gwenbeads

Topological Surfaces in Felt for the Math Nerd in You

2012-02-12T12:59:00.000-08:00

You probably don't know this about me, but I love math jokes. I collect them like I collect beads. Unlike most people, I think they're funny, or at least, I think they're fun. There's an old one that goes like this: Why should you never have breakfast with people who study topology? Because they can't tell the difference between a coffee mug and a doughnut. While this joke probably is not very funny, it does illustrate a nice point. Topology is the study of "properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing." In other words, if they were made from soft clay, you could deform a coffee mug into a doughnut without any cutting.

I've seen a lot of people make topologically interesting objects from metal, wood, rigid clay or plastic, knitting and crochet. But I think felt is a better medium to make topologically interesting objects because the felt is stiff, seamless and flexible; so they hold their shape, but you can still fold them and flip them inside out, like the one I'm holding below.

Since I was just making felted wool cuffs, I decided to make some topologically interesting objects, too. The first set below are all topologically equivalent to a Mobius band with an extra hole. Like a Mobius band, each piece has one face, but the extra hole gives them all two edges. Each can be theoretically deformed into any of the other two. In mathematical terms, each of these surfaces is homeomorphic to the other two.

Just like a Mobius band, each piece in the second set (below) also has one face and one edge. However, these are not Mobius bands. I don't know precisely what they are, but I know they're not that. They're a little more complicated, like a Mobius band with a strap attached.

The brownish piece on the top right was just screaming out to be shrunk down and made into a finger ring. So I made a ring in pink and purple wool, and added some seed bead embroidery to make it look nice.

Topology for your finger.

Then, I decided to do some homework to see what other surfaces I could make. I made this pair of Siefert surfaces of a trefoil knot. In other words, the edges (or holes) of these little guys form a knot and they each have two faces instead of one. As you know, most holes in every day objects are (topologically equivalent to) circles. So, a knotted hole is a very strange kind of hole, indeed! The one on the left is a little bowl with a funny handle.

For this pair, I wanted to see what the edges would look like if I trimmed them with scissors. I think it makes the edge a little more pronounced, but also slightly less durable. It also let me make them a little more symmetric because I could trim off the wonky bits. They're still very durable, but they might fuzz a little on the edges if you fiddle with them for a while, but I'm sure they won't rip with normal usage. I'm not sure what "normal usage" is for such things. I'll leave that up to you to decide.

They are art. They are also mathematical models. They are plushy mind games, cuddly toys for your brain. These are all available in my Etsy shop. Click on the photos to see the listings.

Chaos & Order Day 10

2012-02-11T10:28:00.000-08:00

Yesterday was a good beading day until I got to the end of the bottom right corner. I'm having a hard time gracefully joining the different patterns there. So I decided to put that off until another day.

In case you're wondering what I'm going to do with it, here is my first post. I want it mounted on pins in a shadow box case where the bead work is removable. I need to hire a professional shadow box maker for that. Anybody know a skilled carpenter/ framer in the Bay Area?

Chaos & Order Day 9

2012-02-09T23:59:00.000-08:00

Day 9. I made it to the right border. Now to just fill in the spaces...

Here is a link back to Day 8.

Felt Cuffs in Blues and Greens

2012-02-08T12:39:00.000-08:00

Yesterday was cold and rainy, so I made felt cuffs. I like making felt when it's cold outside because the wet felting process uses lots of hot water, and it warms me up.

I added a few seed beads to the first pair to give them a little more texture. I am very tempted to keep these for myself because they go with half of my wardrobe, but alas, a girl's gotta pay her bills. So they're in my Etsy shop.

I also made a lime green and aqua pair that reminds me of the colors of the ocean. Click on the photos to go to the listings.

New Octahedral Cluster Kit

2012-02-05T12:49:00.000-08:00

We have a new kit available for the Octahedral Cluster Beaded Bead. It's got some pretty marbled pink seed beads and a black lace overlay. I call the color scheme "Black Lace Rose." This is still one of my all-time favorite designs because it is so round and symmetric. I still remember the day I designed the very first one back in the Spring of 2005. I had already patterned the Seven Sisters beaded pendant, with a big 7-star on the front, and I wondered if I could make a beaded bead with 4-stars, six of them oriented like the faces of a cube. For a long time, I had no idea if this new beaded bead design was a cube or an octahedron, but I later decided that it was an octahedron because for the 12 largest beads, their holes lie on the edges of an octahedron. I also made a couple different versions of a Cube Cluster, but I never liked the way the beads fit together in that version. The beaded bead was squishy and the shape was not as round as I like.

Last Fall, I was asked by the editors of Beadwork Magazine to submit a beaded bead design for their contest on beaded beads, and at that point, I reworked the Cube Cluster design until I got something nice and round like the Octahedral Cluster, but significantly larger. In the April/May 2012 issue of Beadwork Magazine, I will finally be publishing my pattern for the Cube Cluster Beaded Bead. So keep an eye out for it.

Chaos & Order Day 8

2012-02-03T00:18:00.000-08:00

I'm still beading along on my commission. I added some new stars on the bottom right.

Here's the lengthwise view. It's approximately six inches wide here and maybe a foot long. I'm about two thirds done.

Here is a link back to Day 7 and forward to Day 9.

Chaos & Order Day 7

2012-02-02T10:45:00.000-08:00

I didn't get too much done yesterday, but there's a bit on the bottom right and top.

Here's a close up of the super right angle weave in three different sizes.

Just in case you just showed up, here is a link to my first post about this commissioned piece for flat beaded angle weaves.

Here is a link back to Day 6 and forward to Day 8.

Chaos & Order Day 6

2012-01-31T10:42:00.000-08:00

More super right angle weave...

Here is a link back to Day 5 and forward to Day 7.

Chaos & Order Day 5

2012-01-30T10:53:00.000-08:00

I'm intentionally adding some negative space on the left, those two big squares. I also finished the edge on the right. I decided not to have too much of the lacy bits meet the edges. The denser stitches provide a border both visually and physically.

Go back to Day 4. Go forward to Day 6.

Chaos & Order Day 4

2012-01-28T00:13:00.000-08:00

Here is my Day 4 progress on a commission for a large, flat, beaded angle weave art piece that I showed you a few days ago. I thought I'd try photographing it with a black background.

If it were a bracelet, which it isn't, but if it were, here is what it would look like.

Here is a link to Days 1, 2, 3, and an explanation of what I'm doing.
Or maybe you want to go on to Day 5.

New Ring Nebula Kits

2012-01-27T10:55:00.000-08:00

We have a new kit colors scheme for our Ring Nebula pattern. I call it Metallic Rose because it's got some nice warm pink and burgundy beads in it and a whole bunch of silver and bronze.

The first six people who order this kit will also receive a free silver pressed glass ring. I would have put them in all of the kits, but I bought all that they had. The color and size matches the Ring Nebula perfectly.

Commission Jan 2012

2012-01-25T11:03:00.000-08:00

I started working on a commission do a large, framed piece of flat beaded art. I started with free form hexagon angle weave, but not so free form as to loose the pretty patterns in it. I purposely started with a few odd bits, rings of 5 instead of 6 and a couple of 4mm beads just to make things challenging. Then, I spent hours trying to "fix the mistakes" by making adjustments so that everything will fit and lie flat. What results is a crazy patchwork design that is a combination of order and chaos, where one pattern drifts into the next as do the colors. I keep coming back to this theme. I think there are some nice metaphors there, about working around the problems, and that order and confusion can coexist. It's not done yet, but I thought you might like to see my progress. Here is what it looked like after the first day of weaving.

Here is my progress, day 2. I included a dime so you can see how big it is.

Day 3: I added some super right angle weave and Kepler's Star. I think I've decided to make it sort of a rectangle shape, working on towards the left.

Go on to Day 4.

Night Sky Bracelet Kits

2012-01-22T11:21:00.000-08:00

I finally got some Night Sky kits available that I showed in my recent post on bead art at the Joint Math Meetings. This kit has been a long time coming since I first published this pattern in 2007. The kit includes all of the materials you need to weave the bracelet, including a piece of ribbon to lace it up.

The kits make a patch of beaded lace as least as large as this bracelet, but you can also use the beads to make a narrower bracelet and have leftovers for a pendant or two, like the Southern Cross and the Greek Cross Pendants shown below.

One of my friends suggested that Night Sky looks like some coloring books she has, and she shared a link to Altair Design. If you don't want to bead right now, you could look at the pretty coloring book pages instead. Fun stuff.

Tutorial -- Twisted Cubic Right Angle Weave

2012-01-20T12:37:00.000-08:00

I just finsihed my newest tutorial on cubic right angle with a twist. Twisted cubic right angle weave is a just like regular cubic right angle weave, but forms a twisted tube. The twist in the stitch allows you to color it like a candy cane. It is suitable for a cable on a necklace or bracelet. You can also join the ends to make a small donut-shaped beaded bead, which is what I like to do with it because you get nifty torus knots and link designs on the surface of the donut.

The pattern gives complete instructions for weaving the donut including the use of several sizes of seed beads and different numbers of repeats around the tube. Of course, I had to make the smallest one I could since you know I'm a sucker for itty bitty beaded beads. This one is just 13 mm across and 5 mm thick.

I end this post with some happy donuts, because donuts make me happy. The smile is also a bracelet, because you can also make jewelry with twisted cubic right angle weave, you know, if you're into that sort of thing.

Bead Art at the Joint Mathematics Meetings 2012

2012-01-08T19:29:00.000-08:00

I just got back from Boston, MA, where I gave a talk on "Using Tiling Theory to Generate Weaving Patterns with Beads (PDF)" at the Joint Mathematics Meetings. This image shows the basic idea of what I presented.

I also showed five of my beaded star weaves bracelets in the Mathematical Art Exhibit which I designed using the ideas I presented. Here I am posing with my bracelets and the handout I distributed at the meeting.

You might recognize some of these beaded bracelets. From left to right, they are Kepler's Star, Archimedes Star, David's Star, Night Sky and Snow Star. You can see my beads at 0:57 in this short video about the exhibit narrated by Robert Fathauer, a regular curator of mathematical art.

Someday soon, I'll finish a complete paper explaining all of the details of my talk, with my coauthor Blake Mellor. Blake and I met at the meeting to review our paper together (version 14), and after years of writing, we are getting close to being done and submitting it for publication. (You might remember Blake as the mathematician with whom I wrote about the symmetry of beaded beads. He is a mathematical rock star as far as I'm concerned. If you don't want to buy the journal's version of our paper, you can download a PDF file of the pre-print for free here: beaded beads paper. The publisher's version has undergone peer review and revision by the editors at the Journal of Mathematics and the Arts. The writers and editors of JMA are many of the same people who spoke gave talks on mathematical art, and showed their work in the mathematical art exhibit.) Here you can see me with about half of the exhibit.

I am happy to report that the JMM mathematical art exhibit has been getting noticeably larger every year as more people hear about it, and the organizers of the meetings provide more space to show all of the entries. This year, there were over 80 artists showing their work, but only three sets by beaders. In addition to me, the folks over at The Beaded Molecules showed three pieces. You can see me standing right next to their giant beaded beads above. Susan Goldstine and Ellie Baker also had a nice set of bead crocheted bracelets, and Ellie let me take a picture of her next to them below.

Susan gave a slick and elegant talk on how they designed their bead crochet patterns right before I spoke. It was nice that they scheduled the talks of beading together. In general, the JMM are amazingly well organized. Mathematicians are good like that.

Here's a little history of JMM and bead art (and me): Last year (January 2011) my Ionic Beaded Beads were the only bead art in the exhibit, and the year before (2010) I didn't exhibit, so I got the task of writing an article about it for JMA instead. The only beads in 2010 were bead crochet bracelets, by you guessed it, Susan Goldstine and Ellie Baker and this time joined by Sophie Sommer. In 2009, there were no beads, and in 2008, Laura Shea showed a few pieces with triangle weave. Laura also showed triangle weave and beaded polyhedra in 2007. In 2006, I showed a selection of symmetric beaded beads, and they were the only beads in the exhibit. Blake and I also presented a talk on our associated paper that I mentioned above.

The first art exhibit at JMM that I participated was in 2005. There were only 21 artists that year and nobody submitted any beads, including me. I hadn't started beading yet, but I did paint, and my piece was gouache and ink on paper, called Symmetry 1. Maybe you can see that what I was doing then with ink and paint is similar to what I'm doing now with beaded angle weave designs. I believe the art exhibit started in 2004, but that year's exhibit is not posted on line. As far as I know, there were no beads in the exhibit or contributed paper sessions before mine in 2006.

Here is a link to the complete list of related mathematical art exhibits organized within Bridges and the JMM, just in case you'd like to sit here a while an appreciate more mathematical art. I know you'll find more of Laura Shea's bead work in the Bridges' conference exhibits there every year from 2006 to 2010, and perhaps a few other pieces of bead work if you search for it. They've got the eye-and-brain candy if you have the time. Go make a cup of tea. Stay a while.

Rivoli Urchin Necklace Kit B&B 2012

2011-12-28T11:47:00.000-08:00

Florence Turnour and I will be teaching three classes together this year at the Bead & Button Show 2012, our first year ever going to this show. This is one of the exact kits we will be offering with our Rivoli Urchin Necklace class.

Here is the sample for the Ubercube Necklace made with Infinity Weave. This exact color scheme is not a kit, and the lampwork beads won't be included, but this necklace is the kind of thing you will learn to make in the class. All of the materials will be included to make all of the beaded beads.

Here is a photo for a Bustier Beaded Bead Necklace, but I still have to design a kit or two with specific colors. I'm hoping to offer at least two different color scheme kits for each class. I hope to see you there.

Felt cuffs: It must be cold outside

2011-12-23T11:44:00.000-08:00

If you love fiber, click on this photo:

It must be cold outside because all I want to do is make warm fuzzy things. I hadn't made any felt cuffs in months, so I dragged out my collection of wool and other fiber delights, and I made these cuffs. I sold out of all of my purple cuffs, so I went with purple and black, and again, purple fails to show its true colors in photos. These photos show much more blue than what I see in the wool. I think they're prettier in real life. See the listing for these felt cuffs.

And then I made this pair is similar colors but in a smaller size. For these, I used yarn that I spun by hand to embellish the cuffs. The base of these cuffs are from a recycled wool sweater, so they are very stretchy, but the wool embellishments are firmly felted into place.

Furry Elf Slippers

2011-12-21T19:55:00.000-08:00

In early November, I had the wonderful opportunity to spend some time with my good friend Zelda, who is, among many things, a costume wizard extroidenaire. I presented her with the idea of designing a pair of slippers, something whimsical with a turned up toe. I was thinking of something you might see on an elf or gnome, large and comical, much bigger than regular shoes to exaggerate the size of your foot because big feet are funny, and adding extra padding makes the slippers warm. Zelda helped me imagine how the tops should look, and I drew a few pictures. We decided that faux fur was the best choice, for so many reasons, not the least of which is the yards and yards of it stashed high up in the closet, leftovers from previous coat projects.

I have never sewed slippers before, but I was confident that if I wasn't afraid to cut up and waste a bunch of fabric, paper and tape, I could eventually figure out a pattern. That's what it takes to make a pattern. You also need a needle and thread, a seam ripper, scissors, pencils, and patience. I also used my sewing machine.

To start, I traced and measured my foot, and drew a paper pattern that I used to cut the ugliest mustard yellow quilting cotton. Ew. I sewed it together, ripped it apart, pinned it, resewed it, inked in the lines, ripped it all apart, and made a new pattern. I did that whole thing again in a different but equally ugly piece of fabric. Two tries done, I realized that I needed to work on the lining FIRST, and THEN use that to design the fur pattern with the curling toe. I was doing it backwards. So I made another draft, but this time of the lining, something that conformed to the shape of my foot. The lining took me two rounds of drafts, and then one more draft for the fur. I made many adjustments at each draft.

And then FINALLY, I was ready to cut some fur. I knew my pattern was still wonky and unlikely to meet my vision perfectly, but it was good enough to make slippers, and my feet were cold. So I made a blue pair which are super comfy, but I didn't include enough ease in sole, which caused the toe to only curl up halfway. My sister wanted them, so I traded for her home made chocolate covered caramel with two kinds of chile and salt. She also gave me a really ugly cookie, that I asked for in particular because I felt sorry for it in the beautiful bouquet of flower cookies. It was yummy.

Anyways, I altered the pattern again, and made myself a pair, finding only a few minor improvements, like trading in the icky polyester batting I was using for nice natural cotton batting. Then I made the pair in the first two photos, and they are just the way I wanted them to be, so I put these slippers in my Etsy shop. I think maybe I'd like to write up and sell this pattern. I'm pretty happy with it. They're super comfy.

Furry Hats with Ears and Horns

2011-12-11T13:40:00.001-08:00

Making fuzzy hats with ears and horns makes me happy because people always seem to smile when they're wearing them. People also seem to smile at me when I'm wearing mine. We call ourselves Horny Hatters.

I'm offering two new hats for sale so you can be a Horny Hatter too. I decided to start numbering them so I can keep track of how many I make.

Pink and Purple Horny Hat #13
I got a bundle of faux fur remnants from the fabric store, and this super thick fur was in the set. I matched it with purple horns in cotton and a pretty purpley pink silk lining from my overflowing stash of silks.

You know I love pure silk, right? Well this one is particularly stunning, the way it shimmers in the light.

Blue Horny Hat #14
After making a pink one, I wanted to make one in boy colors. Here you can see the blue one with the matching coat I made my sweetie.

This blue one has especially big ears. I used a button clasp instead of pom-pom ties, just for a change.

Flashy Blue Labradorite Sunflower

2011-12-06T20:32:00.001-08:00

I made this pendant by capturing a large labradorite coin bead with the fringe method for beading around a core bead. In particular, I used variation of the Rivoli Sunflower design for the pendant. I adore the blue glass beads in this piece and the way the inclusions shimmer in the light. I think the shimmer works well with the blue flash of the labradorite stone.

For the necklace part, I used a variation herringbone weave that I described in my Toggle Clasp & Cable pattern.

For more information and to purchase this necklace, click the photos. Thanks for looking.

Leopard Print Beading

2011-11-30T18:39:00.001-08:00

I just listed this earring and pendant set made with my "picnic weave" but I think this color scheme looks more like a leopard print than a picnic blanket.

Although they look quite different, this weave is an easy variation of my Night Sky weave.

Flower Ring Bouquet

2011-11-28T14:19:00.001-08:00

If I had all of the time in the world, I'd make a large bouquet of beaded flowers like this.

This is a pile of Flower Rings made with the fringe method, a technique for weaving beaded beads that Florence Turnour figured out and showed me in 2004. If you haven't tried the fringe method yet, check out this free beaded bead tutorial that Florence and I wrote together.

Wonka of Wonderland Top Hat #5

2011-11-27T12:32:00.001-08:00

Last night, I finally finished a custom order for another top hat. This one is number 5.

What these photos don't convey is how springing this hat is. If you bend the brim, it will spring right back into shape.

What you also can't see is that inside of the silk and cotton fabrics are stiff double buckram and wire, which together, give this hat its form. Double buckram is two layers of cotton fabric with a thick coating of sizing. Sizing is a combination of glue and stiffener that can be re-wet with water or steam to sculpt it. When it dries again, it stays in whatever shape you left it to dry. To shape this hat, I only used a bit of steam as the wire is doing much of the work. I really love the sculptural possibilities of wire and buckram, but they require a very firm grasp when working with them, and sewing through the buckram requires strong fingers.

I learned that a thimble and pliers are invaluable tools for pushing and pulling the needle through the sturdy buckram. All of that grabbing and squeezing is really hard on my hands. So for the mean time, I'm putting these materials on hold, and I'm going to play with some soft fabrics for a while. I see some faux fur slippers in my future, something elvish with a comically turned up toe.

Steamy Ruffled Cuff

2011-10-26T22:48:00.000-07:00

I had so much fun making the first one, I decided to do it again.

Click the photo to see the listing.

For the Love of Silk Ribbon and Lace

2011-10-25T01:21:00.000-07:00

Last time I was preparing to visit my friend Jennifer to teach at her bead shop, Naturally Jennifer's Gallery and Beads, she asked me if I had any clothing that I wanted to tie dye. See, Jennifer had something around 30 buckets of dye set up in her garage because she was filling a large order of tie dyed t-shirts for a local music festival. As luck would have it, I had just won a HUGE lot of silk charmeuse remnants on Ebay. The fabrics were gorgeous, but some of the colors were a bit boring, like khaki, pale lavender and tan, and this was the perfect opportunity to make them beautiful with some hand dying. Could Jennifer's dyes work with silk? Sure they would!

I wanted a mottled look rather than a traditional tie dye, so Jennifer taught me to "artfully wad" my fabrics in large plastic tubs. With over 30 colors to choose from, I poured maybe six different, related colors of dye into each tub. Here is a photo of one little corner of the purple piece. Pretty, isn't it?

These dyed silks have been sitting in my closet since Spring, patiently waiting for me to figure out how to use them. Last night, I was browsing hand dyed silk ribbons on Etsy, and I saw that a few different vendors were selling ribbon with serged edges. I realized that I could make ribbon by CUTTING strips of of silk from selvage to selvage, and then SERGE a rolled hem on both edges. OMG! I CAN MAKE SILK RIBBON AS WIDE AS I WANT! See, if you've ever shopped for wide silk ribbon, you know it costs a small fortune, often around half the price you'd pay for 45" wide fabric. Silk ribbon is a real luxury item, especially the wide, hand-dyed stuff, and as a consequence, I don't own any wide silk ribbon... until last night!

On my first try, I made a gorgeous yard of silk ribbon in purple and burgundy with black serger thread. At nearly an inch, it's significantly wider than the narrow ribbons I own, and the fabric is a bit thicker as well. Once the machine was set up and the strip was cut, sewing it was pretty quick and easy. It's a little under an inch wide, over a yard long and I tapered both ends to a point. I strung some beaded beads on it, but didn't love the way they hung because they weren't heavy enough to weigh down the ribbon, So, I ruffled the ribbon by sewing a zig zag like in my Doceri drawing below.

I rolled up my silky ruffle to make flowers, folding and twisting it, this way and that. I made some wiggly lines with it. I sat at my cutting mat, rather mesmerized by this little ruffle, all soft and squishy with undulating colors that shimmer in the light like only silk charmeuse can do. I became inspired: I dug through my bags of lace, cut some pieces, and arranged them under my ruffle. I tried some ribbon flowers. Deciding a cuff would be a good project, I found a scrap of black rayon jersey fabric leftover from the lining of my new mini dresses, and I cut a rectangle about 8 inches wide. Starting with the bottom layers of lace, I sewed my appliques to the jersey, layer by layer. I started with hand sewing, and switched to my machine where I could. After all of the lace and ribbon was attached, I sewed on a few pressed glass flower beads. Then, like making up a pillow, I attached a lining made from some purple cotton corduroy. The corduroy lining makes the back soft, adds a little warmth, and hides all of the stitches and thread ends. I left open a side seam to add elastic button loops, pinned the loops in place and finished the last bit by machine, which you can see running vertically below in black thread. I finished it by attaching the buttons, sewing through all of the layers for stability.

As I sewed, I just kept thinking about how super girly girl this cuff is. It's purple and rosy, with flowers, ruffles, and lace. It's beyond girly. It's not my normal style for sure. I've heard people call it a "romantic" style. My boyfriend called it "too much," but the girly girl in me really likes this kind of explosive overabundance of ribbon and lace. A little part of me wants to be dressed head to toe like this, maybe just for a little while. Yes, this style is a bit out of my normal aesthetic, but I like that it all started with a piece of beautiful purple, hand-dyed wide silk ribbon. Yeah for Etsy. Yeah for silk ribbon. Yeah for inspiration.

Click on the photos for more photos and information about purchasing this cuff.