Genie Bottle Update 2

The Genie Bottle, a Burning Man Honorarium Art Project is progressing. Marty Kenny designed all of the cutouts to be cut into the wood, and Paul Brown inserted them into this Solidworks rendering. If you click on the photo, you can see we also added some of our favorite math equations to be cut out of the wood. In the spirit of Arabesque art, we wanted to add some "calligraphy" and in the spirit of genie magic, what's more magical than beautiful mathematics? The math IS the genie!

Using Paul's computer model, Christy Burback and I made a little scale model out of card stock and tape.  It's about 1/18 of actual size. We cut out and traced the pieces using the specs from Paul Brown's design.  Here you can see Christy with her arm up inside the bottle.

While I am the lead artist on the Genie Bottle, for most of the tasks for designing the Genie Bottle, I've delegated them to other crew members.  I've been leading the designers and engineers towards a particular aesthetic for the overall piece, but like the cutouts for the wood and the lighting, other member of Struggletent are leading the efforts to design and build individual components.  The finished Genie Bottle and its burn will truly be the work of a group of people, my campmates of Struggletent.

The one component I'm designing are the tassels, although I won't build them all myself.  Fortunately, we have lots of helping hands.    My vision is to have a set of 10 large tassels and cording to hang inside the bottle for decoration.  This is my drawing for how I want them to look, more or less.  I haven't decided what color to paint the finials yet.

This is some of the wool we will be using.  This is about a pound of wool.  You can also see the wooden finial that Mike Ryan made for me.  It's got a hole drilled in the center, meaning it's a giant bead. Painted wooden finials like this will top each tassel, effectively turning them each into a big bushy mop with a handle.

Making these tassels requires dying a lot of wool, over 7 pounds of soft springy Merino. (In two dye pots, I can dye 3/4 of a pound at a time; so it's taking me days and days to dye it all!)  This is what the purple wool looks like in the dye pot before the dye has soaked in.

Finial Master Mike Ryan also did a practice burn of the bottle last week at a camp out.  You can watch the video of the burn here: https://www.youtube.com/watch?v=7qr6W50dggg
A structure like this will fit inside of the Genie Bottle and will be built inside of it on burn night, tentatively scheduled for Friday at Midnight.  "It is designed to be an anaerobic burn and has minimal oxygen, That's how the smoke is developed. Once a heat source reached a stoichometric point, it ignited."  That's why it shoots fire out the top.

While we're on Burning Man art, I thought I'd share some updates about Bat Country, our previous Burning Man Honorarium Art from 2008, 2009, and 2013.  First, we're published in The Washington Post this week in a slide show titled, "A New Way to Look at Math."  We're #7.

I also got some really nice photos from photographer George Post of Bat Country from 2013.

Here you can see the whole crew at the top as I hold up the very last ball to be attached at the apex.  THIS was a very exciting moment for me and the whole Struggletent crew, and I'm so pleased that George sent me a photo to commemorate it.

And here's a really stunning photo of Bat County and the Temple of Wholiness.

Thanks George Post.  And thank you for looking.
Here you can read Genie Bottle: Update 3.  Here you can see photos of the finished Genie Bottle at Burning Man.

Infinity Dodecahedron Necklace with Lampwork Glass Beads

My favorite way to wear beaded beads is strung simply on cord.  In fact, that's how I usually wear them.

For this necklace, I made 4 beaded beads, including three Infinity Dodecahedron and an Infinity Cube (on the far right). Then, I added 4 borosilicate and lampwork glass beads torched by 4 different artists. Together they make a pallet of aqua, silver and gray. This is an unusual and pretty strand of beads, eclectic yet harmonious.

They're all strung on a 26 inch piece of silk cord, tied simply at both ends. If you enjoy stringing beads, you could use this set as a beginning of a more elaborate necklace, but I would wear them just as they are, strung on cord.

Includes 4 inches (10 cm) of beads. Largest beaded bead measures just under an inch (22 mm).  This necklace is for sale.  Click the photos to go to the listings.  Infinity Dodecahedron Beaded Bead tutorial is available here. Thanks for looking!

Beaded DNA Earrings in Greens

Last night I made a long pair of green DNA Earrings, and today I listed them in the Earrings Section of my Etsy shop. 

With 12 sets of base pairs, these earrings are a bit longer than I typically make. The length of earrings from top of ear wire is 72 mm (almost 2 3/4 inches).

The coloring of the base pairs comes from the enzyme PpiI which is found in the microorganism Pseudomonas putida. Pseudomonas putida is a safe strain of soil bacterium, and is the first patented organism in the world. Because it is a living organism the patent was disputed and brought before the United States Supreme Court in the historic court case Diamond v. Chakrabarty which the inventor, Ananda M. Chakrabarty, won. It demonstrates the ability to biodegrade organic solvents such as oil. The specific base pair sequence shown in each earrings is
GAACN5CTC
CTTGN5GAG

I like the way the spirals look from different angles.

 The helices are stiff, but flexible.  They bend from side to side, but they don't untwist.

If you would like to learn to make your own beaded DNA earrings, try my free video tutorial on how to make DNA earrings with beads.  Thanks for looking!

Bat Country in the Press

Yesterday, was a very good day.  You see, yesterday, my name and my art were published in The Guardian Online Newspaper.  Apparently, the newspaper's online edition is the third most widely read in the world.  Anyway, Alex Bellos writes a column called Alex's Adventures in Numberland, where he wrote about a new book called, 50 Visions of Mathematics, and my art is one of the 50 photos in that book.  This book is published by Oxford University Press, which is the largest university press in the world, and the second-oldest.

The art of mine they published is Bat Country, the Sierpinski tetrahedron jungle gym that I created with Paul Brown and our Struggletent crew with help from Burning Man.  A big photo of Bat Country is in that book.  What's more, we're even on the cover!

Yup, my name and my Playa art are on The Gaurdian website, and on the cover of a OUP math book!

Yesterday was a very good day.

TUTORIAL Conway Bead Beaded with Tetrahedrons and Prisms

I just posted my newest beaded bead pattern.   I'm calling it the Conway Bead.  I named after the great mathematician John Horton Conway in honor of his extensive work on symmetry, especially four dimensional polytopes, on which this piece is based. This particular design is taken from the 03-ambo polydodecahedron.  (Say that ten times fast!)  Alicia Boole Stott discovered this shape last century, along with a bunch of other 4D polytopes, built models of them in paper, and wrote about them.  I didn't bead the whole thing, just a small piece of it.

Although it might sound complicated from that introduction, the structure of this thing is actually quite elegant.  Once you get the hang of it, it's quite intuitive, and my tutorial is designed to give you that intuition.  It's beaded much like cubic right angle weave but with tetrahedrons and prisms instead of cubes.  This tutorial is designed for experienced beaders, and it includes charts like those found on my blog here. This tutorial assumes you already how to do cubic right angle weave and know how to connect two ends to make a continuous strip. If you don’t, check out the links here to learn how.

You should also probably already know how to bead a dodecahedron or at least know what a dodecahedron is before trying this design.   This is a dodecahedron.

One of the things I like about this structure is that it has large holes that run through its center so you can easily string it on chain or cord.

Another thing I like about this beaded bead is that the underlying structure comes from something that is four dimensional.  If you were to try to build the whole structure with bugle beads, it wouldn't work because the angles don't actually match up precisely.  Even the little piece I beaded probably wouldn't work.  It's close, but not exact.  But because seed beads are short and bead weaves are flexible, you just have to be close.  So bead weaving makes it possible to build a little chunk of this 4D thing in 3D, thereby making the impossible just unlikely.  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.

My New Avatar by Tiffany Inglis

If you're like me, you've always wanted to be a cartoon character.  I don't know why.  I guess I just love cartoons. Well, Tiffany Inglis can draw cartoons, and she is also a master in Photoshop.   You see, Tiffany is a computer whiz AND a brilliant portraitist.  She has a PhD in computer science, and she wrote her dissertation on "Pixelating Vector Art."

Clearly, she's not your average computer nerd.  Anyway, Tiffany recently posted a custom wedding portrait on Facebook, and I was blown away by it.  It looked right out of a Pixar movie.    So I asked Tiffany if she would like to trade some beadwork for an avatar.  I was super happy when she agreed.  I sent her some photos of myself and my art, and with her magic, she made this picture of me, complete with wavy red hair and glasses.  Isn't it amazing? 

I actually look like this. 

In my head. 

But now I look like this on my computer too.  You can see that Tiffany managed to include a Rivoli Urchin pendant, a Sweetheart Pendant, a top hat from felted wool sweaters, and a coat I made.  (These are all things I've written tutorials for.)

In exchange, I made her this Rivoli Urchin Necklace in the colors Tiffany picked.  I'm totally sure that I won this trade.

Thanks for looking.