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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  1. Hmmm...that’s a good question. I guess it depends on how you define a magic square. For me, it is a square that builds a larger square, that builds a larger square, etc. The pathway outlined in your post can build rectangles as well, so I’d just call it an infinite pathway (since it’s not limited to squares).

    1. Good point, Robin, thanks :-) So you don't think the triangulation method or the diagonal pathway contributes to the magic square definition as was stated in the Craftree thread ?

    2. Yes, the triangular pathway also contributes, if you want to stay true to the original magic square from the Anne Orr pattern. I tried to honor this by using the same pathway for my magic squares.

    3. Thanks for confirming, Robin.

  2. Very interesting post, but in this case I think these are pathways ;)

  3. Thank you for figuring this "labyrinth" out. I hope if someone tries it, they will let you know how it goes.

    1. I hope so too, Lavi :-) The amount of time I spent on this (something new/different kept cropping up - I kept second-guessing myself) could have easily been used in the actual tatting of this mat ;-P

  4. Great magic square designs!! :)

    1. The continuous pathways let us avoid all that cutting and hiding ends after each motif, don't they! Thanks, Sue :-)

  5. It's always fun to avoid cutting and hiding and always fun to do a puzzle too these are great and very entertaining 🍃💛🍃

    1. Thanks, Carollyn :-) I enjoyed discovering the path ...

  6. Ah, that question crossed my mind too! But in any case, it's great to be able to tat the squares continuously.

    1. Jane, as I write out my post discussing magic squares & pathways, I was faced with a few more interesting questions. It is probably pedantic, but makes me understand better. Will share soon :-)