Nautile aka Charles Hamel's personal pages
MENU
 _______________
PUBLICATIONS  
Page 5
Page 1   Page 2     Page 3   Page 4     Page 6     Page 7

_______________


 Added 2009 July 21rst :

Nautile's HELP FOR DUMMIES  

HOW TO KNOW 
HOW MANY LEADs AND HOW MANY BIGHTs WILL BE
ADDED BY A GIVEN ENLARGEMENT ON A SQUARE TURK'S HEAD KNOT


( this is a sort of follow on the enlargement of SQUARE THK  ( [L - B| = 1 )  from FOUR
very basic  minimalist THK )

Those not wanting or not able for any reason to use the H48 program I wrote that gives
the results of any enlargement on any THK ( not Square ones only ) can use this basic help.

THIS BASIC HELP WORKS ONLY FOR THE CASE ENLARGEMENT OF
SQUARE TURK'S HEADS KNOTS.



HOW TO FIND THE RESULT OF  A GIVEN ENLARGEMENT.

A short pondering led me to find a rule of thumb (and a mnemonic) on how to get the
smallest possible addition of LEAD and BIGHT  :  + 2L  +2B  ( for square THK only )

 
You must start with writing the Number of LEADs ( a LEAD leads in the LOWER  is your
mnemonic ) characterizing the "starting" THK.

*** 2L 3B       ( example given )
the left side  2 (L) is smaller that the right side 3 (B)
so INCREASE the LEFT side = LEFT enlargement ( LEFT side of SPart-WEnd vector )

*** 2L 1B    this time the lesser side is the RIGHT side ( 1  -B- ) so INCREASE the
RIGHT side = RIGHT enlargement

Another way rather quick way is  ( same cases as above  ) :  

- always state the LEAD /PART first  ( a LEAD leads will be the mnemonic )
   <       and        >    the arrow point gives the side of the SPart-WEnd vector where the
enlargement is to be made.

> B then       RIGHT side of the SPart-WEnd vector -------------------->
< B then      < ---------------------- LEFT side of the SPart-WEnd vector



HOW MANY  L and B will be added WHEN IT IS NOT the 2L 2B already seen
that you want.


it will be a BIgger enlargement so BIght will come first in the 'divinator' ( this is your
mnemonic )


> L  ( number of BIGHT greater than number of LEAD ) this means that you go for a
RIGHT side of SPart-WEnd vector------------->
< L ( number of BIGHT smaller than number of LEAD ) this means that you go on
 the <-------------- LEFT side of SPart-Wend ( as the arrow points)

We know which enlargement type it will be.

How many L are added and how many B :
simple enough.
Use the number of LEAD and BIGHT of the pre-enlargement THK

> L    RIGHT ENLARGEMENT will be the biggest of the two

ADDED LEAD    (L - 1) * 2          (  L>1 )
L - 1       ex =  10L 11B     L - 1==10 - 1 = 9           9 * 2 = 18     18 L will be added
giving 28L
ADDED BIGHT     (B - 1 ) * 2       (B>1)
B - 1       ex  10L  11B        B - 1 == 11 - 1 = 10        10 * 2 = 20   20B will be added
giving  31B



< L    LEFT ENLARGEMENT will be the biggest of the two

ADDED LEAD    ( L - 1 ) * 2        (  L>1 )
ex  11L  10B      (11 - 1) * 2 = 20     giving 31L

ADDED BIGHT   ( B - 1 ) * 2      (B>1)
ex  11L  10B         (10 - 1 ) * 2 = 18    giving 28B

summary whatever it is   B>L or B<L if it is not the enlargement adding 2L 2B 
there will be :


(L - 1)*2   LEAD ADDED  
(B - 1)*2   BIGHT ADDED


some examples
5L 6B -------13L 16B
8L 9B--------22L 25B
11L  12B-----31L 34B

6L 5B--------16L 13B
10L 9B-------28L 25B
12L 11B------34L  31B

Of course my HP48 program would tell you that a 31L 34B can be had from a 12L 11B
but here you will have to find yourself your OWN DUMB RULE to easily get it;
AN AWFUL LOT OF LUCK TO YOU !!! ;-O)


 
_______________


Added 2009 August 29th


BURNING TRACKS : ANOTHER ' STYLE ' OF ENLARGEMENT
giving a
different result from the results given by the usual enlargement processes ( those were
explored  in Summer 2008 in Turkshead-2 and Turkshead-3 with drawings, photographies
and text.



Picture of MeltingMELTING THE TRACKS ;-)
Click on the thumbnail to open a big picture
( quite slow if connection speed is  less than
1024 bps ) in another tab or window.


Photo is courtesy of JIMBO ( Jim LONG ).
Any comment just send me an email that I will
forward to Jimbo. (see bottom of page for mail )



Best way (will be less slow to download that a web page full of drawings) to show what
I have found is via a PDF file.

The gist of it is that by "tweaking" a bit one of the two already explored enlargement
processes one can obtain a ' new perspective'.

This preoccupation with enlargement processes is that they allow the knot tyer not to rely
on a whole  batch of stupidly memorized recipes but on knowledge and intelligence.
 So we have only a handful of knot ( root knots ) to know by rote (and even they are not
 fully memorised  with just a wee bit of concentration and thinking one can "find again "
those basic knot just by a small effort of thinking along the right tracks.)

For a 3L 2B THK  :

-- Enlargement Process on the RIGHT side of HP1(SPart-WEnd vector )
will lead to a 5L 4B THK

-- Enlargement process on the LEFT side  of HP1 will lead to
a 7L 4B THK.

In each case it is going from 2B to 4B

WHAT IF I SHOW YOU THAT IT IS POSSIBLE TO GET 5B instead of 4B and 
enlarge a 3L 2B to a 7L 5B
?


Added 2009 September 1rst
PDF is here

A big thank you to JIMBO for having been the guinea pig reader and pointing
some things in need of clarification  such as HP, SPart-WEnd, not given in
full spelling at least the first time or not explained as what is Half-period
( people wanting a bellyful on HP Half-Period : simply explore the Turkshead
pages )



_______________


Added 2009 December 28th

Nautile's tutorials on
HOW TO MAKE STANDARD HERRINGBONE KNOTS

*** 5-PASS

*** 6-PASS



_______________


Added 2010 May 14th

Nautile's EXCEL Worksheet : this is an adaptation to VBA Excel of my HP48GX
program for  Turk's-HeadKnots ENLARGEMENT of Publication_3 ( see user's
 tips  there )


_______________


Added 2010 Sept 17th

IsoGridTracer©
Nautile's NEW PROGRAM that was written as experimental proof of the full
validity of the exploration of isogrid diagram that Nautile did :
a stand alone program
verified as working with  WINDOWS XP HOME ( SP2)  from 2005 Feb and VISTA PRO
 32 bits from 2008.

You will get isometric grids such as those for single strand and multiple strand knots made
on a Turk's head cordage route whatever  the coding but limited to
LEAD = 1 to 41  and BIGHT 1 to 26.

Download available here for
*** stand alone application ( Windows for sure, but may also
works with Linux and Mac with the .dll placed in the same folder.
*** User's manual

A tip = first download the User's manual and after reading it decide if you want to go for
that application.

Another tip = so as to by-pass Net filter the .ZIP file was renamed  .000 so once you have
it on your computer hard disk rename it back to .zip and open it with something like the
very useful ( and free ) 7zip

PLEASE SEND FEEDBACK about how it is working and with what OS.

present version is V-2-0 : this does the whole finished knot diagram 'at once'


ANOTHER FLAVOUR   IsoGridTracer© HPbyHP 
Here is the link to use.

This flavour draw the grid half-period after half-period at your speed while you are making
your knot.

version  V-2-0 == the current HP is in red while the already laid HP are put in black
The last laid HP stay in  red

versionV-2-1 ( retired ) == the last HP, at the next push of the button,  is draw in  black
after having been in red  in  the' finished knot' diagram.

present version  V-2-1-1  this one correct a small bug affecting the COLum-coded type
in the last HP in version V-2-1

Writing a multi-strand version.( GCD>1) for the HP after HP  is mathematically a whole
different kettle of fish !

Just give a swift glance at my old exploration of that in
Multi-strand Non Regular Knots algorithms
(some bad typing and awkward formulation or sentence I will have to put right - read it
again before putting the link and realized I  omitted proofing in the past-)

2010 Oct11th the multistrand version is working. Have to polish it for a stand alone
application.

VERY STRONGLY SUGGESTED READING:

on the Turk's Head cordage route :
THK AND MATHEMATICS  (mathematics made very easy to get, have no fear)
Part ONE
Part TWO

on Turksheads
- THK are NOT braid
- THK or NOT THK


 _______________
Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2012 -(each year of existence)

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