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 in 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 !


  1. I enjoyed reading this! Ok, I think it makes sense to differentiate between magic square and magic pathway. Then the pathway need not necessarily lead to a square. And I'd agree that climbing out of a round in a doily is something different. It's useful to be able to follow pathways instead of joining motifs.

    1. Jane, I don't know when I'll have time enough to show that with the quatrefoil polygons we can create paths along tips rather than sides and mix different shapes in continuous paths and perhaps resulting in a larger fabric of a different shape.

  2. Makes a great read and well thought out😃

  3. I read the entire post, although I cannot claim to have really understood it! It is all so interesting, and you present the material in a logical and reasoned way. I have decided to print the post and study it slowly. It's the reason I enjoy tatting so much, these ideas don't sit easily with me and I can feel my brain stretching!

  4. Very interesting! Thank you for the lesson!! :)

  5. Ah, another interesting post! This is one I will have to re-read to fully comprehend. Isn't imagination wonderful?

  6. Very educative post Muskaan. You put lot of efforts to scrutinize ways of tatting. I understand that tatting a multi round doily in one pass with different techniques in itself has an infinite pathway (right term)☺️. Many times I struggled to get a perfect way to climb up to next round as I love non stop tatting. Yet to try a magic square to find a hidden magic path....

  7. Your theories are always very interesting to read and it shows that you have put a lot of thought and research into them! I agree that the name magic pathways is very fitting (I would also like to tat a magic square and find it a real mind twister). The one-pass doilies are pretty magical too! I wonder if continuing the motifs on such a doily, but mirrored (so no longer circular like a doily, but two motifs side by side), would work... Sort of like creating a zig-zag sequence?

    1. Lavi, I am not sure what exactly you mean by mirroring the motifs ? I'd love for you to explain a bit more, please. Do you mean we tat a zigzag 'line' then turn and go back and fill in the zigs with the zags - I mean crest to trough?

    2. I was thinking of connecting the motif from day 5 of the TIAS for example with the same motif but upside down. But now that I tried to sketch the result, it doesn't work, nor can it be tatted continuously. So not a good idea unfortunately...

  8. This is a good summary of magic squares and magic/infinite pathways. You know, I found another one of my old comments on Jane McLellan's blog post about magic squares...something about not being able to wrap my head around the concept at the time! I think it's because magic squares look really complex, but after sitting down, studying and tatting them, it's not so bad!

  9. Dear tatters, you have made my day(s)! I didn’t expect such interest and am truly thankful for your support.

    Sometimes, trying to arrange and organise the data into a logical yet ‘interesting’ sequence turns the post into a ‘lesson’ format (I look at it like solving a puzzle or maze) ;-P
    That was not my intention, because as I allowed the subject to marinate in my head and followed up on searches or peered over images, many new/hidden facets sprung up – small nuances that we generally miss. As we delve deeper, these percolate to the top :-D

    And we are not done yet! I am Certain the future will bring more pathways and discoveries from ingenuous tatters :-)

  10. Very interesting post, I enjoyed reading it, I am going to come and read again,
    I do intend to try Robins magic square at some point,

    1. Thank you Margaret :-)) Robin's patterns are all so lovely! If only I had time to tat them all...

  11. Great job, Muskaan - bringing together all the various threads of our discussions! I agree that doilies tatted in one pass and one-round doilies don't fit with the magic squares and magic/infinite pathways. They probably need a category of their own... :-)

    1. Oops, meant to click the "Notify" box. Now I have. :-)

    2. Thank you, Grace :-)))

  12. I am glad that my original thread about Magic Squares on Craftree has caused such interesting research and clarification of thought, muskaan. Nicely done. Add Archimedes geometric series to the list.

    1. Thank you, Judith :-)))

    2. You're welcome. Your entry is a suitable summation of the past 50 or so years of tatted lace and the quest to include continuous thread methods.

    3. Judith, thanks for the compliment :-) Appreciate it.