A horseshoe arch of of pale yellow stone contains an intricate zellij tiling of green, turquoise, blue, white and golden brown tiles. Interlaced lines form sixteen-pointed rosettes of two kinds. The symmetrical design has several types of geometric shapes.
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
So I have a book called Fractal Cuts by Diego Uribe, and pretty much every time I try to make one of the designs in it, I end up with something different. It continues to amaze me what can be made with a piece of paper and a pair of scissors. #origami#mathart
Paper that has been cut and folded like a pop up card. It has many steps in 4 different sizes.
Circles with relative radii 1, 2, and 3 fit in a circle with radius 6. This is related to the pythagorean triple 3-4-5 as first picture shows. Those circles can produce circle tilings, second picture shows to the left the straightforward tiling created from the arrangement and to the right a variation with less symmetries. Third picture shows an artistic rendering of the basic apollonian gasket discussed and fourth picture a bigger one derived from the tiling. #tilingTuesday#tiling#geometry#mathart
This was a challenging one for me, since I usually use lots of color. I went with an "*" as the shape and played with transparency, size, and movement.
Over the course of 2022-23, I accumulated several dozen 3D-printed (selective laser sintered nylon) prototypes for jewelry: Spheres banded by loxodromes, cyclides diagonally banded by images of great circles in the 3-sphere, annular portions of minimal surfaces and singular complex-algebraic space curves, and a few miscellanea. Here they are as ornaments for a holiday tree in anticipation of the solstice.
🔱NEW SHAPE ALERT🔱
ðis is just ðe xyz slice(ðe full fractal is 4d ) & it somehow has ðe mandelbrot set as ðe xy plane & burning ship as ðe xz plane(but it gets infinitesimally θin???)‽‽ ðe formula doesn't even have abs literally where did ðis come from‽‽‽
Soo ðis is ðe xzw slice(wiθ some better coloring), apparently ðis ("Hopfbrot")fractal just has higher dimensional analogues of ðe 1d filaments in 2d fractals all over ðe place🤨
🤔🤔 its also suspiciously similar to ðe 3d iqbrot, but not quite
I feel like we could all use a color wheel right about now. I painted this with watercolor, black ink, and colored pencils on 12” square cotton paper. #mathart#watercolor#color
Painting of blocks that appear to be 3D in three hexagonal rings that all fit together like a tessellation. The outer ring is 12 blocks forming a color wheel. The middle ring is 6 blocks forming a muted color wheel. The center is a single gray block. Cats sit on top. Around the outside are doodles of various things like butterflies and space ships.
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.
Four photos of an ornate beaded bead from different angles. It has large faceted beads on the inside and columns of seed beads on the surface, with one column over each large faceted bead.
From the exhibit caption: “an ornate carved ceiling from a palace in Torrijos, revealing the Islamic influence on craft practices in medieval Spain.
The ceiling was built about 1490 using strapwork carpentry, a construction technique that creates patterns from interlacing strips of wood.
An Arabic phrase is repeated in the white plaster ... 'you drink from happiness', suggesting that the original room below the ceiling was used for entertainment. By the 1890s, the palace was in poor condition and the owners sold the intact parts. The V&A bought this ceiling in 1905.
MAKER:
Unrecorded artisans
LOCATION AND DATE:
Torrijos, Spain. About 1490
MATERIALS AND TECHNIQUES:
Pine wood, carved, painted and gilded, with modern plaster of Paris panels”
[1/n] I have been researching the geometric possibilities of the radiant number ρ (aka plastic ratio), the real solution of the equation x³ = x + 1. It has many interesting numerical properties, for example it can serve as the base of a numeral system. Here I present a family of substitution tilings based on squares and radiant rectangles. For the square there are two main possibilities, which with all rotations and mirroring of the partitions and subtiles produce a great number of possibilities. Some possible derived tilings are shown. #TilingTuesday#geometry#tiling#mathart#radiantnumber
Although my online shop Differential Geometry is a primary source of income, I maintain (on a static html site) a list of other creators' mathematical online shops, and I hope you will browse and support us all!
A deep blue mottled annulus surrounds a black hole, or the moon's disk during a total solar eclipse. On closer gaze, silver ant-like shapes follow each other endlessly around a torus. The torus is tiled with a golden hexagonal grid. Each ant is isolated in its own cell.
Deep Mandelbrot set zoom with mostly red/yellow/blue/black colors. The patters appear as thin rings around the so called "Minibrot" set, which is black.
This prompt is a hard one for me to choose for because I’ve beaded dozens of polyhedra over the years, perhaps more than a hundred. I decided to share my favorite of them all, which is also one of my largest.
I call this one a Crater Moon Beaded Bead.
The polyhedron on the outside surface is a truncated icosidodecahedron (4.6.10). The inside layer is (3.4.5.4), also known as the rhombicosadodecahedron.
I painted this one at the end of December 2021 as the Omicron variant was starting to circulate, and I was anticipating the massive wave of illness that was eminent. Here’s what I wrote about it at the time:
This is what normal looks like, a normal distribution, that is, a bell curve. Right now, nothing else feels particularly normal. I’m not sure what those devices do, but they obviously have a lot of functionality. I’m hopeful they’ll get us out of this mess soon. At the very least, they have a lot of shimmering dots of mica paint that twinkle when the light hits them right.
Painting of two aliens twins standing atop a normal distribution curve. They are holding weird contraptions including a platform with a cat sitting on it. In the background are a rainbow, plants and a flight capsule attached to a parachute.
I continue my exploration of integer factorization tiling.
An integer N is represented as N tiles, produced through iterative splitting according to its factors.
This work illustrates N = 2160, with factorization [3, 3, 3, 5, 4, 4]. #GenerativeArt#MathArt#DigitalArt#CreativeCoding#IntegerFactorization