Notices by Gwen Fisher (gwenbeads@mathstodon.xyz)

Twelve years. I started this project twelve years ago, and today I hold the result in my hand. It’s a book that combines bead weaving with math called, “Beading with Algorithms: Cellular Automata in Peyote Stitch.” With help from mathematician and artist Roger Antonsen, graphic designer Zelda Lin, a handful of talented proof readers, and the good people from World Scientific Publishing Company, my dream of combining my loves of math, art, and teaching into a book is finally a reality.

This book is the first of its kind, a recipe book of algorithms that can be used and combined to generate colorful patterns in peyote stitch beadwork in any size and shape you desire. These algorithms could also be applied to other pixelated art forms like tile laying, embroidery, crochet, and quilts. We included projects like bracelets, pill pouches, pendants, beaded beads, and key chains. We also included a bunch of different grids that you can photocopy and color with markers.

Of course I’m biased, but I think it’s a really beautiful book. We included multiple colorful images on almost every page, 172 pages in all. It was a huge layout challenge, but Zelda nailed it. My original goal was to write 128 pages on how to use algorithms to make beaded jewelry, but the more we explored the space, the more we found. Not just millions of algorithms, the space of possibilities is infinite. So of course, we couldn’t include them all. But we used math and Roger’s custom software that he wrote for this project to help us find dozens of the easiest algorithms and more than a hundred more in increasing levels of complexity. We included all of our favorites. 1/2

#MathArt #beading #Genuary #math #beadweaving

Someone: What is calculus useful for?

Me: Calculus is the study of change. The Fundamental Theorem of Calculus compares the instantaneous rate of change, like speed, with cumulative progress, like the total distance traveled.

Covid is another example. We saw reports of new cases every day (change). We also saw data giving us the total (cumulative) numbers of people who got COVID over a week, a month, a year. Calculus allows us to convert back and forth between the daily numbers and the total numbers. #math

And it’s done, my first stylized painting after all those Bob Ross tutorials. I tried really hard to to focus on the quality of my brushstrokes and not to overwork this piece. My success in the regard is debatable.

Two Foxes under an Orange Sky
9” by 12”
Lightfast gouache paint on Arches 100% cotton paper
#painting #art #gouache #watercolor #landscape

@gemlog thank you. Now go make some art, dance, or sing a song. Enjoy the process like it’s the only thing that really matters.

@gemlog thank you. If you focus on making art as a process, then there is no failing at art. You just mix some colors together on a palette, and transfer the paint onto the paper or canvas. It doesn’t need to look good if your focus is on the process, the experience, rather than product, the finished painting. I have made a lot of ugly art that I enjoyed making. I have made mediocre art as a way to learn things and see the world. We don’t dance to get to the other side of the dance floor. We don’t sing to get to the end of the song. #art #painting

Now that I’ve followed seven painting tutorials by Bob Ross, here is my first attempt at painting a landscape using what I learned. Bob encourages his viewers to use his techniques to create their own worlds, and so I used my own color choices and composition here, made up entirely from my imagination. Bob uses a lot more brown and gray than I like to paint. So I let loose and used brighter colors. Unlike Bob, I used a set of five basic mixing colors of Royal Talens gouache in CMYKW. This little painting is 4.5” square on cotton paper. #painting #gouache #art #landscaped

The patch on the knee started wearing down. So I added some more embroidery to reinforce it. Good as new.

This is hitomezashi sashiko stitching on vintage silk. I use the pattern in the weave as the grid for my stitches. #sewing #embroidery #visiblemending

So nice, I made it twice. It’s almost identical to the first one, but this one has a very different lace trim. With over 50 pieces, this jacket is not an easy project. Black is the hardest color to sew becuase it’s the hardest to see. One of the hardest parts was keeping Kepler’s white dog hair off of it. #Sewing

My emotional support gummy bears arrived.

@gemlog hi. Thank you for the shout out. I don’t typically add links to all my posts here on mastodon because people (like you) are smart enough to know how to go look. My old website is quite a relic at this point, but there is still a lot of nice (old) photos to see there of mathematical bead weaving. Now, I post my new work on social media, and everything that is for sale is in my Etsy shop, gwenbeads. I was certainly one of the earlier mathematical bead weavers, went deeper earlier than anyone at the time, but over the years, a large handful of other talented women have explored the space as well. If you’re interested to learn, I have dozens and dozens of tutorials available on Etsy and a few free ones on my websites on the patterns page on the left. If you can manage thread and like solving puzzles, beading feels a bit like doing a puzzle, and when you solve the puzzle, you win jewelry. 💎

Ionic Rhombic Dodecahedron Beaded Bead

It measures 1.25 inches across. It contains 624 beads and a few meters of fishing line to hold them all together. After all of these years of weaving beads, I still find it remarkable that we can make hollow structures with them that have such large holes.

#beading #mathart

Mathober Day 15: Chord

If you want to draw a convincingly round moon with craters, or a Jupiter with swirling vortices, then you need to draw circles in perspective on the surface of sphere. The key is doing this is drawing ellipses that are more circular in the center (eccentricity close to zero) and thinner near the edge (eccentricity close to one).

The precise way to do this requires a geometric construction shown on the right. Choose D, the height of the major axis for your ellipse. Draw a chord with height D on a circle, as far from the center horizontally as you want the ellipse to be. With D as the hypotenuse, draw a right triangle with legs horizontal (S) and vertical. Then D = S cos (alpha), where D is the major axis, S is the minor axis and alpha is the angle between D and S.

Comparison of the two paintings on the left shows how not using this principle (top) or using it (bottom) affect the illusion of that the painting is spherical. 
 #mathober #mathober2025 #mathart #watercolor

Finally finished this light weight, lined jacket. It’s about 60 pieces in all, which is a lot for one garment. It’s composed of four different fabrics including a very old piece of rust colored silk from my grandmother that I used for the lining and bottom ruffle. Everything else is cotton including jersey on the upper sleeves and all of the brown trim. The print is cotton voile from India.

I’ve been looking at what the on-line stores are currently offering, and one thing is for sure, this isn’t what is currently in style. lol. So much of what they’re showing these days is so formal and conservative. Too many sport coats and blazers!

So I added the bottom ruffle in silk because I wanted the jacket to be a bit longer, and I had the scraps left to do it. Plus, ruffles are fun. Finally using up this piece of silk that I’ve been holding onto my entire adult life is giving me a special satisfaction. I think Nana would approve. #sewing

No kings!

www.mobilize.us/nokings/

I’ve been feeling a little unsettled lately. I call this one “A Black Hole Erupts Ketchup and Yellow Mustard.”

4” by 6”
Pigments ink and watercolor on Tomoe River paper

Triangle Centers
A Brief Introduction

The center of a triangle is an interesting idea. Unlike circles, a triangle’s center isn’t always the same point because triangles aren’t generally symmetric, and there are lots of different ways to define what you mean by the center of a triangle. Years ago, when the internet was young, I remember finding Clark Kimberling’s online Encyclopedia of Triangle Centers, which had documented hundreds of different ways to define a triangle’s center. The Encyclopedia now contains nearly 40,000 different definitions.

The four most famous triangle centers are the center of mass, circumcenter, incenter, and orthocenter. These were all known by the ancient Greeks, making them more than a couple thousand years old. All four of these can be easily demonstrated by folding paper. So get yourself some paper and scissors, and follow along.

Remarkably, some triangle centers can fall outside the triangle, especially if you use an obtuse triangle—one with at least one obtuse angle. So start your exploration with an acute triangle. To keep it interesting, try not to make your triangle too close to equilateral. Make each of the sides at least 2-3 inches long. Cut out four copies of your triangle.

This large beaded bead is a truncated icosidodecahedron using my Infinity Beaded Bead technique.

It contains 1620 beads and several meters of thread. It measures about 5 cm in diameter and is probably the most hollow beaded bead I’ve ever stitched.
#mathart #geometry #beads

Three Cats by the Bay

Royal Talens Gouache on Arches cotton paper
6” square

This is the ninth painting in my series of fantasy landscapes in gouache. I never thought I’d enjoy painting landscape this much.

For the record, some gouache painters say that your gouache paint should be thick like heavy cream and not watered down. They say your brush strokes should be well defined and minimal. While those might be good advice more generally, I broke broke both of those rules a thousand times on this piece. I work in many layer, thin to thick, and I pet my painting with my brush. Paint in the way that feels natural to you, and your style will emerge naturally.

#gouache #painting #watercolor

Physicists conjecture that for each cat, there is an anticat of the same size but opposite temperament. Some cats are shifted red and some are shifted blue. I’m not sure I got that all right. I was prety sleepy during the lecture.

Cat and Anticat
Doodle No. 141

8” square

Drawn with archival archival black pigment ink, highly lightfast (fade resistant) watercolor pencils, mica paint on Arches 300 GSM 100% cotton paper

#watercolor #mathart #physics #astronomy #rainbow

I realized that I haven’t showed you all of my black hole doodles yet! This is probably the most recent one. I can tell because the shading makes the holes look more convincing, and that took me a lot of practice to figure out how to do that. Can you find the waterbear?
I call this piece…
Cosmic Ooze
Doodle No. 108
Watercolor, ink, colored pencil 
on 8” square cotton paper
#art #MathArt #BlackHole #surface #watercolor #painting #astronomy #microbes