Friday, 20 April 2018

retreading the path

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magic squares, doilies and magic/infinite pathways - common threads VI.

This post is an exploration to satisfy the researcher in me. There is no absolute right or wrong – it is my perspective or thought experiment. Fair warning - walk away while you have the chance; or stay to humour me? ;-P A new thread in Craftree inspired me to retread the path.


So yes, the pathways in this earlier post were all just that – pathways – a sequence of working and joining motifs continuously without having to tie and cut after every motif. And for this we can use bridging elements or tweak the design to allow us access to next motif.
The magic pathways moved straight along column/row or moved in a concentric spiral. Therein lies one of the major difference with the magic square.

Ia.  Magic Square

I explained the magic square concept in my 2014 post hereAll the magic squares till then had been based on the original Ann Orr triangular corner design. Someone found that one could work continuously from one triangle to the next to create an ever-increasing square – hence the term ‘magic square’.

Last year new interest was generated with the incredible series of new magic square patterns that Robin has spawned, including the reverse/inverted squares. She adapted an existing square into a magic square by ‘breaking’ the square into triangles for a workable continuum. 
She shared her deconstruction of the concept and process in detail, inspiring others to join in with their own magic squares (eg., Jane McLellan and Ninetta Caruso). These also followed the original style of working and the original triangular pathway.

Thus the magic square, characteristically, is made of repeatable square motifs that work as “…building blocks…” (Robin) and follow a diagonal path (triangulation) resulting is as large a square as one desires. The square will get “…opened out just by turning the direction of tatting (Grace Tan), not by the application of bridging elements.


Ib.  Open-ended Motif or Transitioning Elements in Magic Square

There is one aspect that needs to be highlighted before I begin the next segment – the slight ‘asymmetry’ of each motif within the fabric. While working, one corner remains ‘open-ended’/different in order to change direction and continue to next segment. 

For instance, in the old magic square motifs, while 3 corners have chains, the 4th corner is made with rings in order to continue to the next section. Only the final fabric will have all 4 corners completed/identical (chains, in this case).  
Similarly the new squares needed some slight adaptation to transition into a continuous working path as in Konior's original square motif, and the Onion Ring magic squares.  

The reason this happens is clarified in Robin’s own words : You start with a formula (triangular pathway for magic square, or up and down columns for the table runner) and make the design work for that path. A one round square can be redesigned into a magic square, and now I’ve found a bookmark can be redesigned into a table runner.
(Notice that the bookmark is essentially a rectangle. It doesn't strictly adhere to the magic square definition since it follows the straight column/row magic pathway, and well, it is not a square to begin with). 

These transitioning elements are not merely functional, but visually appealing and create lovely patterns to break the monotony.

TIP : Incidentally, Jane’s magic square can be worked as a magic pathway, with each motif intact. Robin’s 2nd Onion Ring magic square can also work along a magic pathway with complete & symmetrical motifs because of the single outward ring which can be worked as a split ring. Clearly, a ring in the corner is an asset!


IIa.  Magic or Infinite Pathways 

During my Quatrefoil polygons, I discovered other pathways which would allow the tessellation to continue uninterrupted and create large fabrics in the same shape as the original motif. Thus I could trace paths for a triangle, square, pentagon, hexagon; and recently the Fortuna Square, by climbing out/in using split rings.

With so many shapes, Magic ‘Square’ seemed like a limiting term to me, hence I used the term Magic Pathways - there is magic in figuring out an infinite route :-)
At the end of the day, though, it is just continuous or one-pass tatting which can go on forever (hence Robin uses the term ‘Infinite Pathways’). During the writing/researching of this post and some recent discoveries, perhaps ‘Infinite Pathways’ is a better term than Magic Pathways. Yet I’d like to spell it out …

IIb.  Rationale for the term Magic Pathways : 

When we have shapes other than a square as a building block; use bridging techniques (climbing out/climbing in); and follow paths other than along the diagonal, then I like to call this one-pass or continuous tatting a “Magic” Pathway, because ….

1. it creates an immediate association to the essence of a magic square – that a large fabric can be worked continuously from the same repeatable pattern

2. it is magical that a simple substitution (eg. 2nd shuttle instead of ball, split ring/chain instead of regular ring/chain, perhaps simply switching shuttles, etc.) can allow us to tat infinitely

3. the straight/zigzag and/or spiral pathway is not limited to a square – depending on the pattern of the motif any geometrical shape/polygon can be tessellated into a large lace fabric. eg. the quatrefoil triangle, pentagon, hexagon and Robin’s mat and hexagon from Dillmont’s triangle. 
  
4. it is magic to puzzle over and trace out a continuous sequence keeping the original motif intact - without changing, tweaking, or redesigning an original motif or creating any transitioning motif.

Future idea : 2 different motifs tessellated alternately/side-by-side through a magic pathway. Note that the transitioning part of the magic Squares tend to automatically create a different motif in the center of 4 motifs.

I hear you ask - If a magic pathway is simply one-pass tatting then wouldn’t a doily worked in one pass also qualify? Hmmm….

IIIa.  Is the magic pathway different from a One-pass doily?

We frequently use climbing out techniques (split rings, split chains) when working on a doily, even if not specifically designed. So if we can complete a multi-round doily in one pass, does it become a magic pathway? After all we are moving in a spiral pathway whether the doily is circular or angular.

I don’t have a clear-cut answer for this. But my guess is ‘not exactly’?

To me, part of the difference lies in tessellation : motif v/s medallion. Each row of a doily comprises of repeatable motifs while the magic pathway is for medallions that we use as motifs. Medallions are standalone complete designs, and the magic pathway allows us to join them continuously and repeatedly to create a large fabric in the same shape as the original medallion and the same pattern as the constituent.

Further, even if we use the same motif in All rounds, we may have to change the stitchcount to prevent cupping or ruffling especially in a round/oval doily. In magic pathways, there is absolutely no change in stitches.

Future idea : It will be interesting to convert a circular medallion into a magic pathway.

IIIb.  What about more elaborate one-pass doilies?

Remember these doilies that are specifically designed to be worked in one pass such as Iris Niebach's TIAS doily and tattingweed's Crinoline Doily?
These take a long serpentine and circuitous route through multiple ‘tiers’ with each repeat, to complete the tatting in one pass. German tatters such as Endrucks designed elaborate one-pass doilies. These do appear magical to even design, let alone tat! 

But these are logistically and practically limiting. Inevitably, there comes a full stop. It cannot go on or be tessellated infinitely. So while magical in itself, it does not conform to the above concept. Or perhaps it is a 'magic' pathway, but not an 'infinite' pathway !!!  


To conclude :

  • Magic Squares and Magic/Infinite Pathways allow us to tessellate infinitely to form larger and larger lace fabric working continuously without snipping off.
  • Almost any square medallion can be modified/redesigned into a magic square, but not all medallions will allow a magic/infinite pathway.
  • In the magic square, one first selects the formulaic diagonal path and ‘fits’ a square medallion to tessellate infinitely; in magic pathway, one selects a polygonal medallion and then figures out a continuous pathway. 

I was amused to read Robin’s comment here. How far she's travelled, now leading the way :-) And only a few days back I rediscovered her Dillmont inspired mat & hexagon where she has already outlined the pathways that I spoke of during the Quatrefoil series and diagrammed in the Fortuna Square!

If you have, thanks for reading. It validates my effort ;-)
I invite you to share your views.


All paths lead to Tatting !

Monday, 16 April 2018

make me pretty please

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Still waiting patiently but the butterfly has not shown up yet. Instead of losing hope, I decided to have some collective fun while we wait.

Ready for a bit of fun to empty your shuttles and use up scrap threads ?

Here's a little pattern - with only 4 rings and a couple of chains. I wasn't going to show a diagram or tatted model, but then succumbed in the fear that you might start throwing your shuttles at me... wouldn't want you to lose or break them now ;-P Hmmm, but I could possibly start my own shuttle collection then - now there's a thought! Bring it on, then ...

The working order and stitchcount is diagrammed on the right (above). 

And below is the written pattern for the ‘skeleton’ -
For directional or fs/bs tatting, rings are worked frontside and chains backside.

“make me pretty” butterfly fun pattern
          
        One shuttle and ball, CTM.
A-Ring : 6 vsp 10 rw
B-Chain: 14 – 3 rw
C-Ring : 4 + (to vsp) 18 – 2. dnrw
D-Ring : 2 + (to C) 18 vsp 4 rw
E-Chain: 3 + (to B) 14 rw
F-Ring : 10 + (to vsp) 6.
         Tie and cut.

I would love for you to decorate this ‘skeleton’ as your heart desires - with picots, beads, or what have you. Be a designer and choose your style & placement of picots, beads, accessories, and colours.

Update: For a list of options, inspiration, and tutorials/resources, please check out Eliz Davis' incredible compilation - An Element-al Approach to Tatting Techniques.

You can post a pic on your blog, social media site, etc., but please do send me a link so that I can share it with everyone.  Or you can email (on my profile page) a pic and I will upload it here.

Do you feel inspired to join? I hope so …
Let’s fly together ! 


Friday, 13 April 2018

magic pathways for fortuna square

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On seeing the Fortuna Squares tessellated into a coaster/mat, I was asked whether it could be worked as a magic square. Always up for a challenge especially puzzling out a maze!

Yes, it can be worked continuously and infinitely using only split rings! You can make it as large as you want. And you can choose between two easy pathways, neither of them diagonal! Moreover, the square motif is completed before moving to the next one, making it easy to keep track.

 Magic Pathways for Fortuna Square
Pattern is Fortuna Square by Henna J Hwang for Tat a Brussels Monument in Pink.

   If you want a pdf download of this notated pic, please let me know
Disclaimer: Since I haven't actually tatted the lace fabric, despite spending hours mentally figuring it out, you might find a mistake or surprise - please do share your feedback with everybody. 

  • Notice that the very first square (red) starts with 2 back to back inner rings and has a single SR to climb out.
  • All subsequent squares will have 3 split rings and are basically worked like the 2nd square (blue) .
  • This numbering sequence (red/blue) follows directional (fs/bs) tatting where the inner rings are worked backside. I chose this because I find it easier to work & keep track of such patterns when worked clockwise. Note that here the motif itself is worked clockwise.
  • The numbers in orange & yellow are for traditional tatting. Notice that tatting is counterclockwise for first motif and when we climb out, the next squares and pathway will follow suit.
But we need we need to decide which path to take after climbing out of the 1st square.

Pathway #1 : Along a Straight Line (pink arrows)
This pathway is ideal for a large rectangle. 
Fig 1
Fig 2
We can continue upwards along a column/side to desired length, then move to the right, tat a square, and move down, joining to the motifs in the previous column. (Fig 1)
Eg. the red/blue numbering with backside rings in fs/bs tatting. 
Instead of up, if we work the 2nd square to the left of the 1st one and continue down this side, then we will be adding new motifs along a row. At the end of row, make a motif to the right and move back down the row. (Fig 2)
Eg. the orange/yellow numbering in traditional tatting.

Thus we can move up & down in columns and new motifs will be added to the right; or we can move across in rows and the fabric will increase downwards.

TWoT Notes : If the first square motif is worked in clockwise direction, then the column pathway will move from left to right. If it is worked in counterclockwise direction then the pathway will move from right to left.
Opposite is true for the row pathways.

And here’s an interesting observation : After completing one pair of columns/rows, we will need to switch the way we do the elements for the next pair of columns/rows. So if we started with shuttle1 as the dominant shuttle for 1st & 2nd columns/rows, when we turn back for the 3rd column/row, shuttle2 will become the default in next pair; and back to shuttle1 for next two .... 

Pathway #2 : Along a Spiral (green arrows)
This pathway is ideal for a large square.
Fig 3
Fig 4
Here we tat squares 1 & 2 (red/blue) as notated in the main image, then instead of moving along upwards, we move to the right to work the 3rd square, and again to the right to work the 4th square, joining back to 1st square. We now have a larger square made with 4 motifs! (Fig 3)

Continue on to the right of 4th motif and then around the four squares as shown in the grid. The next round will have 16 motifs, and this can continue infinitely in an ever-increasing spiral.

For the orange/yellow squares, the spiraling movement will be counterclockwise. (Fig 4)

TWoT Notes : If the first square motif is worked in clockwise direction, then the spiral will also move clockwise. If it is worked in counterclockwise direction then the pathway will move counterclockwise.

Here is a trial of the Quatrefoil Square magic pathway (scroll down to end of post) using this spiral method. 
Note that each individual square motif is worked in clockwise direction, and so the larger 4-square fabric also follows that clockwise spiral, starting from bottom right. 



Now the question arises - Are the above fabrics magic squares or simply pathways? I will discuss this in my next post, and after that there's an edging/necklace pattern that I'm working on.
till then, happy tatting always :-)

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