Jitterbug, one of my best-known origami creations.

Geogebra file: https://www.geogebra.org/m/wsxthyaz
Origami instructions: http://foldworks.net/wp-content/uploads/2018/06/jitterbug.pdf

I first came across Buckminster Fuller’s Jitterbug in Amy C. Edmondson’s A Fuller Explanation (1987).

As I didn’t have dowels and four-way rubber connectors, I made several cuboctahedra that worked as Jitterbugs but were not very reversible. Some were from paper and others from drinking straws and elastic thread. This modular origami version is the most recent version.

Beaded Archimedean Solids!!!

I had lots of fun over the past two weeks making these for the pigeonholes at the TMiP conference.

Each one has an n-colouring on the edges where n is the number of edges at each vertex (so edges that meet each other have different colours) and there's a pair of colours on each one which form a Hamiltonian cycle.

I've found another partition of the fourth root of 2 rectangle (first picture), which is essentially different from the previous one. It produces interesting tilings (second picture). And when the amount of splitting is made dependent of the position of the tilings, one can get nice artistic results (last two pictures). (The appearance of what appear to be flags of Spain (and other countries) in one is entirely coincidental.)
#geometry #tiling #mathart #algorithmicArt #AbstractArt #Mathematics

A noperthedron container printed!

Swirly star

At @recursecenter in our Annotated Turing study group we got talking about diagonalization. I made a joke - then I made a poster and bumpersticker to go with it.

It's always a fun conversation to have - what is real - what can we express - what can we compute

Into the Icosidodecahedron

Tiling of golden rhombus prisms and pentagonal prisms.

As an amateur coder many years ago, I wrote some libre software called ePiX ("epic" with a soft k) to create mathematically-accurate, typographically-matching figures for a paper.

An ePiX source file is a C++ program containing high-level picture commands. When the program is compiled and run, it writes a LaTeX picture environment and optionally compiles that into a stand-alone PDF file; shell scripts manage the details.

There is 3D capability, but it often needs human supervision. Although the code base works, modifying the internals would be difficult. I recommend against looking in there.

That said, writing new high-level features is straightforward. I use ePiX to create all T-shirt and poster designs in my online shop; all images and animations I post on social media; all diagrams in my papers, books, and teaching materials since 2007. I used ePiX to create illustrations for "Lie Sphere Geometry" by Tom Cecil, "Complex Function Theory" by Don Sarason, and two issues (2008 and 2021) of "What's Happening in the Mathematical Sciences" by Dana MacKenzie.

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If there is a current ePiX package for your operating system I recommend installing that; otherwise, install from sources. The project page (below) links to the source tarball.

There is a very short blog post here: https://www.diffgeom.com/blogs/free-online-math-materials/epix-drawing-for-latex/

The project page is: https://diffgeom.org/epix/index.html

There is a gallery of 80 sample images/animations and their source files (the sample files are included with the source tarball): https://diffgeom.org/epix/images/index.html

The sources come with a tutorial/manual. There is also a short Tips and Tricks document linked from the project page (not included with the source package): https://diffgeom.org/epix/epix_tips_and_tricks.pdf

These tilings are based on the decomposition of a right kite (with two right angles) whose sides are in the ratio √2. This decomposition can be done with any right kite, but with that ratio one can make nice drawings in the kites which fit neatly with others in the resulting tessellation.
#TilingTuesday #geometry #tiling #mathart

Eye-popping fractal floor tiles, Aswan, Egypt

#TilingTuesday snaking nonagons on a starry sky.

I have discovered another non-trivial rectangle partition into scaled copies of itself, with aspect ratio the fourth root of 2 (first picture). I've not found on-line any mention of it. Of course swapping rectangle positions more similar partitions can be made. In the next two figures two of the non-periodic tilings which can be derived from those partitions. As this rectangle is closer to a square than the others I know with this property, it is more suited to do a tiling where the amount of splitting depends on the distance of the tiles to the center of the canvas (last picture). I have changed the code which computes colours so that they can be chosen more precisely and not by a single equation.
#geometry #tiling #mathart #algorithmicArt #AbstractArt #Mathematics

A suitably-scaled \(\wp\)-function of the unit square torus induces a holomorphic double cover of the unit sphere branched at \(0\), \(1\), \(\infty\), and \(-1\). By allowing the surface to "breathe" radially, the two sheets can be separated.

Another look at the Apollonian gasket. This shows that the process doesn't use simple inversion, since that would distort the image within each disc.

Happy birthday to #mathematician Karen Keskulla Uhlenbeck (b. 1942), a founder of modern geometric #analysis & winner of 2019 Abel Prize for “her pioneering achievements in geometric partial differential equations, gauge theory, & integrable systems, & for the fundamental impact of her work on analysis, geometry & mathematical physics.” The only woman winner, she donated half the money to orgs which promote engagement of women in math.⁠1/
⁠
#womenInSTEM #printmaking #sciart #mathart #mastoArt

#math #hopf #fibration #mathart
https://www.patreon.com/posts/hopf-fibration-137213197?utm_medium=clipboard_copy&utm_source=copyLink&utm_campaign=postshare_creator&utm_content=join_link

I played with paint today. The packing radii for n-dimensional spheres is $/sqrt{n} - 1$ and spiral of archimedes hypotenuses follows sqrt(n), so I subtracted 1 from each hypotenuse and then added color.

8x8in gouache on hot pressed cotton

ASCII Study #7 - Disponible / Available, link en bio
Stabilo 88 fine 0.4 on A4 200 g/m2
IG: www.instagram.com/angel198
Worldwide shipping
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#angel198 #art #genart #penplotter #mathart #generativeart #artwork #arte #penplotterart #parametric #contemporaryart #computerart #modernart #visualarts #architecture #drawingrobot