Free Pattern for Puffy Heart SRAW and LOVE Letters

So, there's a blog called Bead Love...

It's a blog of inspirations on love and beads, and a group of about 50 of us bead designers are writing it, one post per week for over a year, until we have all had a turn.  

This week, it was my turn to contribute.  So, here.

Tutorial - Bicone Bangle Bracelet Pattern Made with Seed Beads

This beading tutorial explains how to bead weave a bracelet with two sizes of Japanese seed beads and two sizes of bicone crystals. Use Swarovski crystals for a lot of sparkle! No fancy shapes required! The Bicone Bangle Bracelet is hollow and somewhat flexible, but if you reinforce your stitching, it will be stiff like a bangle should be. It measures 11 mm wide and 9 mm thick, 79 mm in outside diameter, 62 mm inside diameter.

This tutorial includes step-by-step instructions for weaving the bracelet into a continuous bangle.

This tutorial is designed for intermediate bead weavers. The weave is a variation on David’s Star, an angle weave like a cross between hexagon angle weave and super right angle weave. If you like angle weaves and want a new challenge, you’ll love this.

Thanks for looking.

Related Bead Stitches - Peyote Chenille Netting Herringbone Pondo SRAW

Here is a comparison of a few related bead weaving stitches, including peyote, chenille, netting, filled netting and herringbone. I needed to see them all together to get exactly how they are different and how they are similar, too.  So I drew this picture.

Netting and chenille stitches look very similar when they are beaded.  Chenille is a tighter weave than netting.  Chenille doesn't stretch the way netting can.  

After making the above drawing, I realized I left a couple of related stitches out, including SRAW and Pondo stitch. 

All four of these here are woven differently but look nearly identical when beaded. All four have the same beads in the same relative placements, but the ways the beads are connected with the thread is different. Another difference is that in Netting and Chenille, all of the blue bead holes are parallel to each other. In SRAW and Pondo, some of blue bead holes are horizontal and some are vertical. They alternate row by row. Netting is the fastest and stretchiest of the four. My personal favorite is SRAW because it's strong, and I can weave it in any direction. It's also pretty fast because you pick up 5 beads at a time on most stitches.

Happy Holidays!  Thanks for looking!

More on Puff Beads, a design for the beaded bead connoiser who loves right angle weave

I finished a new tutorial last week, called Puff Beads.  The Puff Bead technique is shaped Super Right Angle Weave (SRAW) with some embellishment to make it stiff.  I'm pretty sure that puffs are not the most visually beautiful jewelry I've ever created, but structurally, mathematically, they are quite nice... fascinating, really.  If you are a connoiseur of beaded beads, and enjoy making them as an intellectual activity, I think you will really enjoy making this design.  I think what makes Puff Beads interesting is that you bead the surface of a shape made out of cubes, in particular, a torus. I mean, who doesn't like doughnuts, right? 

But seriously, most beaded tori include the whole doughnut, including the volume on the inside AND the surface on the outside: the cake AND the frosting.  Puffs are just the frosting.  Certainly there are peyote stitched tori where you only bead the surface, like my Nuts and Washers below, but with peyote stitch, the beads sit so close together, you can't see through the beadwork.   

In comparison, when you bead just the surface of a doughnut with SRAW, you get a square lattice of beadwork with holes that let you see inside the doughnut, like right through the side. 

In particular, you can see the big hole through the little holes from all different directions, and I think that makes this technique rather unusual. Thinking further, one could apply this technique to cover all kinds of crazy surfaces made out of cubes, like these pink cuboids, for example.  I just learned that a shape assembled out of cubes placed face to face is called a "cuboid."

My tutorial is designed to teach you the theory behind bead weaving cuboids with SRAW, and I chose the torus as my explicit step-by-step project because I like the idea of beading a hole through the center of a sphere.  At the end of the tutorial, I also show examples of beaded beads using the structure in figure C above, with some discussion about how to apply the techniques to this cuboid design, but I don't give explicit step-by-step instructions for how to do it.  My goal is that after you learn how to build a torus, then simpler shapes will be easy for you figure out how to bead without me telling you every step.  That's my hope, anyway.

... because there is so much cool stuff you can build with cubes.  For example, you could use the Puff technique to bead weave the surface of a trefoil knot, like this beautiful wooden puzzle by Tom Longtin.

I'm not saying it would be easy, just possible.  (I just thought I'd throw that challenge out there to see if I get any takers.)  Of course, you could also build this knot with cubic right angle weave, like I did for my Highly Unlikely Triangle. That would also be nifty.  

So if you really love cubes, and you want to learn the Puff Bead technique, you can find the tutorial here:  https://www.etsy.com/listing/210844618/

And for those of you who just want to look at pretty pictures, or want some beads but don't want to make them yourself, I put this pink necklace up for sale, you know, just in case you like pink.  Thanks for looking.

Hyperbolic Surface Tilings Woven with Beads and Thread

I've been beading hyperbolic tilings all week, and I can't stop!

I've seen lots of people crochet hyperbolic surfaces, most notably at the Institute for Figuring.  The typically technique is to crochet around and around the edge adding lots of extra increases in every round to make the edges ruffle.  Beaders sometimes do the analogous thing, making ruffled bracelets and necklaces that incorporate increases on each round.  But for these beaded pieces, I'm doing something a bit different.  I use hyperbolic tilings, also called tessellations.

Flat Bead Weaving

But before I go on, I want you to understand what I'm doing, so I'm going to digress a bit.  Consider flat bead weaving, like you might use to make a bracelet.  For example, you might bead a flat bracelet by using a tiling of squares.  With bead weaving, you can place one bead on each edge of a square tiling, and you get right angle weave (RAW).  This picture shows a few different flat bead weaves and the tilings used to generate them.

The bottom illustration in the picture above suggests that you could use the square tiling to make a different weave from RAW.  In particular, you could weave four beads in a loop for each square, and then add one extra bead on the edges to connect the loops.  That describes super right angle weave, or SRAW.  (I call that an across-edge angle weave.)  If you've ever done RAW or SRAW, you know that four loops at each corner make the beadwork lie flat.

Round Bead Weaving

If you use loops of four beads with three loops around each corner you end up with a beaded cube (generally called cubic right angle weave or CRAW).  If you start with SRAW and weave three loops around each corner you get a the photo below (which I named cubic super right angle weave or CSRAW).  You can think of this as the across-edge weave of a cube.  (It's also an edge-only beaded truncated octahedron, but that's not important right now.)

Sorry, that was a lot of jargon I just threw at you.  Forgive me.  What's important here is that you have flat weaves that can go on forever like a plane (e.g., RAW and SRAW), and you have round beaded beads that close up on themselves (like a single unit of CRAW and CSRAW).  Mathematically, if flat curvature is zero, and beaded beads like round spheres have positive curvature, then it reasons to question: What beadwork has negative curvature?  Hyperbolic surfaces have negative curvature.  Intuitively, you can think of negative curvature as ruffles.  Mathematically speaking, ruffles are the opposite of spheres.  And flat sheets are in the middle.

Hyperbolic Surfaces

Hyperbolic surfaces are really interesting.  In fact, they have their very own hyperbolic geometry, quite different from the Euclidean geometry you probably learned in high school.  For one thing, in hyperbolic geometry, the parallel postulate is false. But what's most interesting to me, as an artist, is that there are lots of different ways to represent hyperbolic surfaces.  For example, this circle uses the Poincare disc model of hyperbolic space.

The square tiles are colored in pink, purple, blue, green and yellow.  That's right; those are squares (or maybe they're rhombuses).  I know they don't look like the regular squares you're used to, but that's just the Poincare model doing its thing.  Imagine that those four sided things are squares, and every black side is straight and the same length.  If you make this with bead weaving, you can make all the edges the same length.  For example, you could put one bead on every edge and weave a loop of 4 beads for each tile (an edge-only weave of the drawing).   I didn't do that.  Instead, I used an across-edge weave, something akin to SRAW.

In particular,  I weaved loops of four beads of the same color for each square (rhombus), and then attached the loops by one bronze bead on the edges.  Notice I used five colors just like the illustration above. The bronze beads are on the edges with the holes are perpendicular to the edges.  Here's another view of the same piece. 

And here you can see how big it is.  This little guy is looking for a new home if you'd like to adopt him: https://www.etsy.com/listing/188233621/

I used to think that a beaded hyperbolic surface looks like just a ruffled mess of beads.  I beaded a few in 2012, and I went to great length to try to bound them into symmetric submission by adding bigger beads into the folds.  Like this:

I showed this piece to Vi Hart, and she encouraged me to bead a different tiling without the extra big beads holding them in place.  That's why I beaded the...

Snub Tetrapentagonal Tiling

Ah, the beautiful snub tetrapentagonal tiling.  No, I didn't name it.  That's what everybody calls it.

Here is my beaded version.  I used pink beads for the pentagons, green beads for the triangles and yellow beads for the squares. Relatively speaking, this piece is flat-ish.  What I mean is it has less negative curvature than tiling one above.  I had to add a lot more beads before it started to ruffle.

Vi likes this tiling because it's chiral, which makes it unusual.  See the little pinwheels in the holes below?  If you look at the other side, you'll see the mirror reflection with the pinwheels spiraling in the opposite direction.

Then, I beaded the...

Rhombitetrahexagonal Tiling 

which I first noticed in John Conway's book, "The Symmetry of Things."  But I got this drawing from Wikipedea because it's in the public domain, and Conway's book isn't.

This is called the rhombitetrahexagonal tiling.  I didn't name this one either.  Notice the blue and green checkered stripes.  I like those stripes.  I wanted to emphasize those stripes in my piece, so I made the blue and green squares the same color.  They're all green in my beaded version below.  Maybe it's just me, but it seems a little peculiar to have a ruffled thing with stripes.  I guess you could make a ruffled skirt out of striped fabric, and then have striped ruffles.  Anyway, here it is. 

In my beaded version, I made the hexagons pink, and the squares green and purple.  The edges are a few different colors depending on which tiles they touch. Here you can see how big it is.  It's for sale so you can enjoy it in the comfort of your own home.

It's got a lot of personality, this little fellow. Now notice that this tiling has three squares and one hexagon around every vertex.  It's probably easiest to see that in the red, blue, yellow drawing above.

Let me say that again: three squares and one hexagon around every vertex.  So does this piece of beaded Faujasite have three squares and one hexagon around every vertex.  You have to be careful where you look to see that because some places appear to have two hexagons and a square.  Those are places where I stopped adding beads.  If I kept going and made this piece infinitely large in every direction, they'd finish with three squares and a hexagon just like the rhombitetrahexagonal tiling above.  (I'm going to need more beads for that.)  So, this piece below is a different representation of the same hyperbolic tiling right above.  Wacky. 

There are some fascinating artistic implicatons to that last thing I said.   So stay tuned, 'cause I'm playing around with that idea.  And if you actually made it this far, thanks.  You're awesome.

Beaded Super Right Angle Weave Quilt for a Group of Order 18

Here's my latest piece, a quilted wall hanging. The fabric is pieced cotton and silk, and appliqued with bead work. I call it, "Super Right Angle Weave: 18 Patches in 3 Colors and 3 Sizes" because I'm not very creative with titles. Florence suggested I call it "RAW Diamonds," which I like.  So that's it's artsy name. The whole piece measures 13 inches on a side. This quilt was included in Juried Exhibit accompanying the 2014 AMS Special Session on Mathematics and Mathematics Education in Fiber Arts at the Joint Mathematics Meeting in Baltimore, MD. It will be at the Ohio State Mansfield’s Pearl Conard Art Gallery from Monday, November 9 to Tuesday, December 8, 2015 in the Math & Art exhibition, "In the Realm of Forms." This quilt was also featured on the Scientific American website. This piece is SOLD

This piece began as a study in color for what I call Super Right Angle Weave (SRAW), a bead weave based upon the regular tiling by squares. Each beaded patch is 6 square by 6 squares of the tiling.  I weave loops of four beads in each square face and attach these loops across the edges of the tiling with a single bead between the loops.  For this set, I use a coloring with three bead types (two types for the faces and one type for the edges).  I chose three colors in each of  three sizes (albeit the purple beads are slightly different shades of purple across the three sizes), for a total of nine different bead types.  This set of 18 patches answers the following question: What are all of the possibilities if I weave SRAW with three colors, one color in each of three sizes, where the colors are arranged as shown?  The patches are arranged in sets of three, where each row uses the same three bead types, but arranged differently.  Here you can see it as a work in progress before I picked out the fabrics. (You can click on the photos to make them bigger.)

When I found the fabrics that matched the beads, I was delighted.  Each little square of bead work measures about 1 1/8 inches square. Here's a close-up of the beadwork. 

At some point, I realized my little patches formed a nice mathematical set.  When I arranged them in different ways, I found that the columns had things in common, as did all of the diagonals.  They formed sets in the sense that you could pick an attribute, and all three in the set were either the same on that attribute or all different.  It's like that game of Set, but my set has 18 cards instead of 81.  At some point, I realized I had a group of order 18.  Each element in the group corresponds to one patch of beading, up to automorphisms.  This group has two complete copies of 9 elements.  Within each set of 9, you can partition them into cosets vertically, horizontally, and along both diagonals. In other words, my arrangement shows different ways to build cosets with 3 elements in each coset (6 cosets * 3 elements =18). But if you group cosets across the two sets of 9, you only get 2 elements in each coset (9 cosets * 2 elements =18). 

A quick Google search told me there are 5 different groups with 18 elements, but I had no idea which one I found.

Lucky for me, mathematician Tom Davis was kind enough to help me identify which group of 18 elements this is.  After a few highly detailed emails, he concluded that it's the generalized dihedral group for E9.   Here's his argument:

I identified each patch with something like this...
Let me call the three colors Yellow, Green and Blue (Y, B, G), and the position attributes of say, the bottom point: yellow, green, blue (ygb).

Then each pattern can be classified by a 6-character code, like this:

(tuv)
(wxy)

Where t=largest, u = medium, v = small
and
w = bottom, x = left corner, y = other

Fore example,
(YGB)
(bgy)

distinguishes the size and position attributes.

Now, if we consider, say, (YGB) and (ygb) to be the "correct" order of the beads in both categories, then I can treat both the top and bottom parts of the pattern representation as a permutation away from the "correct" patterns. I can combine them into a single permutation, like (YBG)(gyb) or (BG)(gy) where you never mix the capital letters with the lower-case ones since size and position are independent.

Then your group operation is trivial: it's just the multiplication of the permutations, and (using Mathematica) I found that the total group size is, in fact, 18. (In other words, none of the multiplications take you outside of the patches you've made.)

So you CAN consider them to be group elements, but depending on which of them you chose to be the identity, the operation table would be different. I had Mathematica make a group operation table, but it translated the elements into numbers and here it is included as a screen snap.

It's clearly not commutative and it's not the dihedral group, so it's either the direct product of S3 and Z3 or the "generalized dihedral group for E9" whatever in the heck that is :)

I don't think it's S3xZ3. I've also included the screen snap for that (it's the one with the group named "dp" (but it could be: I'm not so good at comparing tables where the elements aren't necessarily listed in the same order).

In fact, it IS the "generalized dihedral group for E9." Here's proof. I had Mathematica draw the Cayley graphs of your group and of S3xZ3 (called "dp") and they're completely different. Included is a screen snap of the Mathematica result:

Now let's give Tom Davis a big round of applause.  Thanks Tom! 

Deltahedron Doughnut with CSRAW

Last year, I wrote a few posts on cubic super right angle weave.  Recently, I revisited this stitch to see what else I could do with it.  Here are 8 little connected cubes in the arrangement of a diamond-shaped doughnut.

It's made with size 11° seed beads in just two colors.

Here you can see a spinning one I got from Wikipedia.  This gif was my inspiration.  Nifty huh?

The shape is called a deltahedron, because all of the faces are triangles, and the capital Greek letter delta is a triangle. On my beaded version, each triangle corresponds to a loop with 6 beads (3 of each color).

 Thanks for looking!

Wisodom Mandala Pendant in Blue and Gold

Here's my latest pattern, the beaded Wisodom Mandala, named after the five Wisdoms.  Te photo shows the front and back of the same pendant. 

Playing with seed bead colors can be really fun and challenging. It took me a bit of practice to reliably get color combinations I like with the Wisdom Mandala, but I think I nailed it on this one.  For this mandala, I stayed within an analogous palette of blues, green and gold.  One side is basically just blue and gold, very simple.  The other side shows all three analogous colors: blue, aqua, and gold.  Staying simple helped make it work. 

One of my favorite things about making these pendants is that you get to use lots of different colors of beads, and you get two chances to get the colors to look the way you want.  By limiting my colors to I think I was able to get a harmonious design on both sides.  Nice.  See more Mandala Pendants here.

New Pattern: Beaded Wisdom Mandala

Here's my latest pattern, the beaded Wisodom Mandala, named after the five Wisdoms.

The Beaded Wisdom Mandala is a symmetric beaded pendant that is reversible. It is woven with two layers of seed beads throughout most of the piece except for an abundance of crystals that show through the windows of seed beads. The layering creates a pendant that looks different on each side. It has five-fold symmetry on one side, and nearly ten-fold symmetry on the other.

 The mandala hangs from a beaded tube with jump rings to make an easily wearable pendant. The 22 page pattern shows a variety of pendants in different colors, a few of which I show here.

Beaded Wisdom Mandala

In the pattern, I explain how to make the pendant and the hanging tube in three different sizes so you can make a complete necklace, like this Earthy Mandala Necklace. The mandala is woven with a combination of double outline stitch, loops, square stitch, and peyote stitch.  Here you can see one of my early Wisdom Mandalas, before I figured out how to link the mandala to the hanging tube with jump rings.

The hanging tube is woven with super right angle weave (SRAW) with embellishment.

I really love that the front and back are so different.  Measuring just 1 3/4 inches across, and the complete pendant is just 2 1/2 inches tall, they are pretty detailed for their small size. If you like playing with color (and size 15° and 11° seed beads), you'll love making these.  Thanks for looking!

Put beads on that felt

Every time I make felt, people say, "Put beads on it." So here, I put beads on it.

The beads are not sewn on the felt; they're sewn around it. Because they're beaded beads, they move up and down the felt. 

Here you can see the same pink bracelet with an earlier purple one.  I took this photo before I added beads.  I kept the purple one for myself because it's not good enough to sell.  It's too flimsy, in my opinion, because I didn't use enough wool.  

What's interesting about the design of the purple piece is that when I rewet it, I was able to reform it into a very different shape.  Below,  you can see the same purple bracelet on the top of this stack of bracelets. It was originally round.  That honey comb shape of the lace, it's that shape that allows me to deform the felt from spherical (positive curvature) to cylindrical (zero curvature).

If you rewet the pink bracelet, you can reform it so that the bars twist around your arm.  Neat-o.  Felt is really magical stuff.  Everyone I've taught to make natural wool felt seems to fall in love with the stuff.  Click the photos to see more.

Beaded Molecules: Menthol CRSAW

This beaded bead represents a single molecule of menthol with 31 atoms: 10 carbon, 20 hydrogen, and one oxygen. Each atom is represented by a single beaded cube made with cubic super right angle weave. The bead work is gray, black, white and red, just like standard molecular molecules, and exhibits tetrahedral bonding.

Menthol is an organic compound made synthetically or obtained plants such as peppermint. It is a waxy, crystalline substance, clear or white in color, which is solid at room temperature and melts slightly above. Menthol's ability to chemically trigger the cold-sensitive TRPM8 receptors in the skin is responsible for the well-known cooling sensation it provokes when inhaled, eaten, or applied to the skin.

The bead work is stiff yet flexible, and shows a variety of moods when posed. My favorite part of this molecule is the ring of six carbon molecules (called the cyclohexane conformation) with its 3mm hole visible in the photo below and its "chair formation" visible in the first photo.

This model has many other holes as big as 2mm to string it. It's hard to measure how big it is precisely, but it's longest measurement is about 2 1/4 inches (55 mm).  Here it is sitting on a quarter dollar.  It's for sale.  Click the photos.  Thanks.