 stitches onto right hand needle  (to 190),  take yarn across work, purl 103.

Row 11.        Knit  the entire row, increasing once every 4^th stitch.
Total stitches are 366.                        

Row 12.                Use new colour eg dk green,  or you could make row 11 in dark green.
Pearl 366.    This all makes upper part of seashell.

Do 2 more rows of 366 stitches.   Or you could do a few more….be flexible and try different ways.

Then make hyperbolic fan shape.  Every knit row make 4 stitches into 5.  Until 1 stitch remains.

Pearl the alternate rows.

Please see diagram of maths numbers.   Click on images of diagrams or tables to see more clearly.

***  to keep a copy of pattern,  highlight text, press control and c together to copy.  Bring up new Word page, press control and v for paste.  Or,   for diagrams, click image,  right click and download image to computer, save and print out later.

To crochet this model, work backwards.  Ie.  begin with 1 stitch and make the hyperbolic fan and then the shoulder.  I use size 2 crochet hook.  Thick wool might be too hard to configure.

I hope to make  more shell models with crocheted pattern in these posts.  Please note, some corrections to text patterns have been made 23/9/2017.  Please advise me of any problems making these models.  Thank you. 

I have made some  mention and images for this in a previous post, before all the videos were put on.  The green model began as quite an unpromising shape!  I even had to undo all the knitting up to 366 stitches to make the work longer by doing decrease rows  every second row.  I could do later try to do decreases every third row to make the column taller.  I am just guessing how to do all this;  many mistakes along the way.  I hope these Patterns are ok for you folk.  Glad to get any help ideas or criticisms!

Sewing up:
It takes quite a bit of wangling to get the central column in line.
Stitch along suture line.  Sew 235 stitches row  onto first part of 366 row  (row 11).  Begin at tip. 
Seashell spiral is clockwise when looking from the top.
 I use a kind of back stitch, turning the edge in a half turn to try to make a "shoulder". The edge is given a half turn under (a bit like a kind of moebius strip?) - see photos
 I padded with an old cotton sock, cut into strips to fit narrow tip, and one full sock padded the opening.

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More 21/9/2017

Notice that padding is a worn out old green sock.  Cut it as strips for narrower part of spiral.  Final padding is one entire sock in wide opening area.  Use whatever is handy to you.  Back stitch,  make a shoulder.
Please note, some corrections have been made 23/9/2017.

**I am sorry--- the text pattern has simpler pattern -75, 75,  95, 95.
 I incorrectly put directions for a lip.

The actual model made has the lip of 10 stitches, but I didn't put it into text of pattern.
  Model pattern is  75, 95, 115, 135....at start.
The diagrams are correct.
Very sorry.  a bit stressful trying to write this up and get it right!
----------------------------------------

How to make a small Kelp Shell.

Small Kelp Shell.                PATTERN.       This post continues on from 20/7/2017 post.

Cast on 131 stitches.

Row 1.                  Cast off 5, knit 50, turn, leaving the remainder of stitches on needle.

Row 2.                  Slip 1, purl 50, knit 1.

Row 3.                  Cast off 2, knit 80, turn.

Row 4.                  Slip 1, purl 79, k 2 tog.

Row 5.                  Cast off 1, knit  100, turn.  The above makes a small lip edge of 10 stitches at top of work.

Row 6.                  Slip 1, purl 99, knit 1.

***The beginning of every knit row is the mouth of the mollusc shell.          To make a flared edge, indent 3 stitches.  Ie. At end of purl row. turn, knit 3, turn, slip 1, purl 1, knit 1, turn.  Begin the knit row.

Row 7.                  Work entire row of 121 stitches.    Knit 3, knit twice into 4^th stitch,  then  entire row, increase every 4^th stitch;                Thus 121 to 151 stitches.  
You can knit this row in another colour, to mark the 151 row.
You can mark this row with another colour eg black as in photo of green one, threaded between stitches, if you are making a one colour model.

Row 8.                  Knit 1, purl 149, knit 1.
I always knit each end of purl rows to stop work curling too much.  You may prefer to just do purl.       Row 9.                  Knit 151.  

Row 10.                Knit 1, purl 149, knit 1.

Continue, decreasing every knit row, knit 3, knit 2 together. until 1 stitch only remains.

**This makes the hyperbolic fan shape which is typical of this spiral shaped model.

Remember to indent at mouth edge.

Photos describe how to sew up.  Pad with teased out cotton wool as you go.

**in the white model  I knitted 121 stitches in row 7.  Then I changed to green wool to knit increase row in row 8,  thinking it might be easier to sew up if I did this.  Then rows 9 and 10 etc were as above, in white.  The variegated green shell had the same number of stitches, but the yarn was thinner, maybe 2 ply.  I think the white cotton was 3 ply.

I used  gauge 2 (ie 2 mm) knitting needles;  these are size 12 in English. Or size 14 if you wish.

2 or 3 ply cotton for knitting.  There are problems with configuration if you use too bulky a yarn for these small models.  It might be hard to find such yarn these days….

some more later....

18/9/2017
sewing up......edge to row 7....more info asap........gathering diagrams etc.  sorry to take so long!

--
More 21/9/2017
note, corrections have been made to above Pattern.

Please click on image to see it better.  Right click to save on downloads or favorites.. or new word doc page...then print.
Patterns - highlight text,
press control and c,  to copy;
then bring up a new blank word doc page,
press control and v, to paste.
Save and print.

Notice the black line, marking row 8 to which the suture edge is stitched.

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The next  new post is for green seashell model of 366 stitches at max.

A Discussion Eclectic.

Why have I posted and shared all the previous videos?  Well, it is because there is some connection.

1.  The 4D bottle does look like a seashell, especially with the pearly colouring.   I suspect something funny happens at the tip of the seashell, and along the suture, where it grows.  Some direction and dare I say it, life force, must come,  from astral and spiritual dimensions,  ie 4D, 5D, etc.   They say that our endocrine glands are in same place as the main chakras.  Even seashells have glands in the mantle, doleing out colour pigments etc, exactly and mathematically.
That is why I posted a previous video of the hilarious and wonderful motor protein carrying its load of endorphin  along a microtubule in a cell.   There are many such videos describing what happens biochemically, in colour animation.  I studied biochem in the late 1960s  and much has happened since then!
I also used to talk to an airforce man who was the working in cybernetics in the 1960s.  This topic is gangbusters now!

2.  They have 3D printers,  and are working even on 4D printers.   The Large Hadron Collider is said to be some kind of spiritual (alien, even) technology.   Using ultra small particles, they say (ie Simon Parkes says) they are trying to force a hole into the 4th dimension, the astral.  But Gaia did not permit.  An explosion.   However "they" do not give up.  Japan and China are planning to build similar and bigger,  and who else?........Cindy Kay Currier of "Rise Together"  has a video which  says that the Earth was destroyed in 1996 by the LHC;  we are presently living in a Simulation,  one of an infinite number according to a former NASA artist.  There is a natural Earth,  which is still intact.  What do you think of flat earth stories?  Some very compelling ideas.  Trees made  of silica not carbon, hence all the sand on earth due to their deforestation by "Nephilim"  in ancient times...see Russian named baldmonstrosity, he has videos and much original thinking!!!

3.  I was aztonished to find video on drawing the higher dimensions - video 3.

4.  The video on Simulation is dinkidi science, even mentioning the golden rule 0.61803.... which has something to do with black holes...

5.   The Mesopotamians used base 60 in their calculations.  There was a news clip August 24 2017 about these two mathematician gentlemen from the University of NSW, who cracked the code.  I wonder if there is any connection with the post I made in 2013 "Playing with Pythagoras",  where I followed right angled triangles (triads)  whose sides were square roots of adjacent Fibonacci numbers, leading to my finding a new value for "Phi" = 1.79.......I shall have to study the shape of a Ziggurat to see what I can figure out.....

6.  There are most engaging videos on YouTube, of 2 gentlemen, eg  one is "are you a reincarnated nature spirit?"  All this looking at astral and other dimensions (which are intimately and infinitely connected co-incident with our solid material 3D) makes me think of the elementals.....I haven't shared it.....too much at once....

How can we Knit a Tall Pointy Seashell?

Insert 18/8/2017

New Photo .   Sewn up;  Pattern needs correction then will be published.

--------------------------

Work is in progress.

Next Photo .   Top LHS piece has 366 stitches at max, with 235 stitches at suture edge.

Smaller one has 151 max, with 121 at suture line.

Same for image 2

Still not good enough to create a proper knitting pattern...........

I am using the rule to increase or decrease every 4th stitch to make it easier.

Series 4 to 5 is- ..., 8, 10, 12, 15, 18, 22, 27, 33, 41, 51, 63, 78, 97, 121, 151, 188, 235, 293, 366, etc.

(not quite Fibonacci Series......0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, etc.)

******23/9/2017.  Patterns are now posted.  After the next videos.
Please scroll up,  top right hand side of blog  page.
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Fibonacci Poetry

Yes!  Poetry in accordance with the Fibonacci Sequence!

Wordsworth did it:-
I wander'd
lonely as a cloud
that floats on high o'er hill and vale
and all at
once I saw a crowd
a host of golden daffodils
3, 5, 8;  3, 5, 8;
Only kidding.  It is 8, 8, 8, 8, .

Amazon has e-book by Virginia Gow.  "Escarpment".
I used to live in the Blue Mountains, west of Sydney,
and I can relate to the landscape.  I love it.  And I love Virginia"s poetry.
It is Fibonacci sequence:-  
1 syllable
1
2
3
5
8
13
21
13
8
5
3
2
1
1

There is more online on the subject.
I am just posting this to show I am still here.
Today I posted myLetter,  "Dear People" on www.awhatifworld.blogspot.com.
There is a lot to think about.
And I am still working on my seashell maths.
May all be well.

Christmas tree

It has been traditional for me to feature some Christmas item each year.
Remember we used to roll up a newspaper, cut from top to halfway down all layers, and then pull out the inner tip - to make a tree?

Like so:-

from strips of paper of fibonacci lengths, I wondered how many spirals up there were as we increase the length of paper:-

This might help in elucidating a method to crochet seashells with tall spires.

.....................................

This next is my best work done this year:-

This is Fibonacci series made in a flat spiral.  It works out as a 6 1/2 sided polygon, with crests.  I published the earlier work to 233 stitches perimeter in Post of ...24/12/2015....

This one is 377.   All the mathematics is in  previous post mentioned.

You need to click on images to enlarge them.

Then right click and you can save, or download, to print out Pattern, if you so desire.

38  rows more and we could have 610, but I will not attempt it.

......................

here is a model of striped seashell, not yet perfected....

from this:-

The real things:-

.........................

My new solar system.  One panel on the roof;  inverter;  12 volt;  I can charge up my mobile phone etc  but we still do not have internet or proper mobile phone reception in our town!  I am typing this in IGA , seated in cool area, before catching taxi home to my caravan out of town.  That is why so few posts.....Better luck next year. 

Happy Christmas everybody.

....................................

Biomathcraft Index, from the Beginning in 2010.

BIOMATHCRAFT INDEX

------------------------2010------------------

1.        How to create models from Nature.    3/30/10

2.        How to crochet a Hyperbolic Seashell.                        4/29/10

3.        Fibonacci Series Pattern.             5/19/10

4.        Instructions for Making a Model of a Mollusc.          5/25/10

5.        Photogallery of Seashells, crocheted and knitted.   5/25/10

6.        More Seashell Gallery.      5/25/10

7.        Photo Gallery of all my Seashells so far.          5/25/10

8.        Variations on a Hyperbolic Theme.       5/26/10

9.        How did I begin this Adventure?           5/26/10

10.      Hyperbolic Crochet on Radio.    5/26/10

11.      Who was Fibonacci?         5/26/10

12.      Unpacking the Fibonacci Series and the First Model.          6/21/10

13.      Here are the Bivalves.       6/23/10

14.      Heterodontus does Crochet.      6/24/10

            The Bifurcating Series.      6/24/10

            Heteronympha Fluttered By.      6/24/10

            An Important Message.    6/28/10

            One Big Family.  Ancestors!      8/15/10

15.      Fibonacci Equations.         11/21/10

16.      Fibonacci Series;  Mistakes.         12/5/10

17.      More Series, and IFF.        12/20/10

18.      A Theoretical Fibonacci Christmas Tree.          12/21/10

------------------------2011---------------------

19.      Fibonacci Series Table of First 100 Numbers.            4/16/11

20.      Fibonacci Cones, Type 1. 4/16/11

21.      Fibonacci Cones, Type 2. 4/17/11

22.      “Fibonacci Ripples”, Type 1.       4/17/11

23.      “Fibonacci Ripples”, Type 2.       4/21/11

24.      The Tip of a Drop.  4/21/11

25.      Beyond Zero.           4/21/11

26.      Make a “Fibonacci Pyramid”.     4/24/11

27.      Giza Pyramid.          4/24/11

28.      Imaginary Giza-Like Fibonacci Pyramids.        4/24/11

29.      Our Solar System.  4/24/11

30.      Crafting the Vortex:   the Beginning.    4/28/11

31.      More Crocheting the Vortex.      4/28/11

32.      Pattern 1 for “Fibonacci Vortex” to 233.        4/28/11

33.      Pattern 2 for Vortex to 4181.     4/28/11

34.      Pattern 3 for Imaginary Vortex to 196418.   4/28/11

35.      Discussion on Pyramids.  5/2/11

36.      Horns, Tusks, Fangs and Thorns, Spines and Prickles.         5/3/11

37.      Equations for a Frilly Edge.          5/3/11

38.      Tribute to Helle.      5/3/11

39.      To Crochet a Cephalopod.           5/3/11

40.      More Molluscs.       5/25/11

41.      New Models of Snails, made last year…          5/26/11

42.      The Giant Clam!      5/26/11

43.      More on the Bivalves.       5/26/11

44.      Real Seashells.         5/26/11

45.      “Fibonacci Bivalve Equations”    5/26/11

46.      Fibonacci Equations Having the Number 9.   6/5/11

47.      It looks like a Clam…          6/16/11

48.      Australian Seashores,  Identification of Shells.         

49.      Playing With the Number 9.       6/16/11

50.      Parallel Universes. 7/20/11

51.      Time Flies!    11/22/11

------------------------2012-------------------------

52.      A Proper Pattern for a Fibonacci Seashell.     1/19/12

53.      Make some New Fibonacci Seashells. 

54.      Now it’s Getting Closer to the Real Thing!       2/24/12

55.      The Seashell Model for 2012.     2/24/12

56.      On  the Trail of the Fibonacci Snail.      19/3/12

57, 58.                       Tribute to Tom Bass.

59, 60.           Tribute to Trudy.    19/4/12

61.      A Small Model, and a cute mermaid.   6/13/12

62.      More Mermaids.    8/1/12

63.      Visuals for Fibonacci Series.        8/1/12

64.      Errors Galore! And a Beautiful Solution.         10/25/12

65.      Responding Literally.         12/12/12

66.      Our Place in the Universe.           12/12/12

67.      Powers of Pi.           12/12/12

68.      Mending Mistake # 1.       12/12/12

69.      Powers of Phi.         12/12/12

70.      Powers of Further Phi.     12/12/12

71.      Geometry of a Theoretical Sunflower.            12/12/12

72.      Real Sunflowers.    12/17/12

-----------------------2013--------------------

73.      Angles for Fibonacci Series, 137.5 degrees.   1/7/13

74.      Angles for Sunflowers.     1/7/13

75.      Angles for Giza Pyramid. 1/7/13

76.      More Data, on angles, and Phi(s).         1/7/13

77.      “The Whole Bang Lot”.     1/7/13

78.      Planck and Phi.       1/7/13

79.      Continuing from last posts…..     1/31/13

80.      Phi Furthermore.   1/31/13

81.      Mathematics at Large.      1/31/13

82.      The Vedic Connection.      1/31/13

83.      Diorama with Mermaid and Seashells .           1/31/13

84.      Kind Advice.             3/25/13

85.      Refinding Phi – Introduction.     5/4/13

86.      Extra Dimensions.  5/4/13

87.      The First 135 Fibonacci Numbers.         5/4/13

88.      Real Seashells.         5/4/13

89.      Internal Structure of Seashells.  5/4/13

90.      Refinding Phi, Part 1.        Anatomy of Phi.     6/13/13

91.      Refinding Phi, Part 2.        6/13/13

92.      Refinding Phi, Part 3,        6/13/13

93.      Refinding Phi, Part 4, The Giza Pyramid.         6/13/13

94.      The New Parliament House, Canberra, Australia.  A Temple Pyramid!  8/23/13

95.      My Summary of Fibonacci-type Series and Phi-type Series.         8/23/13

96.      Phi and the Square Root of 5.    8/23/13

97.      Playing With Pythagoras.            11/26/13

98.      Fibonacci Spirals.   11/26/13

99.      A Shaman Mentions the Fibonacci Series.      11/26/13

100.   Proportional Calipers.       11/26/13

---------------------------2014------------------------

101.   A Late Christmas.   11/6/14

102.   A Brand New Calendar!    2/1/14

103.   Adding Time and Spce to Seashell  Models.    2/1/14

105.   The Torus.    2/5/14

106.   The Human Torus. 4/16/14

107.   The Latest Seashell Model.          4/16/14

108.   Swirling Shapes.     4/16/14

109.   Are the Robots Waking Up?        4/17/14

110.   Closer to a Better Pattern.**      5/19/14

111.   A Paper Model.**              7/31/14

112.   Some People and the Models They Make.**             8/22/14

113.   The Yellow and White Model.**           8/22/14

114.   The 144 Model, Crocheted.**   9/12/14

115.   Review of Algorithmn 13 to 21 for Fibonacci Series Crochet and Knit Work.**         9/13/14

116.   A New Equation!    Fibonacci and Lucas Numbers.  9/13/14

117.   Rummaging Around in an Equation.    9/13/14

118.   Combining the Fibonacci Series and the Half Fibonacci Series.**           9/13/14

119.VIDEO.  (OfficialMovie) THRIVE:  What on Earth Will it Take?

120.VIDEO.  Pi The Torus and Consciousness.  Arthur Young.      9/25/14

121.VIDEO.  A Stunning New Map Reveals For the First Time Where Our Galaxy Fits Into……9/25/14

122.   A Discussion of the Torus.           9/26/14

123.   An Hyperbolic Crochet Torus.**           9/26/14

124.   A Hyperbolic Crochet Apple.** 9/26/14

125.   a Rainbow Torus, Algorithm 9.**         9/26/14

126.   A Hyperbolic Crochet Donut (Torus).**          10/7/14

127.   A Golden Ring, Crocheted.**     10/7/14

128.VIDEO.  Science to Inform Conservation – Ningaloo Marine Park. 10/1116/14

129.   More Models – Hyperbolic Crochet Spheres etc **            10/19/14

130.VIDEO.  Bead Crochet Demo – Seven Colour Torus in Pony Beads..           12/6/14

131.VIDEO.  How to Crochet With Beads.** 12/7/14

132VIDEO.   The 4 & 7 Colour Mapping of Reality.  Arthur Young.         12/7/14

133.   A Red Blood Cell, Crocheted.**12/7/14

134.   A Fibonacci Christmas Tree-  Crocheted Cone.**     12/7/14

135.   Information for US and UK Crocheters.**     12/26/14

136.   Beach and Rock Platform, Little Bay, Sydney.           12/28/14

---------------------------2015----------------------------

137.VIDEO.  Soft Coral Habitiats in the Port Stevens-Great Lakes Marine Park.         1/25/15

138.   Crochet Coral Reef:  The Book    1/25/15

139.VIDEO.  Soft Corals Inside the Ex-HMAS Brisbane, -September 2010        1/25/15

140.VIDEO.  Heron Island Coral Reef.  1/26/15

141.VIDEO.  Conserving Cuba’s Coral Reefs.  1/26/15

142.   Fibonacci Ripples Merge into a Spiral.**        1/26/15

143.   Mathematical Model for a Seashell with a Tall Spire.**     2/11/15

144.   Auger Shell  with Tall Spire, model making continued…**                        2/11/15

145.   The Seashell Models Continue.** tall pointy             3/10/15

146.   Seashell Models.**            3/20/15

147.   A Gallery of Seashell Models.**            4/2/15

148.   A New Knitted Seashell**            4/2/15

149.   Nature Spirits!         4/2/15

150.   Making a Pink Seashell.**           4/15/15

151.   Blog Problems.        4/23/15

152.   Making a Pink Seashell, Part 2.**         6/3/15

153.   Making a Pink Seashell, Part 3.**         6/11/15

154.   A Pink Seashell, Part 4.**            7/4/15

155.Table For the HALF Fibonacci Series and the Algorithm 4 to 5 Series.       9/18/15

156.   The Operculum of a Gastropod.  And the Abalone. 9/18/15

157.   New Seashells.        9/18/15

158.   The Body of a Gastropod.            10/1/15

159.   Some Eternal Protocols for Building one Fibonacci Number into the Next, part 1.    11/9/15

160.   An Eternal Protocol, Part 2.        11/19/15

161.   Eternal Protocol, part 2, continued.     11/22/15

162.   Eternal Protocol, Part 3.  11/22/15

163.   Eternal Protocol, part 4.  The 3, 6, 9, etc        12/17/15

164.   Eternal Protocol, Part 5.  Prime Numbers.     12/17/15

165.   Eternal Protocol for Building Numbers;  Summary! 12/17/15

166.   Theoretical Fibonacci Ripples IAW the Protocols.     12/24/15

167.   Christmas Baubles.            12/24/15

168.   Theoretical Fibonacci Vortex Christmas Tree.**       12/24/15

---------------------------2016-------------------

169.   Variation on Ripples,  and 7920.           1/29/16

170.   The Holy City, New Jerusalem,  and 7920.     3/14/16

171.   To Make a Multi-Sided Polygon.**       3/14/16