Found Mathematics on the Playa

I've been sorting through my photos from Burning Man, and I found this set of photos of the dried playa ground.  The playa is composed of a very fine particle dirt or dust that is wet mud in the winter and dry, flat earth in the late summer.  As the lake bed dries, cracks are formed in the mud.  The resulting cracks nicely demonstrate the idea of the self similarity of fractals in nature.

The idea is that as you zoom in, you continue to see more and more detail, and the over all shapes at every level always look the same, at least in theory.

Zoom, zoom, zoom.

Of course, this is the real world and not theoretical mathematics, so that perfect self similarity breaks down if we zoom in far enough.  That reminds me of a riddle.  What's the difference between theory and practice?  In theory they're the same, but in practice, they're different.  This is like that.

Anyway, the above photos were taking is the shade of bright daylight.  Below is what the Playa looks like at night with blue and green laser lights shining on it. You can still see the cracks, but instead look at the patterns in the lights.  

This pattern is quite complex since the lights are projected with more than one periodic pattern superimposed on top of one another.   See how the blue forms one repeating pattern, and the larger green clusters of dots form another, but one doesn't quite match up with the other.  And maybe you can even make out a repeating pattern in the smaller green dots.  Pattern on top of pattern on top of pattern...  This pleases me. 

Infinity Truncated Rhombic Dodecahedron Beaded Bead

This beaded bead has a really long, and very descriptive name.  The weaving technique is Infinity Weave.  I use this name for the weave because there are an infinite number of polyhedra that can be realized with Infinity Weave.  The mathematical shape of this particular beaded bead is a truncated rhombic dodecahedron. I think of it first in terms of its symmetry, which is that of a cube (or octahedron).  I imagine that on each face of the cube, there is a smaller square. This beaded bead has 6 squares holes just like this:

Square Face of the Truncated Rhombic Dodecahedron

The shape is further modified by replacing each edge of the cube with a hexagon.  Since a cube has 12 edges, so does this beaded bead have 12 hexagons.  In the photo below, see how the hole in the center has six sides?  That's the hexagon.

If you would like to read more about this beaded bead, and see photos of it from other angles, click on the photos above.

I brought home some carnivorous plants last month

...and I can't stop looking at them.  So I photographed them, so I could share them with you.  

The first one is of a baby sundew leaf doing her best impression of a Valentine.  

That stem is less than a millimeter wide, by the way, so she's satisfying my love for itty bitty sparkly things pretty well.  I also found the limit of how small my camera (a Canon G12) can shoot.

Next is a pair of Venus fly traps, just hanging out in a crowd, waiting for a fly.  I think the one on the left just told a joke and the one on the right is laughing at it.

These are American pitcher plants, a particularly brilliant cultivar called 'Scarlet Belle' with some bladderwort flowers, and sundews showing off their sparkling dew.  Three different species of carnivorous plants are growing in this one pot.

 Here's another sundew, a rotundifolia cross breed.  These colors just scream, "Summer!"

Below is a tiny patch of bonus sundews, "weeds" that grew in the pot of one of the American pitcher plants.  After I took home these pots, I realized there were entire ecosystems growing in them.

This last photo shows maybe 1.5 inches across of turf. At last count, I found 20 itty bitty sundews in this one pot.  Small stuff.  Some of them are so small you can barely detect there's a plant, but the dew sparkles in the sun.  I'm enjoying their mini-ness.  Unfortunately, I haven't figured out how to bead any of these things yet, so you'll just have to be satisfied with the photos.  I purchased all of these beautiful, healthy plants from the good people at California Carnivores.

How to Make a Digital Flipbook Animation on How to Tie a Slip Knot

The first stitch to start crochet or knitting is typically a slip knot.   Here is what a slip knot looks like.

 

I illustrated how to tie a slip knot with this Doceri video.  To make this movie, I created a digital flip book of sorts, and the video shows different ways to play it back.

 

To explain how I did it, here I show you what my Doceri control panel looks like when I am authoring or playing back Doceri files.  Specifically, here is what I see at the end of the 8th page of my 13-page digital flip book.  

At the top of my iPad screen, you can see lots of buttons and ways of controlling my presentation, both for authoring and for playing back my drawings.  The relevant controls are labeled below (with the help of Doceri, of course).  

At the beginning of the video, I played the file, frame by frame, by touching the "forward to next stop" icon repeatedly.  I similarly touched "back to previous stop" to play the file backwards.  Later in the video, I showed the file by repeatedly pressing the "play" button.  There, you can see each frame played out separately, where each stroke plays separately.  I did not design this file to be played back with the play button, but I wanted to show you the difference, since I play most of my movies with just the play button.

To make a flip book movie like this, I drew several layers for the knot at a time, one right over the next.  After I got at least two layers drawn, I went back in time on the Doceri "time line," and I added a "white stop" by touching the "windshield wiper" icon on the top right of the control screen.  The 12 different white stop markers on the time line above each indicate that the screen is cleared at that point in time.  In the images above, you can see that our point "you are here in time" is just before a white stop.  White stops can be added and deleted just like any other stroke on the time line.

Since the screen clears after each complete image of the knot is shown, when I play back the file by forwarding to the next stop, an animation results.  It's just like the flip charts I used to make in the corner of my notebooks as a kid.  But since it's a Doceri file, I can easily color and edit my work.

How to Make an Easy Tutu without Sewing Part 2

Last time I presented part 1 of making an easy no-sew tutu.  This is the second half.  


Next I added strips of tulle from the 6 inch wide roles.  My strips were about 2 feet long for the blue.  I added them with the same kind of knots I described in part 1.  Then, I added 1.5 foot strips of white tulle.  In each case, I equally distributed the strips around the waist.

Notice how my strips keep getting shorter on each round.  The layering creates a nice rounded skirt shape.  At this point, I decided I didn't like the look of the blunt ends.  So I cut the corners into points like in my Doceri drawing.

This photo shows most, but not all, of the blunts ends cut off.  I definitely prefer the look of the pointy ends.

Next I cut strips of ribbons.  For the ribbons, I cut off corners or I folded the ends to cut notches in the ends of the ribbons. Here is my Doceri drawing showing my method for cutting notches.

I knotted strips of the various ribbons to the grosgrain waistband, just as I'd done with the strips of fabric.  The thinner the ribbons, the longer I cut them.  I pulled the ribbons down into the skirt so that they would hang from the inside.  Here is the finished tutu and headpiece.

Here is the bridal nymph in her natural habitat.  Isn't she beautiful!  This was Day 1 of our bridal shower weekend.

On Day 2, the bridal nymph ditched the silly headpiece I made her in favor of sunglasses, but still wore the tutu on our daylong hike.   

Yes, tutus are suitable for hiking, as long as there's no serious rock climbing.  The netting might catch a few bugs, however.  Fortunately, this is a pretty bug-friendly group of nymphs.

How to Make an Easy Tutu without Sewing Part 1

A good friend of mine is getting married next month, and we decided to throw her a bachellorette party.  In celebration of her love and life, and with an excuse to single her out in a foofy fairy princess costume, I made her a tutu and matching veil.  Here's how I made the tutu.

Step 1: Buy a boatload of tulle and organza ribbon and fabric in a variety of blues, aquas, and white.   I got two cuts of fabric from the bolt: 1 yard and 1.5 yards of brighter blues to add color.  I also included 5/8" grosgrain ribbon for the waistband.  Grosgrain is stronger than other types of ribbon and will hold up better to repeated tying and untying. Lastly, I also bought a fabric covered hairband for the headpiece/veil.  I spent $29.90 on everything.  I went a little nuts. I could have bought about a third less to make this work, but I wanted the large combination of colors.

Step 2: Cut a piece of grosgrain long enough to fit around you waist (or lower) plus enough extra for a generous bow.  I used 8 feed 3 inches.

Step 3: Cut fabric into strips.  My fabric pieces were 1 yard and 1.5 yard cuts, but I never measured the bolt width.  To cut the fabric, I held up each large rectangle to determine which side was shorter, and cut them like I show in this Doceri drawing. 

My strips measured about 2.5 feet by 0.5 feet, but I didn't worry about them all being exactly the same size as I cut the fabric.  I used light blue organza and dark blue tulle.  I cut the strips a few at a time as I added them to the waistband, and I decided to save some for the headpiece and maybe other projects later.

Step 4: With strips in hand, I was ready to tie knots.  First, fold a strip in half to make a loop.  Slip the loop under the grosgrain waistband from the top side.  Always push the loop under from the top or the knot will be upside down.

Pull ends through loop.

I pulled tighter, but not too tight.

I decided to tighten later when I knew what I was doing, but I eventually learned that you could tighten the knots pretty tight at this point.  They will still slide easily along the grosgrain, which is mostly what I was worried about.

After tying a few knots, I decided that small tidy knots would be a good thing so as not to have too much puffiness around the waist.  So, I improved my technique for making smaller knots by twisting the organza a bit before folding it in half for the loop.  Just a few twists right where the knot will be makes for a smaller knot.  See how the left knot is smaller than the puffy one on the right.

 I added more than a dozen strips of organza around the grosgrain.  The "scarf" is my leftovers.

I learned that the puff was only a problem with the organza fabric.  The tulle didn't really require the extra twist to make small, tidy knots. In the photo below, you can see the darker tulle knot between the organza knots.  Notice the second layer is a bit shorter than the first.

Also notice how poorly the shirt matches the tutu.  Egads.  Click ahead for part 2: the exciting conclusion of "How to Make an Easy Tutu without Sewing."  Not only do I show you how cute the finished tutu and headpiece looked on the beautiful bachellorette, I will find a better shirt to go on the dress form.

More Beaded DNA Earrings

I've had a few people point out to me that the base pair coding on DNA actually happens on the rungs of the ladder and not on the edge, as I did in my beaded DNA video.  So, I found this image and came up with the version below. 

Notice that I removed the bugle beads on the rungs of the ladder and replaced them with a row of 3 beads.  I used two size 8/0 for A and G, and one 3mm fire-polished crystal for T and C.  Now the color coding is on the rungs where it's supposed to be.

You can see from these photos that this new version is wider.  The design in the video is shown below.

Personally, I prefer the more delicate look of the original, patterned design, but conceptually, I like the move towards scientific accuracy in this new version.  Which do you prefer?

Click the photos to go to my Etsy listings for these earrings.