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 here. All 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.
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.
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.
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 !!!
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 !
