Tag Archives: fractal

Pattern: Tatted bubbles

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Four repeats of the motif, starting and ending at the center of the left-hand side.

I am terrible at naming things. It may show in this post. However, I am at least a little better at coming up with tatting patterns. Today I want to share another tiling, lies-flat design that is entirely my own invention. The repeat unit is a square that the thread enters and exits on opposite corners (more discussion of why this is cool, and fractal tatting, here). It’s a little more complicated than my other square tatted tile, and involves a (perfectly simple) technique that I haven’t seen anywhere else in tatting, which I will walk you through after giving the bulk of the pattern.

Motif:

  1. Chain 4ds, shoelace trick sometimes (discussion below)
  2. Ring: 6ds, picot or join to a neighboring motif, 6ds, picot A, 6ds, picot B, 6ds
  3. Chain 4ds, picot or join to neighbor, 4ds, shoelace trick always
  4. Ring 6ds, picot or join to neighbor, 6ds, picot or join to neighbor, 5ds, picot C, 7ds
  5. Chain 4ds, join B, 3ds, 4 single stitches on the same side (discussion below), 3ds, picot D, 4ds
  6. Ring 7ds, join A, 5ds, picot or join to neighbor, 6ds, picot or join to neighbor, 6ds, shoelace trick always
  7. Chain 4ds, picot or join to neighbor, 4ds
  8. Ring 6ds, join D, 6ds, join C, 6ds, picot or join to neighbor, 6ds, shoelace trick sometimes
  9. Chain 4ds, picot or join, and continue straight into the chain beginning the next motif

Shoelace trick: the shoelace trick is a single overhand knot, used to switch the positions of the ball thread and needle thread. This is used to make chains curve “backwards” from how they would otherwise. If you want, you can achieve this with two needles/shuttles instead, which if you work with different colors on the different shuttles could give some neat effects with patterns like this.

Where I say to shoelace trick “sometimes”, that depends on how you want the motifs to join together. If you are just plain-old rastering—making one row of motifs, then coming back and making another row of motifs—the shoelace trick is only used at the ends of the rows, on both sides of the chain from the last motif of one row to the first motif of the next. You can make more elaborate patterns, fractal or otherwise, by choosing when to make a shoelace; a shoelace at the start of this connecting chain changes the location of the next motif (by deciding which way the chain faces) and a shoelace at the end of this connecting chain changes the orientation of the next motif (whether the wavy chain down the middle is vertical or horizontal). The swatch shown below was made by simply rastering the motifs, but alternating their orientation from one motif to the next.

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Piece with motifs alternating orientation. Note that the bottom-right motif is not flipped; the decision to alternate was made after the second motif was started.

4 single stitches on the same side: If you’re familiar with making friendship bracelets out of embroidery floss, you probably know this as a Chinese staircase, or two repeats of the basic knot. It also bears some resemblance to the Josephine knot in tatting, although I am using it for an entirely different purpose. The goal of these four stitches is, like with the shoelace trick, to switch the direction that the chain curls. Unlike with the shoelace trick, this does it mid-chain. Unlike the Josephine knot, you should not be trying to persuade the stitches to lie flat; you actually want them to process around the needle (or the thread, in shuttle tatting). It doesn’t matter which single stitch they are—the first half of a ds or the second half—so long as they are all the same; the stitches will have a natural direction that they progress around the needle which depends on which stitch you are using. One caveat is that I have only tried this with one thread (#10 cotton), one needle size, and my own crafting idiosyncrasies—so if you are finding that four stitches takes you too far around the needle or not far enough, please feel free to change the number of stitches, adjusting the number of ds on either side so the total chain length stays the same.

Joining motifs together: Each motif has two picots along each side, plus the one made in the joining chain; these line up (pretty well, at least!) no matter how you orient the motifs, but depending on your particular arrangement of motifs may join chains to chains, chains to rings, or rings to rings. For that reason it’s a little hard to write up a pattern, but just join to the closest picot, keeping the piece flat, and it should all work out.

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Pattern: Tatted tiles

100_0963 (903x1024)Today’s pattern is one of my favorites; it comes from the Encyclopedia of Needlework by Therese de Dillmont, via Project Gutenberg. I love sifting through these old pattern books, which you can find by image-searching for tatting patterns and then clicking the black-and-white pictures; the Antique Pattern Library is another great resource. In particular, this pattern is based on figure 511; I made some alterations including working out how to turn corners and modifying the scalloped edging part a bit. I will also talk about using this pattern as a fractal-tatting motif (see also this post). It is also where I got the inspiration for the headband pattern in this post.

The basic motif is: Ring 6ds, large picot, 6ds; chain 6ds, picot, 6ds;ring 6ds, join to first ring, 6ds; shoelace trick and repeat. By “shoelace trick” I mean tying a single overhand knot with the ball and needle threads, switching their positions, so that the next motif has its rings facing the opposite way than the first motif. In this way you can build up a strip of arbitrary length, like:g4083where the short, thin lines and the small circles are picots (and large picots, respectively); the ovals and arcs are rings and chains. So far so good, and by itself this already makes a nice, small edging. The Encyclopedia suggests making a strip in the desired length, then cutting the thread and making another strip, joining rings to rings and chains to chains along one side, repeating to desired width, and then adding a fancy scalloped edge.

bottom (1024x768)Fancy scalloped edge: Follow the Encyclopedia if you prefer, but I have modified the pattern to omit the non-joining picots. Begin with a Ring 5ds, join to a pair of rings, 5ds. Chain 2ds, picot A, 3ds. Ring 6ds, join to a chain, 6ds, picot B, 6ds, slightly large picot C, 6ds. Chain 3ds, join A, 3ds, join D (omit or picot in first motif), 5ds. Ring 5ds, join C, 5ds; chain 12ds; ring 5ds, join C, 5ds. Chain 5ds, picot D, 3ds, picot E, 3ds. Join a chain to a picot on the wrong side, as follows: either simply pass the needle through the picot, use your fingernails to form a cow hitch in the picot on the needle and pass the needle through, or use the needle to tie a cow hitch in the needle thread on the picot. The first is easiest to do, but if you pull your chains tight it will tend to pull into a smooth curve, whereas you want the chain to bend sharply backwards here; the other two methods are tricky but in my opinion worth it. Chain 3ds, join E, 2ds. Repeat from start. If your strip of edging ends on a pair of rings, finish on a ring 5j5; if it ends on a chain, omit picot B from the large ring, and finish on the first small ring that joins picot C (as shown).

One thing I hate in tatting patterns is cutting the thread and starting a new piece, so the first thing I did with this pattern was figure out how to corner:g3910-1-1It’s a little awkward and requires additional shoelacing, but lies reasonably flat. After you have made however many repeats you want (in my project, this was the height of the purse), finishing with a shoelace, make a ring: 6ds, picot, 6ds. Shoelace again and make a chain: 6ds, picot, 6ds; and a ring: 6ds, join to most recent pair of rings, 6ds; shoelace. Repeat these steps once more, and you are ready to begin working back along the first strip, joining rings to rings and chains to chains.

Constructing the purse proceeds as follows: Make a strip as long as you want the purse to be tall. Corner and build up new rows until you have a piece as twice as wide as you want the purse to be. Finish by joining the last row to the first row, forming a tube. Cut the thread (yes, I know!), and add a top flap by joining the first row to one side of the top edge; if you had more foresight than me you could do this by simply making one side of the bag longer than the other in the first phase of construction, although this forces you to have an even number of repeats in the width. Add a strap by making two long rows, joined at the ends to matching rings and chains in the top corners of the bag. Add decorative scalloped edging on the end of the flap and the bottom of the bag, using the one on the bottom to close the bottom edge, joining into two picots at once.

You may notice a couple things about the cornering: first, it adds a new row on the side that the last pair of rings face; in a flat piece that rasters back and forth this means you will have an even number of whole motifs. Second, the cornering procedure adds a half-motif of width; if you are making a tube you will have to make all the later rows a bit wider than the first, then come back and finish the first row at the very end. In a flat piece, though, you can’t come back and fix it—so we need a new way of thinking about the motif.Instead of the ring/chain/ring/shoelace motif, which is basically a square with the thread entering and leaving at the center of opposite sides, what if we think about a motif of half-chain/ring/shoelace/ring/half-chain? This adds a half-motif at the beginning of the row, and the corner is simply a couple of motifs with an extra shoelace thrown in and doesn’t have to be broken down into its constituent parts. To my mind this is a little harder to see at first, but a lot more elegant than the original motif.text3085-4-3The revised motif pattern is chain 6ds; ring 6ds, picot or join, 6ds; shoelace; ring 6ds, picot or join, 6ds; chain 6ds; with shoelaces between the rings and chains as needed to make the corners. This also makes the motif a square with the thread entering and exiting on opposite corners—which is a much more interesting beast. Fractal diagramSquares that connect on their sides can be tiled in one direction, but squares that connect at their corners can be tiled in two dimensions, and can be tiled fractally. Consider the image at right; the thin lines are the sides of a square motif, the thick lines connect the corners that the threads enter and exit on, and the numbers are the order in which the motifs are made. A large square can be made up of nine smaller squares, and the large square is, again, a square with the thread entering and exiting on opposite corners. The motif has to be altered a little bit to allow cornering, because tatting chains have a natural curve to them, but not by much.

A variant on this fractal pattern can be created by omitting the outside ring on the cornering motifs; I tried this purely because the double-shoelaced ring is a little awkward and doesn’t want to lie flat. The result is:

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which started in the top-right corner (omitting the starting half-chain and first ring) and makes a square of 81 motifs (nine blocks of nine motifs) before starting on another (the tail on the bottom left). It makes something of an interesting pattern, but I think in future I will keep the outside rings.

Random note: the pattern I gave has a lot of units of 6ds, and is suitable for smaller threads; if you are working in larger threads, you may want to do 8ds or even more every time I called for 6. The purse is in a nominally size-10 thread, but I think is mis-sized, and using a smaller needle; the flat fractal piece is a more standard size-10 cotton with a #5 needle, and I used 8ds-picot-8ds rings.

Fractal tatting 1

fractal_2

First up: if you don’t know what fractals are (or if you do, for that matter) don’t be scared! It’s a pretentious name for a pretty easy concept.

Difficulty: I will assume comfort with basic tatting, including rings, chains, picots, joins, etc. You will also need pretty good spatial reasoning, depending how big an object you want.

Notation: I use a pretty aggressive shorthand when writing up tatting patterns for myself. A very simple edging pattern might be: “R6j6p6p6, C6b6, repeat”; R and C of course stand for Ring and Chain; the numbers indicate numbers of double stitches (ds); p means picot, j means join, and b means a picot with a bead on it. Joins before any picots join to the previous iteration of the pattern, so the first time you do the repeat unit, do picots where it says j. For more complicated patterns, I will give the p’s and j’s subscripts, so jA joins to picot pA and so on. I like this shorthand because it fits on a card small enough to fit in my tatting carry-case, but will give long form as well in the blog.

Today’s pattern is actually a set of very simple procedural rules. With them, you can generate flat 45-45-90 triangles or squares of arbitrarily large size, suitable for doilies or shawls or purses or whatever. It is made of three elements: the basic motif, the turning ring, and the turning long chain. Chains and rings in this pattern always connect in the usual way, i.e. you never need to swap threads/change shuttles.

If you want beads, thread a bunch onto your ball thread before you start. I make beaded picots by simply sliding them up the ball thread onto the picot as I make it. There are other methods involving joined picots, but that is not how I am beading today. If you don’t want beads, simply omit them, either replacing “bead” in the pattern with a decorative picot (never join to them) or omitting entirely.

Basic motif (M):

  • Short pattern: R6p6p6, C4p6b6p4, R6j6p6.
  • Long pattern:
    • Ring: 6ds, picot or join to another motif, 6ds, picot A, 6ds.
    • Chain: 4ds, picot or join, 6ds, bead, 6ds, picot or join, 4ds.
    • Ring: 6ds, join to picot A, 6ds, picot or join, 6ds.

Whether you picot or join, where unspecified, depends on where in the overall pattern you are, and will be noted later.

Turning stargate [ring with legs] (S):

  • Short pattern: C4, R6p6p6, C4.
  • Long pattern: Chain: 4ds. Ring: 6ds, picot or join, 6ds, picot or join, 6ds. Chain: 4ds.

Turning long chain (L):

  • Short pattern: C4p6b6p4.
  • Long pattern: Chain: 4ds, picot or join, 6ds, bead, 6ds, picot or join, 4ds.
MSMLMSM

Diagram-style tatting pattern showing an MSMLMSM repeat; M motifs in red, S in blue and L in green.

I am using size 10 crochet thread, a size 5 needle, and size 6/0 glass beads. If you use a different combination of materials, you may need to alter the chain lengths to get it to lie flat–particularly the middle segments of all the long chains, which is currently 6b6.

Now we have three basic elements, we need to connect them into a larger whole. Using the abbreviations above, if you tat M-S-M (all connected; don’t cut your thread!), you will get two motifs sitting chain-side to chain-side, connected by this stargate piece. If you join the first picot of the chain in the second motif to the last picot of the chain in the first motif, it should sit flat. If on the other hand you were to tat M-L-M, the two motifs sit ring-side to ring-side, and joining the first and last ring picots in the second motif to the last and first picots in the first motif should be natural. You can imagine building up larger pieces in this way: M-L-M-L makes a small cloverleaf with chains on the outside, M-S-M-S-M-S-M-S makes a larger square with rings sticking out. (MSML)x4 makes a bigger box, and so on.

One of these arrangements is special, and now comes the time for some mathy talk. It’s special because it’s a fractal–that is, it’s self-similar at different length scales. Technically this kind of fractal should be infinite in extent, but since I don’t actually have infinite thread, time or patience, I’m going to ignore that requirement. Self-similarity is interesting, though, and can give beautiful results. It is also what’s known as a space-filling pattern; fractals like the Mandelbrot set that you may be familiar with have these gaping holes in the middle and a background where nothing is going on, but space-filling fractals (and other space-filling curves) fill up all available space.

The special arrangement is this: tat MSMLMSM. Name this pattern N, N=MSMLMSM. Now you could continue tatting: N(the piece you’ve made)SNLNSN. Notice that’s the same sequence of motifs and turning pieces, just the motif is bigger. If you want, continue this pattern: name O=NSNLNSN, and tat OSOLOSO. Note you are quadrupling the size of the piece with every step, so doing this many layers is a pretty serious investment of time. But you can see what’s going on by doing a little tatting or a little drawing.

overlay

Photo of tatting sample with diagram overlaid, showing the self-similarity. The sample contains 32 M blocks, or 8 N blocks, or 2 O blocks. There are some extra beads along the bottom edge relative to what’s in the pattern; please disregard.

Self-similarity just means that different parts of the object are the same as (or at least similar to) each other. All of the M units are the same, because you do the same steps to make each one. Self-similarity at different length scales is a bit more special–this means that different-sized parts of the object are the same. Motifs M and N and O are similar, despite being 4x as big or small as each other. That is, they are all 45-45-90 triangles, they all have chains along the hypoteneuse (long side) and rings along the legs of the triangle, and they all connect to their neighbors in the same way. You may protest that M is more of a circle than a triangle, which is true, but if you include half of the turning pieces on each side, it looks more triangular, and it takes up a triangular space in the larger pattern.

As the piece gets larger–MSM or MSMLMSM will be plenty–you start to see the 45-45-90 triangle pattern emerge. Another way to think about this special arrangement is this: you make a 45-45-90 triangle. If there are chains on the hypoteneuse of the triangle, do a long chain and repeat what you have done so far. If there are rings on the hypoteneuse, do a stargate and repeat what you have done so far. Your thread will always be coming out one of the sharp corners of the triangle, and you will always do what’s necessary to reflect around the closest short side and repeat what you’ve done. No matter how big your triangle gets, this is always always what you do to make it one step larger.

Bonus: you can make this arbitrarily more complex; (M=R6p6p3p3,R3j3p6p3p3,R3j3p6p6; L=C12p9,R3j3p3,C9p12; S=C12,M,C12) joined in MLMSMLM fashion for instance has clover-leaf motifs joined into dense clusters, in the same fractal framework. For the love of whatever, though, don’t try this until you’re comfortable with the way the normal one joins.

clover_lace

Clover-leaf fractal pattern. I wanted to see if it would lay flat right away, so it’s not exactly fractal–disregard the first two clover-leafs in the bottom right. Be warned that large, obvious cross patterns appear as you continue.

Disclaimer: this pattern owes a lot to finding this but because I am not a member of intatters I can’t linkfollow and give proper attribution. It’s not quite the same, as I’ve changed numbers around to fit my own aesthetic purposes and run away with the fractal concept.