Nautile aka Charles Hamel's personal pages
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MY BAT'S BELFRY !
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Added 2013 February 24th

SPRING SENNIT TRANSFORMABLE in USE:
HAND BAG CONTENT POSITION INDICATOR

A lady friend who always put her car keys in the same interior pocket is always face with FOUR choices and of course has ONE chance OUT OF FOUR to find it right away.
So, fascinated by Jimbo's find she immediately an opportunity of having it as "indicator in place of the elephant key ring and ask to have one.

Here it is (I had to do the chirality inversion trick to get it stiffer and with a shorter step.)



_______________

 

Added 2013 February 21rst

WHAT IF THE SPRING SENNIT it is its label now (see topic just
under this one )was to be made in  Z-LAY CORDAGE ?    (CONTINUING second topic under )


We saw the RIGHT single line making the OVER.

Now let us see the LEFT single line making the OVER.

and then COMPARE them.

Even before launching this new trial my hypothesis was that the chirality of the LAID
cordage would influence some of the characteristics of the result obtained.


One note worthy of attention IMO :   in 3mm laid cordage this sennit is WAY-WAY-WAY EASIER to make than it is the case in braided cordage : absolute ease in fairing and setting due to the "ratchet effect" at the point of contact between two parts of the cordage.



********** THE SHORTER SPRING :

RIGHT single line ( see ) makes the OVER crossing with the LEFT single line so this crossing is of SIGN MINUS and is a 'Z' crossing.

The crossing orientation is CONGRUENT with the cordage orientation : both 'Z'

The helix is an 'S' ( or LEFT or ANTI-CLOCKWISE )


********** THE LONGER SPRING

LEFT single line ( see ) makes the OVER crossing with the  RIGHT single line so this
crossing is of SIGN MINUS and is a 'Z' crossing.

The crossing orientation  'S' is OPPOSITE to the cordage orientation :'Z'

The helix is an  'Z' ( or RIGHT or CLOCKWISE )



The 'S'  helix is the FAST one and the 'Z' helix is the SLOW one.

FAST one ==  shorter radius than the SLOW one so higher curvature 
FAST one ==  longer  STEP  than the SLOW 
so "climb" faster along a 'developed' route that is shorter  than for the SLOW one.

Were they flight of stairs you would have to  step higher but you would have to do it along a shorter distance than with the SLOW one.

It is my opinion ( no proof  as I cannot test an  'S'-lay cordage in the same material and diameter.) that the fact that the cordage is laid or twisted  (so can un-twisted when making 'turns"    (  see  )   (  see ) ( with LAID cordages there are COMPULSORY ways to handle the cordage so as to "respect is lay : look at
http://charles.hamel.free.fr/knots-and-cordages/ropes_cordages.html

also if interested
http://charles.hamel.free.fr/knots-and-cordages/ropes_cordages_2.html
http://charles.hamel.free.fr/knots-and-cordages/ropes_cordages_3.html


If you go the "wrong" way you "open" the lay and destroy it fractionally.
( see )   ( see )   


In BRAIDED cordage the two helices ( 'S' and 'Z'  ) are MIRROR image BUT in LAID cordage the two helices are really different one from the other : in radius, in step...

I have the feeling that with  Z-lay cordage going for  'Z' crossings between the 'single lines" yields an 'S' helix with shorter radius and longer STEP or FAST helix while going with 'S' crossings between the two single lines yields a 'Z' helix or SLOW helix as if the  Z-lay is somewhat  cancelled out by the 'S' crossing so the cordage does not stay as stiff while in the first case both  reinforced each other a bit like when making "cockles"
( see )   ( see )   ( see )   ( see )   by over-winding the cordage.

Just my two cents .......of Euro ! ( 1€ == US$1.32 today  ;-)   )




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2013 February 21rst  CONCLUSION

SO 4-STRAND SPRING SENNIT TRANSFORMABLE IT WILL
BEGIN TO BE.

UNDERSTAND  4 "STRAND FUNCTIONS" rather than "STRAND STRUCTURES" taken up by 2-STRANDS but it is in fact 4-STRAND as it can also be done with 4-STRAND seized together so the "structure" is really 4-STRAND in "basic nature" and it is done with two for expediency and aesthetics.


Added 2013 February 19  18:00

ABOUT NAMING THE SO-CALLED
JIMBO's SPIRAL / HELICAL SENNIT


[open quote Michel SINCE]
Pour le nom à lui donner je pense que la priorité revient à JIMBO perso j'aime bien ta
deuxième proposition
Ressort Hélicoïdal  Transformable

As for the name to attribute to it I think that the priority belongs to JIMBO himself , I like your second proposal
Transformer helical spring sennit
[End quote Michel SINCE]


[open quote Constant XARAX]
....
   I see that you fell in love with this strange object / creature ! Unexpected, and beautiful – one can not escape from the seductive combination of those two properties...
   Is there any other helical sennit out there ?
   If not, “helical sennit” would be a fine, short, descriptive name. If and when somebody discovers another one, he would add a “#2” , or “II” . However, I do not believe that there are other helical sennits as simple as this one. Just a gut feeling, of course.
[end quote Constant XARAX]

My personal feeling is  that helical sennit is quite perfect but I would like to"push" the special properties of auto-conformation while being tied, springiness and "morphing" into a different chirality or into a true spiral




This exchange went on


*****[open quote Jimbo 2013 /02/20]
Except it's not a helix, is it?

It's not even a Helicoid, either, although that's a step nearer...

I'm still leaning toward "Spring Sennit" which captures the falling-on-the-floor
aspect, and the fetches-up-on-a-rail aspect; and leaves room for both a Helical Sennit and a Helicoid Sennit...

But it's not my call, and it could be confused with the season or Springrolls.  I'd be fine with
/....
[end quote]



*****[open quote Jimbo 2013 /02/20]
Of course, us low-born Yanks would put the adjective first, but
"Transformable Ressort Hélicoïdal" sounds exactly like what it is. 
To me, anyway.  A transformable, helicoidal spring sennit...  Pedantic.  Onerous. 
Bombastic.  Let's go with "PIGTAIL"!!  :^D

(sorry to act silly in such august company...)
[end quote]



*****[open auto-quote 2013/02/20]
Discarding "everyday unguarded parlance" I will say :

I think it IS an helix , when and if considered "ideally", or "archetypal" or to honour one of XARAX's country greatest mind "Platonician" (we are here considering the whole thickness of the knotted cordage - which does not form a flat/flatish  plan) as an "ideal thin line"
.../


from this mathematician's site
http://www.mathcurve.com/courbes3d/helicecirculaire/helicecirculaire.shtml
http://www.mathcurve.com/courbes3d/heliceconic/heliceconic.shtml
http://www.mathcurve.com/courbes3d/heliceelliptic/heliceelliptic.shtml
http://www.mathcurve.com/courbes3d/heliceparaboloide/heliceparaboloide.shtml
http://www.mathcurve.com/courbes3d/helicespheric/helicespheric.shtml


For me this is not an helicoid
In French Helicoide correspond not to a line but to a flat plan running in helix , 
this sennit is not such a surface
http://www.mathcurve.com/surfaces/helicoid/helicoid.shtml
http://www.mathcurve.com/surfaces/helicoidregle/helicoidregle.shtml
http://www.mathcurve.com/surfaces/helicoidcercle/helicoidcercle.shtml  ( the
section of the sennit is quadrangular not circular so it is not even nearer this one )
http://www.mathcurve.com/surfaces/helicoidminimal/helicoidminimal.shtml
http://www.mathcurve.com/surfaces/dini/dini.shtml
http://www.mathcurve.com/surfaces/helicoiddeveloppable/helicoiddeveloppable.shtml


You are the 'inventor' so the naming chore/duty/honour is yours we are just here to help you with offering  several choices. This is the more so as you will have it published in Knot News, our PAB newsletter : be careful this will remain as the officially published name !!

PIGTAIL is a nice nickname to propose if people are shy of using grand words
[end auto-quote]



*****[open quote Constant XARAX 2013 /02/20]
“Spring sennit”  is fine ! ( because most “springs” are helices ! SmileSmileSmile )
[end quote]

*****[open quote Constant XARAX 2013 /02/20]
“Helicoid “ is a different thing...
 [end quote]

*****[open quote Jimbo 2013/02/20]
Is there a name for a Helicoid which has thickness?  I.e. not a plane?

(And you can stop beating me up over "spiral"...  You see what a mess this is!)
(No, I don't actually think you have been "beating" anything, especially me!!  But before shot the first picture I went all the way through "Helicoid" before noticing there's nothing I can find which ACTUALLY fits. 
Hence the simplistic vernacular use of "spiral", in the sense of a CFL bulb or a staircase (Constant) or the tail of a pig.)

See, "Pigtail" is not just an avoidance of pedantic words.  It's a nod in the direction of the fact  that I can't find the "real" name of this type of structure...

[end quote]


*****[open auto-quote 2013/02/20]
Well Jimbo you did it you pay for that properly naming it
As goes a Spanish saying " God told to Man : take ( make / do / think...)  whatever you want, take it......and pay for it "

If using a geometric figure as namesake you cannot escape the fact that you must accept to use an "idealized" figure as this real "composite, bumpy," knot cannot be found in geometry (at least by little myself) except if you take its centre line axis with all the "real cordage" irregularities taken out" as "its true self"
Now this is "anatomy" naming if you want "behavioural" naming then you introduce "spring"   and "transformation"

Now the PIGTAIL  is good if denoting 'Tail of a Pig' because it "somewhat helical" but also not a real helix plus is moves and change while still being recognisable.
STILL if it denote the hair-do then its downfall is that PIGTAIL is  in my French mind map- is NOT  an helix but a "straightish" braid
http://en.wikipedia.org/wiki/Pigtail  not really corkscrewing at all

Your name has to be somewhat not culturally tattooed and a bit international as your fame is already international
[end auto-quote]




*****[open quote Jimbo 2013/02/21]
I'm going to go with Constant and Michel here, and put my insignificant imprimatur
on this:

4-Strand Spring Sennit Transformable

It shouldn't take too long for the "Transformable" part to drop away, which is Good,
since by then everyone will know that. 
That leaves "4-Strand Spring Sennit" ("Spring Sennit" for shorthand) with room for
you guys to make a 3-Strand one and a 5-Strand one and so on.

So...

Can I get an "amen" to "4-Strand Spring Sennit"?
[end quote]

*****[open auto-quote 2013/02/21]
Well Jimbo this is a nice multi-stage name that can like sea birds shed its juvenile feathers as they grow up

4-Strand Spring Sennit Transformable

4-Strand Spring Sennit

Spring Sennit

As Don WRIGHT is wont to say : AMEN to that !


Still for Michel and I it will remain Jimbo's Spring Sennit I guess when we will speak of it though as Constant said it there is some believable doubt that there is another one around


You see there is a wee bit  of irony here : both you and I never adhered to Ashley's opinion that the "same" sequence of crossings but laid in a different manner are different knots.
I still believe that Ashley was mistaken and that topology makes the both of  us right BUT.. if you do not speak of "the way to throw it in the rope" but instead we speak of the way it behaves once it  is thrown, faired and set then I believe we have two different "behavioural entities" with same topology, quite different geometry and quite different behaviour and usage.
[end auto-quote]



*****[open quote Constant XARAX 2013/02/2011]
   So, let us now see this not-4 strand spring sennit ! Smile ( I believe the 4-strand adjective will be forgotten... because there will be no other such spr-ing th-ing...Smile)
[end quote]


SO 4-STRAND SPRING SENNIT TRANSFORMABLE IT WILL
BEGIN TO BE.

UNDERSTAND  4 "STRAND FUNCTIONS" rather than "STRAND STRUCTURES" taken up by 2-STRANDS but it is in fact 4-STRAND as it can also be done with 4-STRAND seized together so the "structure" is really 4-STRAND in "basic nature" and it is done with two for expediency and aesthetics.

Michel SINCE who is a modest but knowledgeable person immediately made this remark about STRAND structure versus function
[open quote Michel SINCE]
Oui c'est comme le sifflet de bosco 1 brin plié en deux  pour faire une jolie boucle  mais on peut très bien le faire avec 2 brins et dans ce cas beaucoup appellent ça un diamant


which translate to

Yes it is like the Bosun's whistle knot made with one middled strand to make a nice loop but you can easily do it with 2 strands and in this case many call it a diamond knot
[end quote]


_______________


Added 2013 February 19th

WHAT IF THE JIMBO HELICOIDAL SENNIT  was to be made
in  LAID CORDAGE ?


I always thought that when speaking about a knot (the more so if a "tool" or 'utilitarian' knot) one should *always* specify the cordage used : nature of its construction, material, diameter and that one should never extrapolate what  one knows about a knot made with a laid cordage ( the more so if in traditional hemp ) to one of the modern fibres and construction cordage without due attentive evaluation trials

So I was tempted to make the helical sennit using a Z-lay 3-S cordage and see if the result was different.
As I was loath to use my rare first grade polished hemp I used its copy in SPLEITEX
(polypropylene)

Of course it should also be done with the OVER being made by the LEFT single strand and with the OVER and UNDER using an 'S'-lay cordage



_______________



Added 2013 February 19th
in direct relation to the topics at the bottom of this page
Added 2013 February 4th  A TWO COLOR SPIRAL SENNIT"


FINDING A NEW DESCRIPTIVE (as opposed to "attributive") LABEL FOR THIS SENNIT PROPOSED BY JIMBO

[open quote Jimbo]
I'm honored and flattered that you keep using my name.

BUT...

Could you post this on your page?
============================
Charles,

I'm flattered that, as a shorthand way of talking about it, you've started hanging my nickname on this bit of kinkery.  However, I'd hate to have that "stick", at least without some demurring!!

Maybe we could start calling it a "Spring Sennit"...  Or a "Self-Helical Sennit"...  4-Strand Helicoid Sennit works for me, if you recall our earlier discussions of this
wee bit of knot magick...  Plus it makes people aware of the difference between a Helix (a line) and a Helicoid (a 3D helical structure)... 
Obviously I'm open to suggestions!

Not that I'd seriously object to joining Mr. Walker!!  But not without at least asking for a better name for this.

SO, is there anything besides "Jimbo's Sennit" that names this?

Just asking.  I'm fascinated by the discussion!!
...
It would flatter me to be remembered, but I can't sit idly by and let that happen. 
Besides, it's the Adjustable Ancient Sling that I actually DID invent "from scratch". 
I got too much of this from TIAT to take full credit.

[end quote of Jimbo]

TIAT, IMO was the guy who gave publicity to this sennit algorithm plus a rather
bizarre IMO nothing more than an astute commercial gimmick for me) label but I will never believe that he was its 'inventor'.
It is a much too simple algorithm not to have been found before by several of the so many knots tyers since humanity began playing with rope. His proposed  'avatar' of this knotting algorithm is soft, without any mechanical special characteristics, yours have very special mechanical characteristics and in all what I have seen this TIAT person did not even begin to hint at that.

If  a rose grower pre-existing takes a pre-existing rose and with much  creativity gets
a new mutation from it he owes nothing to the rose diffuser of the rose he starts with since then it is a completely different flower that is  proposed.

For my part I see this sennit that you offered as a WHOLE DIFFERENT ENTITY from the one shown in  
http://www.youtube.com/watch?v=emiLkv4BrWM
and anyone with functional eyes and brain can easily see that.

Still it would be nice to have some proposal if only just for the fun of it.

I tend to favour "descriptive" so I am all for :

self-conforming helical spring sennit

or fancy name   
Transformer helical spring sennit



_______________



Added February 17th   16:05


TRIAL WITH Constant's XARAX IDEA as exposed here

I first did it TIGHTENED ( and not "relaxed" as in the pictures XARAX shared in The Mother Of  All...)  in 10mm diameter before going to the 2.8mm polypropylene cordage and 23"bumps" or pair of "loops" like  ladder rungs for the sake of maintaining comparability.
as shown in this illustration.

I sent this last illustration to the "gang" with those comments :

[begin self quote]
Well I am in two minds about this one :
in its "relaxed" avatar, it has, as I find most XARAX's idea an appealing geometric aesthetics and as "proof of concept" I had for it sufficient interest to sustain me on going on with the test despite my others feelings (mind you feeling are *not* truths* there are just subjective experience and as such subject to all human failings (Japanese have a beautiful concept ! "the suffering of being of the human condition" BUT as a sennit tying experience (warning : in the domain using small cord : 2.8mm  polypropylene blinds cord ) I found it "not very pleasant a a wee bit on the irritating side" ( please, each and all of you try it in at most 3mm cordage - in 10 mm cordage it does not have the same "existential properties"

Well here it  is and I cannot say that as a "practical object" (as opposed to proof of concept object) I care very much for it is PITA to lay and fair, better in setting, readily form an helix but which has NONE of Jimbo's sennit characters : a very mild "memory of form" (rather on the side of chewing-gum", ungainly in the laying phase not real gripping/holding power )

I am waiting ( to enrich my page ) for your own  reports : as they say in France :
" des goûts et des couleurs on ne doit pas discuter"
 " of tastes and colours one should not discuss"

STILL I do not regret the experience, despite having felt a bit exasperated at having to do it 7 times to get it about "acceptable as a botched trial".
I do not regret the experience may be because as goes the French joke :
 "feeling unwell, just hammer on your fingers, you will see it feel SO GOOD when you stop" ! ROTFLOL
I hereby solemnly declare that I will not be attempting the others 3 hybrids that can be done with this new algorithm.
NO ! I am just pulling Constant XARAX's leg :the proof of concept being put into cordage is quite worthwhile and NOTHING BEATS THE "EXPERIMENTAL METHOD" of which the French Claude BERNARD was the proponent and theoretician....
[end self quote]


_______________


Added February 17th 15:55

HOW I LABEL THE PARTS OF JIMBO's SENNIT

This illustration shows it
Note : this is only *my* way and not  THE way. You can use anything you like as long as you do it EXPLICITLY AND IN DETAILS PRIOR TO ANY COMMUNICATION so that all participants have this "common ground"


_______________


Added February 17th  15:40

XARAX's  The Mother Of All... continued


February 16th Constant sent to me a diagram and those words:

 [open quote]
As shown at the pictures of the symmetric “Mother of all Jimbo s sennits” Smile, the yellow lines can “jump” from the one node to the other. If they do this, at each and every node, the one yellow ( green, in my picture ) line can go around the pair of the green ( orange, in my picture ) lines following always a clock-wise path, and the other yellow line following always an anti-clockwise path ( of course, “clock-wise” and “counter-clock wise” terms can not mean anything – but the use of the one term for the one green line and the other term for the other green line can Smile. At each and every node, the one yellow line encircles the pair of
the crossed green lines in the same way ( clock-wise or counter-clockwise ), and the other yellow line in the opposite way ). I believe that this helps to have an as stiff, symmetric and straight sinnet, as possible. With fewer or no “jumps”, the sinnet become very sensitive to the “over/under” and “inside/outside” asymmetries, and leans towards the one, or the other, or both directions. Perhaps Jimbo weaved Jumbs Smile, and then he had the idea to remove them, so the initial stiff sinnet would become more flexible. Then, he have seen, that by weaving the lines in a always “over” or “under” way, he was able to make this flexible sinnet to twist and lean at the same time, and so form an helix.
[end quote]

Alas I was unable to fully interpret and understand Constant's idea  because I was unable to trace his drawing from this picture which is how we do Jimbo's """spiral""" sennit "there are FOUR RED BEHIND the TWO GREEN and TWO RED IN FRONT of the SAME TWO GREEN"

Xarax answered with those words

[open quote]
Here I see FOUR green
 
Because you see a cross section of two nodes.
 
 
and a red (which does not cross or jump )
 
The red is what the line does, when it does not jump.
The yellow is what the line does, when it does jump.
 
Perhaps you can find better terms
[end quote].

I sent this diagram of mine and this drawing of mine. with those words

[begin self quote]
'nodes' I took as meaning knots

so the section is a VERTICAL or SAGITAL one  of a vertically held sennit ?

because I see with an HORIZONTAL section of a vertically held sennit what is in my attachment here.
In a three-fourth front side view the "modular" character is more easily perceptible and I guess that the LOOP / TURN / LOOPING is what you labelled JUMP
[end self quote]

Xarax answered with a modification of one of my drawings and those words.

[open quote]
  If the one red line turns around the crossed pair of green lines clockwise, the other turns counter-clockwise – no matter which is the “clock-wise” and which is the “counter-clockwise” turn. Can we call the red lines “enantiomorphic” ?
   I believe this is the symmetric “Mother” of Jimbo s sennits. This is how the sennit in the picture I have sent to you was weaved – so there would be no asymmetry whatsoever, at any point of it, in order to achieve the most stiff, straight sennit possible. Starting from this, and inducing asymmetries, the sennit will ‘respond’, to minimize the tension, by twisting and turning, i.e, by following a helix. 
[end quote]

About the enanthiomorphy I quite agree for the reason shown here.
Indeed the two "loops" or "turns" are as mirror image (this led me to make an illustration of how I label the parts of this Jimbo's sennit ( topic just above this one ) and I am going to try this XARAX's variation in the 2.8mm cordage and 23"bumps" or pair of "loops" like  ladder rungs for the sake of maintaining comparability.



_______________


Added February 17th  15:00

THE HYBRIDS MADE

HYBRID ONE         HYBRID TWO       HYBRID THREE       HYBRID FOUR

COMPARING THE FOUR

As you can see TWO and FOUR are MIRROR images or OPTICAL ISOMERS
but  I am a bit surprise at the quite different aspect of ONE and THREE, I would have
thought that they would be mirror image one of the other.
I will have to make a new copy of them to be sure



_______________



Added February 16th  16:00


PROPOSAL ABOUT TRIALS OF HYBRIDS  OF THE INSIDE
the red hole AND OUTSIDE  the red hole TYPES

I suddenly (the biologist in me ? ) asked myself  "what about making some hybridization of the OUTSIDE and INSIDE procedures."

Here  the FOUR TYPES are illustrated in "exploded" views to show what they are to be and here I made (in large cordages) just a test run for each.

It seems that the curvature is accentuated, but this has to be verified in the small 2.8mm cordages so as to  "maintain comparability".
Here is a view allowing easy comparison of the hybrids with the "pure parental types".




_______________


Added February 16th   11:00


Mails received from Constant XARAX :  THE MOTHER OF ALL
JIMBO's HELICAL SENNITS

Constant provided his own pictures to illustrate his ideas.

[open quote]
On 14/02/2013 18:39,
That is what I think is the symmetrical ancestor of Jimbo's sennit.
If one “breaks” this symmetry, by reversing the order of the over/under crossings of the "single and/or the double line, and does this at each and every node, the sennit is forced to twist – and the accumulated twists at each node, towards the same two orientations, generate the helix.
[end quote]

 I then asked permission to used his images and words and received this response

[open quote]
Of course you can ! ( But I had tied this sennit very quickly ( so it is not weaved with the proper care...), just to illustrate what I meant by the “over/under” symmetric way of weaving the yellow lines ( green, in my picture ) – because I could not express it with words.
[end quote]

As I made the remark that it was not ultra-tightened as per Jimbo's instruction Constant brought the following precision

[open quote]
I had tied it only to show what a symmetric ( relatively to its axis ) sennit would be, one where the alternating over/under crossing happens to the single as well as to the double line– which would not twist to either direction, and so it will not form circles or helices. ( And even this form is not absolutely symmetric – so it can be tied in two slightly different ways )
[end quote]




_______________



Added February 15th


A GOING BACK ON A PREVIOUS EXPLORATION OF THAT JIMBO'S SENNIT

In the topic Added February 10th  21:00  I followed Constant XARAX suggestion of going OUTSIDE rather than INSIDE the "red hole" as explained in Jimbo first tutorial but I was not really happy with using rather thick cordages so I decided to do a comparison of the INSIDE "normal" procedure and the OUTSIDE procedure in the same knotted structure.

Curiously what happened is a kind of PERVERSION and the part made by going
OUTSIDE is not so 'harmonious" and has not the same "stiffness"

See this illustration showing 4 perspectives of the test : top (limit is pointed by the white pin's head) is made with the INSIDE procedure with which the helix appears rather rapidly and after that it was the OUTSIDE procedure that was applied.



_______________



Added 2013 February 13th


SUPPOSING THAT INSTEAD OF A CONSTANT LEFT TO RIGHT or RIGHT TO LEFT FOR THE OVER WE DO AN ALTERNATE RIGHT TO LEFT/LEFT TO RIGHT
WHAT WILL WE GET, STILL AN HELIX OR SOMETHING
ELSE ?


[open quote]
If you alternate right then left, the result won't spiral, but what fun would that be??"...
[end quote]


I beg to differ my Friend 

YES IT WILL NOT MAKE AN HELIX (3D)
BUT
the result DOES SPIRAL ( 2D), REALLY!  

At first I thought it was going to get a full circle but going on it was clear that this was to be
A SPIRAL

FUN !

Here the curvature is not LATERAL ( seen from the staring position shown in the tutorial)  PLUS ALTITUDE GAINING as with an helix but it is STAYING IN THE SAME PLAN and the curvature is ANTERO-POSTERIOR.

INTRIGUING AND FUN
Remind me of  fern frond and the differential growth or circinate vernation that explains the unfurling of the frond.  
Here it is not differential growth but differential tightening.
 




_______________



Added February 11th 18:40

PERVERSION WITH JIMBO's SPIRAL SENNIT.

Thinking " tendril perversion"  was obvious with my training and background.

So I immediately launched into the creation of a modelisation of that curiosity.

In relation to the perversion look at this illustration taken from another of my pages.

cordage is 2.8mm (braided sheath on linear core) polypropylene.  I think that the
nature of the fibre may have an influence : nylon would not be good in my hypothesis.
 
I began with two lengths (red and green) 450-452cm each ( when middled 2*225)

The linear length of the helix in the model : 64.5cm
Those 64.5cm are made with a total length of cord  229cm  (163.cm red and 65.5cm green)

In the same disposition that your tutorial show I am left with
green == 2*159.5cm
red==2*61.5cm

Read :
http://math.arizona.edu/~goriely/Papers/2002-JNLS%28perversion%29.pdf
IF and ONLY IF link is broken use      link1   

http://math.arizona.edu/~goriely/Papers/1998-PRL%28tendril%29.pdf  
IF and ONLY IF link is broken use     link2

http://www.phys.ens.fr/enseign/fip/seminaires/rapports/tabor.pdf  
IF and ONLY IF link is broken use    link3

http://phys.org/news/2012-08-uncoiling-cucumber-enigma-biological-mechanism.html 
IF and ONLY IF link is broken use    link4
This link is "cool as a cucumber" !

http://math.fullerton.edu/tmcmillen/papers/Dissertation.pdf
perversion and whips, static and dynamic problems of elastic filaments
IF and ONLY IF link is broken use  link 5


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Added February 11th  18:30

HOW THE TOPIC JUST UNDER CAN EXPLAIN THE
CONSEQUENCES OF THE CHIRALITY REVERSAL
SHOWN IN SECOND TOPIC UNDER THIS ONE.

In fact this chirality reversal is a MIRRORING so the image of an inside-out as with a glove finger is false because this inside out corresponds to
INVERSE ( x , y , z ) ( -x ,- y ,- z ) Changing all three axis at once
see :  http://charles.hamel.free.fr/knots-and-cordages//Geometric-transformations.html


MIRROR ( x , y , z ) ( -x , y , z ) or ( x , -y , z ) or ( x , y ,- z ) depending on the plane used. It is inversion of DEPTH ( -x or -y or -z ) only
ONLY one Cartesian axis is changed and it is the one along which the axis of  the helix run.

So the external "wall" stays the external "wall" and the internal "wall" stays the internal wall.

So from where does come the change in "energy level" that explain the dramatic
augmentation of the stiffness and the notable shortening of the helix STEP.


NO ANSWER: JUST MORE QUESTIONS /

My tentative hypothesis is that the reversal of the helix axis just yields a (structural and/or functional)  modification that augment the tightening  of the already "a bit more" tightened
"wall"



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Added February 10th  21:00

TRYING TO UNDERSTAND THE HELIX APPEARANCE IN
JIMBO's ''''SPIRAL''''  SENNIT
(again spiral are 2D and the3D figure is an helix)

My hypothesis is that as it is  the same green side that  constantly goes over the other green side this induce a functional asymmetry that is somewhat "fixed or glued" by the tight setting and this "glueing" cannot happen with a "normal or relaxed" setting.

Granted  this does not explain the why/how of the result.

I made a first experiment : using a white 5mm core I applied the green cordage in the same way.
On the first two crossings on the left side of the picture the white core was not tensioned enough to forbid any deformation while for the rest of the crossings  the tensioning of the white core relative to the tensioning applied to the green cord was sufficient to hinder any movement of deformation from the white core.

As can be seen the first two crossings on the left shows the beginning of an helix formation while the remaining crossings stay in straight linear formation.

Showing must not be confused with Explaining (I can show you a volcanic eruption but that does not explain volcanism ) but  let me try to just show and it will be for better minds to do
the full explanation.

Starting position ('exploded' is like in this picture ( in this particular one it is the RIGHT
 green 'leg" that consistently makes an OVER when crossing the LEFT green 'leg')

When it is the RIGHT green 'leg" that constantly  makes an OVER when crossing the LEFT green 'leg' the hard setting yields an 'S' helix

When it is the  LEFT green 'leg" that constantly makes an OVER when crossing the RIGHT green 'leg' the hard setting yields a 'Z' helix

I think that (when looking at the face that is shown in the starting position ) it is not the same lateral 'wall or side' that provides the "morphing mechanism":

Case RIGHT green 'leg" makes an OVER when crossing the LEFT green 'leg
and 'S' helix then the tightening happen "sooner and stronger" during the tightening effort on the RIGHT side which so is a wee bit shorter than its LEFT counterpart so the curvature happens to have its concavity on the  RIGHT side hence the 'S' helix


Case LEFT green 'leg" makes an OVER when crossing the RIGHT green 'leg
and 'Z' helix then the tightening happen "sooner and stronger" during the tightening effort on the  LEFT side which so is a wee  bit shorter than its  RIGHT counterpart so the
curvature happen to have its concavity on the LEFT side hence the 'Z' helix

I think that this illustration and also this one will help you understand what I wish to convey.

The spatial disposition explains the way the different segments of the cordages arrange themselves relatives to the other ones, explaining the torque and the slow yielding of an helical curvature.

Of course for this to appear the setting must be "tight" enough to constrain each segment to adopt the "least volume occupation" position ; in a relaxed setting there is always ' room enough" for each segment to be allowed to yield a straight linear alignment like in the undifferentiated soft sort of caterpillar labelled "Endless Fall".

After reading that topic Constant XARAX suggested

[open quote]
Try to pass the strands of the Double Line ( yellow) outside of the round turns – between the Single line bights ( green ) and themselves. Will this sennit still form an helix ? If the yellow lines do not play any role on this, it will.
[end quote]

Here is what that  new procedure yields: HELIX !



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Added 2013 February 10th  15:00


JIMBO'  SPIRAL SENNIT :  AN EXPERIMENT ON INSIDE-OUT REVERSAL OF CHIRALITY

Here it in sequenced pictures.

This was pointed to me by Jimbo who discovered it.

For that I am using the helix I made as test for Jimbo's tutorial ( see topic dated 2013
February 4th in JIMBO'S_TUTS )

Let us put the helix (3D ) of "S" chirality or LEFT hand oriented ,( no, NO !  NOT 'of Left handedness', an helix neither has any hand nor any neuro-psychological preference for using one of them which is the proper definition and use of the noun 'handedness' )  in its 2D avatar or TRUE SPIRAL with the terminal ( the working end) extremity  at the centre.

Then we push that central extremity towards the other side of the spiral mat.

This yields  a " Z" helix ( so opposed to the "S" we began with)

Not only the chirality is changed BUT THE STEP of the helix is SHORTENED and it 
is now noticeably STIFFER.

Note that putting an helix upside down DOES NOT change its chirality so this is a real change of chirality that this manipulation yields and not just a change of orientation but  also a change in mechanical characteristics.

Decidedly Jimbo's  finding is really full of surprise

Now WHICH particular event in the Jimbo's PROCEDURE OF ULTRA-TIGHT SETTING yields an helix depending on the green "leg" that constantly makes an OVER with the green "leg" on the other side of the two red stands?

As no one can at the moment offer an explanation which is an explanation and not a simple description of steps to follow I researched this question and it will be the object  of the very next topic in this page.



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Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2014 -(each year)

Url : http://charles.hamel.freeL .fr/knots-and-cordages/B