Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Tuesday, November 19, 2019

Doodle No. 34 In one hole and out the other

This shows another version of the Poincaré model of hyperbolic space with microbes, space junk, aliens, and a few plants. 
Some are real. 
Some imagined. 
Some are totally unbelievable. 

I’ve worked in these colors before. 
I suspect I’ll use them again because they match the furniture. 

5.75” diameter circle.


Drawn with archival Prismacolor black ink, Faber-Castell Polychromos pencils, mica watercolor paint on Stonehenge 250 GSM 100% cotton paper. 


Sold

Monday, November 4, 2019

Doodle No. 33 Tribert Makes Thymine



The design of this is based upon the Poincaré model of hyperbolic space. Ask a mathematician about it. It’s probably their favorite model of hyperbolic space. 


5.75” circle
A lot of people photograph their oakk in brings of flowers with real flowers. I don’t paint flowers. So I thought these Polyhedra seemed appropriate. 



NFS 
Thanks for looking. 

Tuesday, October 29, 2019

Doodle No. 32 Adam Explains How Holes Work

These weren’t the colors I thought I would get, but in the end I’m happy with how they turned out. It took a lot of layers of colored pencil to get there


This piece is for someone who likes old wooden furniture and modern art.  It would look nice in a fancy guilded frame.

6.5” by 9.5” oval 
Not for sale

Sunday, October 27, 2019

Doodle No. 31 Adam Makes an Atom

This is what happens when I let Melanie Schrader pick the colors.

Mike Ryan pointed out that the atom has three electrons, so it must be lithium. He cares for bipolar. Here is a detail of Adam and his lithium atom and the flash of the mica paint. 
4” square
Prismacolor black ink, Faber-Castell Polychromos pencils, Finetec mica watercolor paint on Stonehenge 250 GSM 100% cotton paper

 NFS

Monday, October 21, 2019

Doodle No. 30 Too Many Holes

In Doodle No. 24 Six Holes, I asked, “How many holes are too many?” The answer I was given was infinitely many. So then I spent the next several days trying to figure out how to draw infinitely many holes. The answer lied in the Poincare model of hyperbolic space. Here, I present “Too Many Holes.”



5.75” diameter circle.

Drawn with archival Prismacolor black ink, Faber-Castell Polychromos pencils, Finetec mica watercolor paint on Stonehenge 250 GSM 100% cotton paper. 


Sold
thanks for looking. 

Sunday, August 4, 2019

Doodle No. 27 Bunny in a Triangle

Bunny spends some time in a Sierpinski triangle thinking about lunch.


3.5” by 5.5”

Prismacolor black ink, Faber-Castell Polychromos pencils, and mica watercolor paint on Stonehenge 250 GSM 100% cotton paper.



Wednesday, July 31, 2019

Doodle No. 28 Moth Fractal

3.5” by 5.5”
Moths and a few copies of my dog, Kepler, inhabit a #fractal. The lizards and other doodles along the sides and top are very much in the style of Marty Kenney. 


The last several pieces I’ve done have a lot of coloring, a lot of pigment. This time I tried to use light colors with a lot of white, in part, to see if it would take less time to color, and it did! I’m sure I’ll go back to my saturated colors though. I love color, but this pink is nice for a change.

Drawn with archival #Prismacolor black ink and Faber-Castell #Polychromos pencils on #Stonehenge 250 GSM 100% cotton paper. 


Monday, July 8, 2019

Doodle No. 26 Rainbow Alternating Steps



The rainbows came back. They always come back if you wait long enough. 

The image is 3.4” by 5.6” 
set it in a 5” by 7” black mat.

Prismacolor black ink and Faber-Castell Polychromos pencils on Stonehenge 250 GSM 100% cotton paper with a bit of mica paint for metallic details.
 


Thursday, July 4, 2019

Doodle No. 25 The Devil’s Staircase

The young cashier at the paper store convinced me that I really needed to open an Instagram account. And so I did. I’m planning to use it to share my artwork. So, now you can follow me there, if that’s you’re thing. https://www.instagram.com/gwenbeads/


The Devil’s Staircase (AKA, the Cantor Function) is a weird fractal function that I studied in graduate school. What I seem to remember the most about it is how to draw it. 

The colors were inspired by a Vincent Van Gogh painting “Bedroom at Arles” from 1888.

The image is 3” by 5”. 

Prismacolor black ink and Faber-Castell Polychromos pencils on Stonehenge 250 GSM 100% cotton paper. 



Yip yip!

Monday, July 1, 2019

Doodle No. 24 Six Holes



How many black holes is too many black holes?

This is one of the largest pieces in the series so far. It certainly took me the longest. The image is 7” by 8.8”. 

Here you can see how the details of silver mica shimmer in the light. I quite like the effect. 

Saturday, June 29, 2019

Doodle No. 23 Pythagorean Tree and Me


Image size: 3.8” by 3.8”

Drawn with archival Prismacolor black ink, Faber-Castell Polychromos pencils, 23.5 karat gold paint on Stonehenge 250 GSM 100% cotton paper. 


Sold

Thursday, June 27, 2019

Doodle No. 22 Bunny and Owl


The image is 3” by 3”. 
The paper is 4.5" by 4.5". 

Drawn with archival Prismacolor black ink and Faber-Castell Polychromos pencils on Stonehenge 250 GSM 100% cotton paper. 


Sold

Sunday, June 2, 2019

Doodle No. 15 Pitchfork Bifurcation

Doodle No. 15
Pitchfork Bifurcation
Faber-Castell Polychromos pencils
Neenah acid free paper, 80 lb
5” by 7” image on 7” by 9” paper


I have a complicated relationship with yellow. I’m pretty sure it has something to do with the yellow and orange bedroom I had as a child. Everything was covered in a print of orange and yellow California poppies, and all of the furniture was painted yellow. Tying it altogether was a huge carpet in a perfect shade of yellow mustard. After the yellow experience, I had more than my fair share for years, and I didn’t like orange much either. I eventually brought orange back into my pallet a number of years ago after a friend successfully convinced me that bright orange is the color of happiness. Yet, that yellow carpet haunted me. With this piece I decided to put my biases aside and go full yellow mango on the background. 

Overall, this color palette is very 2019. Search for “color pallet 2019.” And you’ll find these colors. So if you don’t like them yet, you should reconsider.

The pitchfork bifurcation was the kind of thing I studied in my graduate abstract algebra course. The class had something to do with resolving “bad” points in the solution set for an equation by introducing another variable and changing your point of view. I didn’t really understand the symbolic representations and manipulations very well, but I could reproduce the kinds of pictures in the textbook in great detail. My professor seemed to think that showed enough understanding of the material for me to pass the class. It seems the biggest change between then and now is the cat. 

And yellow. 

And a lizard for Marty. 


This original is sold.

Thanks for looking.

Monday, December 11, 2017

Truncated Icosidodecahedron in Beads Crater Moon Beaded Bead

Meet Crater Moon.
and Crater Moon in White...
https://www.etsy.com/listing/579082293
Each Crater Moon is composed of nearly 2700 beads.
https://www.etsy.com/listing/582628369/
The American Mathematical Society recently posted a photo of an amazing structure on their Facebook page with no comment of who made it. They called it a rhombicosidodecahedron (3.4.5.4) because that is the name of the polyhedron in the very inside layer, but Susan Goldstine noticed that the outside layer is actually a truncated icosadodecahedron (4.6.10). This object is a multilayered compound of unusual polyhedra.
With help from Susan, I figured out how to weave it with seed beads and thread. Susan built this model below using Zometool, and wrote, "This is what the structure above each triangular face of the rhombicosadodecahedron looks like. I feel better about not being able to make out what's going on from the original photo. The cavity has a triangle, six trapezoids, three pentagons, and the hexagon at the top." Furthermore, "Above each core pentagon is half an icosidodecahedron (3.5.3.5)."
To bead it, I used an edge-and-cover weave with 3 mm bugle beads for the edge beads and size 11° seed beads for the cover beads. (There's one exception, where I used 11° seed beads for the short edge beads under the squares.) In other words, every n-gon has 2n beads, including n edge beads alternated with n cover beads, all sewn in a loop.

Here you can see how I started to weave the inside layer, showing the edge-and-cover weave for (3.4.5.4), also known as the rhombicosadodecahedron as I mentioned above.
This is a photo from Ivona Suchmannova of Spiral Beading, showing the first layer curled into a ball.
This is the complete first layer of Crater Moon with 6 mm bugle beads and 11º seed beads. This piece will finish a lot larger than the others because the bugle beads are longer.
Here is the start of the second layer on Ivona's bead. She stitched loops of triangles around the pentagons, connected by at the bugle beads.
This shows the start of layer 2 with the longer, 6 mm bugles. You can see the 5 triangles around the pentagons and the 3 trapezoids around the triangles. The short edge of the trapezoids is the aqua 8°. All other beads are 11° and 6 mm.
 
Next, the center front is still just one layer, 
but layer 2 is nearly complete.  Layer 2 
consists of 30 little 3D pentahedrons sitting 
on top of the squares in the first layer. Four 
little walls like a camping tent, the four other 
sides of the pentahedrons include two 
triangles and two trapezoids. The short sides 
of the trapezoids are the one place where 
we use an 11° instead of a bugle bead.
 
 
 
 
 

 
 
These show the second layer finished. The seed beads in the center of the Xs (aqua below, burgundy above) are the tops of the tents, the one place I used seed beads for edge beads.
This is the start of the third layer. It's triangles and pentagons. Here are the pentagons.
And here you can see both pentagons and triangles.
You can add the pentagons and triangle in two steps, or you can stitch them together.
Here you see 3 of the 12 rings done.

Four more to go!
 Here all 12 are done.
In the fourth layer, I finished the space under the 30 squares, adding two trapezoid loops per square.

The fifth and final layer requires adding 720 size 15° seed beads to the outer surface.  Only then does the Crater Moon really hold its shape neatly.
You should make one.
It's just 11°, 15°, Toho 3 mm bugles, and Fireline 6lb.
And a whole lot of stitches.
Here you can see how big it is, just 1.75 inches across or 45 mm.
If you would like to have your very own Crater Moon, you can find the white one in my Etsy shop here: https://www.etsy.com/listing/579082293/
The larger Crater Moon is available here: https://www.etsy.com/listing/582628369/
Thanks for looking.
P.S. If you'd like to try weaving beads, but you think that the Crater Moon is a little beyond your skill set, have a look in my Etsy shop for tons of other tutorials for all skill levels.
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