Geometry Links - July 19, 2026

Probability density map of the single electron of hydrogen
https://x.com/cosmosarcive/status/2075167136067293476

Volume 28, Issue 3 of the Nexus Network Journal, articles selected from the papers presented at the Nexus Conference 2025 in Vicenza, Italy, amidst the extraordinary legacy of Andrea Palladio
https://link.springer.com/journal/4/volumes-and-issues/28-3

All elementary functions from a single binary operator
Paper: https://arxiv.org/abs/2603.21852
Illustration: https://x.com/pickover/status/2075588890006573227

A Neural Sheet Discovers the Shape of Data
https://x.com/mathelirium/status/2075617210135945601

The different forms DNA takes

https://x.com/mathemetica/status/2076310833953755380
Editorial Comment: DNA and the origin of life have been among my tangential interests since high school.
And in recent news: "Scientists have discovered all five canonical nucleobases (adenine, guanine, cytosine, thymine, and uracil)—the fundamental building blocks of DNA and RNA—in pristine samples from the carbonaceous asteroids Ryugu and Bennu. Researchers also found precursor compounds like amino acids and ribose sugars, strongly reinforcing the theory that meteorites delivered the molecular ingredients for life to early Earth.”

The Escherian Stairwell at Rochester Institute of Technology
https://www.youtube.com/watch?v=iBY4HaAngaA

Patterns set by Bessel function zeros
https://x.com/mathemetica/status/2076705550688211241

Spinning the Yin/Yang symbol
https://x.com/Rainmaker1973/status/2077050486906065198

Orbital resonance in the solar system
https://x.com/cosmosarcive/status/2077326272775217498

Resonance nodes on a circular plate - cymatics in 2 & 3D
https://x.com/mathemetica/status/2078170771269341501

Weird geometry, kisrhombille, forsythia, whelmer, drifter, writher, clouder, powerbox, source, documentation, animations and graphics
https://fleen.org/
hat tip Cliff PIckover

Physical realities beyond the Standard Model
https://x.com/Dragonmaurizio/status/2078490402295107707

Editorial Comment: I’m seeing more interesting geometry in my feeds these days. Ideas are exploding it seems.

Geometry Links - July 10, 2026

Sand watch
https://x.com/spydenator/status/2062867816534143162

Icositetrahedron with twelve regular heptagonal cross-sections
https://www.facebook.com/reel/1721999075896555
hat tip Kirby Urner

Skeleton of a stingray
https://www.tumblr.com/wewantnothing2/819977959294337024/the-skeleton-of-a-stingray

Mesh Module
https://designawards.core77.com/Toys-Play/143113/MeshModule-A-Playful-Modular-Mesh-System-for-Creative-Construction

Complete notebooks of Leonardo da Vinci now online
https://teche.museogalileo.it/leonardo/ricostruzioni/index.html?lang=en

Gerald De Jong’s "mobile tensegrity at scale"
https://www.facebook.com/photo?fbid=10164141494898948&set=pcb.10164141517248948
https://fluxe.art/

Monorhaphis Chuni - the structure of an 11,000 year old deep sea sponge
https://timesofindia.indiatimes.com/etimes/trending/this-deep-sea-creature-can-live-up-to-15000-years/articleshow/115060151.cms

Polyèdres et particularités mathématiques
https://www.facebook.com/groups/196165767185827/

A common roadmap for mathematical models of brain rhythms
https://x.com/VFD_org/status/2073180094835589537
https://x.com/VFD_org/status/2073180094835589537/photo/1

Canonical Projection Tiling (4 → 2)
https://edmund.mathematicians.org.uk/shaders/4to2CPT/

Visualization of the building blocks of matter in a dynamic 3D spiral
https://x.com/mathemetica/status/2075199649443643770

Zernike polynomials Z_n^m form an orthogonal basis set over the unit disk
https://x.com/mathemetica/status/2074936053304320113

Geometry Links - June 6, 2026

Growth ratio set in motion
https://x.com/mathemetica/status/2049938085345972598
Thread on Riemann Hypothesis
https://x.com/mathemetica/status/2050084790918107396
Editorial Comment: @mathemetica does good work

Local universe fly-through of 55,486 galaxies
https://x.com/S_Conradi/status/2050292756619166006

Stable three-body solutions
https://x.com/Rainmaker1973/status/2050242433099731261

A short history of geometric Algebra by Tim Havel
https://web.mit.edu/tfhavel/www/IAP-02/lect1.pdf

A Tensegrity-Based Side Table Made out of Pipes
https://www.core77.com/posts/143987/A-Tensegrity-Based-Side-Table-Made-out-of-Pipes
More Pipe DIY at https://www.instagram.com/pipepipediy/

Mapping birdsong
https://x.com/pascal_bornet/status/2051165179883528280

Square to triangle
https://x.com/olurkanka/status/2052821752468627656

The geometry of butterfly eggs
https://bsky.app/profile/ariaa.bsky.social/post/3mlntqbhbx22j

Charting Aquinas' Summa Theological and the Catholic Liturgical Calendar
https://owen-cyclops.myshopify.com/

Anthony James geometric reflections
https://bsky.app/profile/arepublic86.bsky.social/post/3mlu2c6arqk2a
https://www.anthonyjamesstudio.com/

Neither zero nor one but a third state, qutrits in quantum theory
https://www.facebook.com/photo?fbid=122217749198545093&set=a.122112138236545093
https://www.youtube.com/watch?v=ipSxO6UIs3I
hat tip: Bob Whelan

Suspension-Based Outdoor Chair - not quite tensegrity but...
https://www.core77.com/posts/144235/Sagas-Transat-a-Suspension-Based-Outdoor-Chair
https://saga.now/

Geometry Links - April 2026

Gaosu Sheying’s slow motion art
https://x.com/IntVideos_x/status/2036445478468956476

The Plenum-to-Particle Loop Sequence of Field Structure Theory (FST) by Don Bridell
https://fsi-group.mn.co/posts/97325920

The Splash of a Drop
https://publicdomainreview.org/collection/the-splash-of-a-drop-1895/
hat tip Cory Doctorow

Harmonious Geometry: The Hirajoshi Wave
https://x.com/mathemetica/status/2045190962364956840
hat tip Lucas Gonzalez

A streamlined paper plane
https://x.com/buzz_video_buzz/status/2045363954025926909

Extruded cubic cells (24 faces, 36 edges) tessellated via snapology origami
https://x.com/mathemetica/status/2046092594162373007
Editorial Comment: from Harvard but I wonder if anyone there still remembers Dr Arthur Loeb and his Design Science course, let alone the Philomorphs

The stars from Mars
https://x.com/MindProbe/status/2046394310396940665/photo/1

Cellular landscapes
https://www.reddit.com/r/CrazyFuckingVideos/comments/1sxgtw8/the_crowded_interior_of_a_cell/
https://gaelmcgill.artstation.com/projects/Pm0JL1
https://www.digizyme.com/cst_landscapes.html
hat tip Massimo@Rainmaker1973

Jon Foreman's Rock-Based Land Art
https://www.core77.com/posts/143878/Jon-Foremans-Rock-Based-Land-Art

Penrose Triangle
https://x.com/Y4lP2012/status/2049512113727504834

Luca Pacioli’s Rhombicuboctahedron: Description, Construction, and Architectural Reception
https://link.springer.com/article/10.1007/s00004-026-00885-9

Ice XXII - the most recently discovered form of ice with a crystal structure which repeats its pattern every 304 molecules
https://www.quantamagazine.org/physicists-discover-the-most-complex-forms-of-ice-yet-20260427/
hat tip boingboing.net

Geometry Links - March 25, 2026

Puzzlebomb 2 & 3 D jigsaw puzzles
https://puzzlebomb.com/collections/browse-all-puzzles

Star 3D Sensory Fidget Toy
https://www.tiktok.com/@george_grm/video/7532161413297638658

Ruth Asawa exhibition at MOMA, photographs by Elizabeth Resnick
https://www.facebook.com/photo?fbid=10225437769486204&set=pcb.10225437776886389

Ulam’s spiral of primes
https://x.com/PhysInHistory/status/2015029114621804612

Resolving a topology puzzle
https://www.quantamagazine.org/two-twisty-shapes-resolve-a-centuries-old-topology-puzzle-20260120/
hat tip to boingboing.net

Rinus Roelofs’ Compound of 5 Tetrahedra to Tetrahelix
https://www.facebook.com/reel/935963982231517
and Icosahedron to Tetrahelix
https://www.facebook.com/reel/2570762116675763

Hypertiles toy
https://funinmotiontoys.com/products/hypertiles

Kirby Urner’s Cascadian Synergetics
https://docs.google.com/presentation/d/1zcJsWYuV_DW1HKZirsoufacPMNlXQgWoYHeYPOPS1kY
https://www.youtube.com/watch?v=4G0sHXgpZxA

Visualizing Climate Conference 2026 - Bologna, Italy, November 4-6
https://climate.copernicus.eu/visualising-climate-2026

Mapping all the connections in a fly’s brain
https://www.nature.com/articles/s41586-024-07686-5
BBC article: https://www.bbc.com/news/articles/c0lw0nxw71po
If you meet a paywall: https://archive.ph/ivKQL

Beading with Algorithms: Cellular Automata in Peyote Stitch - "Can you weave beads so that each new stitch you take depends upon what you have already beaded? To answer this question, we explore how the mathematical concept of one-dimensional cellular automata can be applied to beaded peyote stitch, in other words, beading with algorithms.”
Beading With Algorithms: Cellular Automata In Peyote Stitch by Gwen Fisher, Roger Antonsen, Zelda Lin (Artist)
https://www.worldscientific.com/worldscibooks/10.1142/14357#t=aboutBook
30% off code: RECMATH30

Icosahedral wind machine
https://www.instagram.com/reel/DV0zPcUj-FG/?igsh=cjBqY3NhNWJiYTlt
https://www.instagram.com/geowind.kr/
https://geowind.kr/
hat tip to Marshall Spriggs
Editorial Comment; I wonder if it can go through a Jitterbug transformation

Geometry Links - January 10, 2026

Angela Cupertino - scholarship winner at Pacific Coast OrigamiUSA Conference 2025
https://www.facebook.com/photo/?fbid=1128729186042290&set=a.502627711985777

Kinetic furniture
https://www.core77.com/posts/139276/Experimental-Kinetic-Furniture-Design-Aaron-Preyers-Blooming-Project

AI that builds machines called Noyron trained a Large Computational Engineering Model [LCEM] and designed his hypersonic precooler which uses a fractal folding algorithm to chill down superheated air
https://x.com/BrianRoemmele/status/1989759968959156297
hat tip Karl Thideman

8th grader Miles Wu folds origami that can hold over 9000 times its own weight
https://www.youtube.com/watch?v=QCODaKLzL-w
hat tip to boingboing.net

283 trillion colors of fractals
https://www.facebook.com/reel/1988387765038458
hat tip Vinay Gupta

The mountains of Pluto
https://x.com/MAstronomers/status/2005055593502179767

Best Northern Lights photography of the year - the geometry of our electromagnetic atmosphere
https://capturetheatlas.com/northern-lights-photographer-of-the-year/

Natural motion of a pendulum
https://x.com/Saganismm/status/2007795854145712410

New Kosticks design
https://www.facebook.com/watch?v=1540874743631158

Aqua Swimming Sea Bike
https://x.com/SalmanGreen/status/2009188815756480841

Frost flowers
https://www.instagram.com/p/DRuTEkoEWTP/
hat tip to boingboing.net

Robert Fathauer mathematics art
https://www.mathartfun.com/robertfathauer.com/index.html

Geometry Links - Halloween 2025

Geometric and mandala programs
https://www.omnigeometry.com/

Tesla valve - a fixed-geometry passive check valve
https://x.com/Rainmaker1973/status/1965645158734557427

Two from Daniel Ari Friedman
Quadmath
Code: https://github.com/docxology/QuadMath
Paper: https://zenodo.org/records/16887800 QuadMath: An Analytical Review of 4D and Quadray Coordinates
QuadCraft -- this is a (functional) work in progress, it is a browser-based video game that is like "MineCraft but in the Isotropic Vector Matrix (close-packed spheres) rather than Cubic setting"
https://github.com/docxology/QuadCraft/

Callen Schaub artworks
https://www.facebook.com/reel/1147623173958331
https://callenschaub.com/
hat tip Nathan Koenig

Truncated Icosidodecahedron in Beads Crater Moon Beaded Bead
https://gwenbeads.blogspot.com/2017/12/truncated-icosidodecahedron-in-beads.html?m=1
Whole Movement - folding circle geometries
https://www.wholemovement.com/
https://www.wholemovement.com/gallery

A box with a reversible butterfly lid
https://www.core77.com/posts/138856/A-Box-with-a-Reversible-Butterfly-Lid\

Kirigami parachutes
https://www.core77.com/posts/138862/Inexpensive-Inside-Out-Parachutes-Based-on-Kirigami

Jeremy Frey - 2025 MacArthur Fellow - basketry weaver artist
https://www.youtube.com/watch?v=e_PBNBFM-_g
https://jeremyfreybaskets.com/

NYTimes on the Bridges Conference, featuring the work of Rinus Roelof
https://www.nytimes.com/2025/10/10/science/mathematics-art-roelofs.html
If you meet a paywall try: https://archive.ph/Uhige

Ghee Beom Kim digital geometric art
https://www.facebook.com/ghee.b.kim/reels/

Ekaterina Lukasheva kusudama.me with Klara Mundilova @klara.mundilova made for an exhibition “Connecting Artifacts” at @tachi.tomohiro lab.
https://www.facebook.com/watch?v=1154415900127186

Geometry Links - September 8, 2025

2024 Information Is Beautiful Awards
http://www.informationisbeautifulawards.com/news/680-announcing-the-2024-winners
hat tip http://boingboing.net/2025/07/21/information-is-beautiful-and-heartbreaking.html

Torus to Moebius
http://www.facebook.com/1206771269/videos/1305447411151210

Fibonnaci fastener
http://www.core77.com/posts/137908/Former-Industrial-Designer-Develops-Tool-Free-Joinery-Method-Based-on-the-Fibonacci-Spiral
More work from the designer, Anton Gaia: http://antongaia.com/#index

Teacher of Islamic geometric patterns
http://www.samiramian.uk/
Flat folding measuring spoon - interesting design but an expensive product
http://www.rejoiceto.com/products/polygons-flat-3-in-1-folding-measuring-spoons-2

1890s geometric images made from soundwaves
http://publicdomainreview.org/essay/picturing-a-voice-margaret-watts-hughes-and-the-eidophone/
hat tip boingboing.net
NB: Looks a little different than cymatics (from earlier editions of Geometry Links):
Acoustic healing for hearts (and cymatic forms of heart cells)
http://stanmed.stanford.edu/listening/innovations-helping-harness-sound-acoustics-healing.html
hat tip Marjorie Farrell
Milford Graves - a jazz drummer who made music and animations from his heart rhythms
http://www.nytimes.com/2020/08/05/nyregion/milford-graves-drummer.html
http://www.milfordgraves.com/
http://vimeo.com/user92466694 - Graves’ videos
http://www.fullmantis.com/welcome - remarkable animations of heart music around 32:00
Chaldny Figures, Cymatics, and the visualization of sound
http://publicdomainreview.org/collection/chladni-figures-1787
http://youtu.be/Yw13EAX3cZk - visualization starts about one minute in
Visualization of sound - cymatics
http://www.cymascope.com
Photography of musical notes in a bowl of water
http://www.saltspring.band/2018/11/08/photography-of-music-notes-in-a-bowl-of-water/
Blasting sound waves at water and gallium: cymatics tests for forthcoming project
http://vimeo.com/163041604

Bloom patterns: radially expansive, developable and flat-foldable origami
http://royalsocietypublishing.org/doi/10.1098/rspa.2025.0299
News Article: http://www.nytimes.com/2025/08/19/science/origami-bloom-patterns.html
If you hit a paywall, try http://archive.md/EG10h
hat tip: Vera Viana

Edna Andrade: Imagination Is Never Static - August 30, 2025–January 4, 2026, University Research Gallery, Harvard Art Museums
http://harvardartmuseums.org/exhibitions/6455/edna-andrade-imagination-is-never-static
There are also a series of talks and events associated with the exhibition and many illustrations of her work at the website

Turning steamed buns into a variety of shapes
http://www.reddit.com/r/oddlysatisfying/comments/1n056ci/turning_steamed_buns_into_various_shapes/
hat tip: Michelle says: Be kind. Always. ‪@snarkysillysad.bsky.social‬

Ten martini proof and Hofstadter’s butterfly
http://www.quantamagazine.org/ten-martini-proof-uses-number-theory-to-explain-quantum-fractals-20250825/

Modular hex by Anna Drozd-Tutaj
http://www.facebook.com/reel/706892609058365
More at http://www.instagram.com/anna.drozd.tutaj/

Geometric deconstruction
http://www.instagram.com/reel/DNvogO24gz4

Geometry Links - July 21, 2025

Harnessing the Universal Geometry of Embeddings: "A new paper shows all language models converge on the same "universal geometry" of meaning. Researchers can translate between ANY model's embeddings without seeing the original text."
https://arxiv.org/pdf/2505.12540
hat tip: Ethan Mollick

A Tour in the Wonderland of Math with Python - A collection of python scripts for drawing beautiful figures and animating interesting algorithms in mathematics.
https://github.com/neozhaoliang/pywonderland
hat tip to Karl Thidemann

One of Robert Boyle's "Curious Mathematical Forms" (1670)
https://x.com/pickover/status/1931542696474079529
hat tip to Karl Thidemann

Expanding Racks from Henry Segerman
Video: https://www.youtube.com/watch?v=iWknov3Xpts
Printable plans: https://www.printables.com/model/1305045-expanding-3-4-5-triangle
Article: https://www.core77.com/posts/137381/Expanding-Mechanisms-Designed-by-Henry-Segerman

Glynn Fractal
https://x.com/pickover/status/1831016941785407558
Glynn Julia Set
https://www.flickr.com/photos/subblue/3647227394
hat tip to Karl Thidemann

Geometric animations
https://x.com/Yann_LeGall

A new tetrahedron that always lands on the same side
https://www.quantamagazine.org/a-new-pyramid-like-shape-always-lands-the-same-side-up-20250625/
hat tip boingboing.net

Culture changes perception: circles or rectangles?
https://www.science.org/content/article/culture-literally-changes-how-we-see-world
hat tip: @BernieDoesIt@mstdn.social

Emily Dickinson’s Herbarium - pressed flowers and designs from a unique poet at an early age
https://iiif.lib.harvard.edu/manifests/view/drs:4184689$1i
hat tip: https://www.themarginalian.org/2017/05/23/emily-dickinson-herbarium/

Geometers Circle - geometric art and tutorials
https://geometerscircle.com/

Kinetic model of a tesseract
https://www.creativeapplications.net/project/round-about-four-dimensions-exploring-the-unknown/
hat tip: https://www.core77.com/posts/137789/An-Eye-Popping-Kinetic-Representation-of-a-Tesseract

Rinus Roelofs' exhibit at the Bridges conference
https://www.facebook.com/1206771269/videos/pcb.10239412001017345/2107838516375795
https://www.facebook.com/1206771269/videos/pcb.10239412001017345/709305988673842
https://www.facebook.com/1206771269/videos/pcb.10239412001017345/1800623344186058

Geometry Links - May 23, 2025

 Lunar moth - biological design

https://www.youtube.com/watch?v=puejRndICqQ

Archimedean Solids in the 15th and 16th Centuries
https://veraviana.net/history-of-science/archimedean-solids/

Specimens of “fancy turning” from 1869
https://publicdomainreview.org/collection/fancy-turning/
hat tip boingboing.net

Geometry homebrew animation
https://x.com/LimbaTrip/status/1905481692619702507

The Schrödinger Equation
https://www.facebook.com/watch?v=1008462380657737
hat tip Gil Friend
Another visualization for one dimensional Gaussian wave packet and Non Relativistic Schrödinger equation
https://x.com/PhysInHistory/status/1922617024246612302

Hopewell Culture and mound-building geometry
https://www.bbc.com/travel/article/20221204-the-us-2000-year-old-mystery-mounds

The Blossom of Dimensions - Meditative 3D Mandelbrot Zoom - Music by Art of Chance
https://www.youtube.com/watch?v=-1x9cGWs9yE

A sculptural desk organizer
https://www.core77.com/projects/136193/KIIR-A-Sculptural-Desk-Organizer-for-Creative-Workspaces

A crow’s math skills include geometry
https://www.npr.org/2025/04/12/nx-s1-5359438/a-crows-math-skills-include-geometry

GeekMom's LED deltoidal hexacontahedron covered with 3D printed diffusers with "two #Pixelblaze controllers work in sync to provide a fast frame rate for patterns on the 1200 LEDs”
https://mastodon.social/@geekmomprojects/114354417573389621

1903 Japanese book of wave and ripple designs
https://publicdomainreview.org/collection/hamonshu-a-japanese-book-of-wave-and-ripple-designs-1903/
Earlier:  
from https://geometrylinks.blogspot.com/2023/05/geometry-links-may-24-2023.html
Hokusai’s Quick Lessons in Simplified Drawing in Three Volumes
https://cdn.flipsnack.com/widget/flipsnackwidget.html?hash=ftcsgji5x&bgcolor=EEEEEE&t=1481362893
https://cdn.flipsnack.com/widget/flipsnackwidget.html?hash=fti4xlqen&bgcolor=EEEEEE&t=1481363446as
https://cdn.flipsnack.com/widget/flipsnackwidget.html?hash=fdcj01ckg&bgcolor=EEEEEE&t=1481364640
Article:  https://inaminuteago.com/free-drawing-lessons-great-master-hokusai/
Catalogue Raisonne of Hokusai:  http://www.hokusai-katsushika.org/index.html
from https://geometrylinks.blogspot.com/2020/07/geometry-links-july-23-2020.html
Geometric Hokusai from 100 Views of Mt Fuji
Through a Spider Web:  https://www.pinterest.com/pin/365495325984645798/
Torigoe:  https://commons.wikimedia.org/wiki/File:Hokusai,_Fuji_at_Torigoe.jpg
At Sea (note the Escher transformation long before Escher was born):  https://theconversation.com/how-hokusais-great-wave-came-into-the-world-77750

Bastien Dausse, Gravity Explorer
https://www.instagram.com/bastiendausse/?hl=en
hat tip:  https://www.core77.com/posts/136812/Acrobatic-Artist-Bastien-Dausses-Low-Tech-Wall-Walking-Invention

Geometry Links - March 21, 2025

 Packaging design

https://x.com/gunsnrosesgirl3/status/1876944504051114400

A laptop stand from a single sheet of paper
https://www.core77.com/posts/134948/A-Laptop-Stand-Made-from-a-Single-Sheet-of-Recycled-Paper

Animated Mandelbrot zoom video with pastels and sepia pencil
https://www.youtube.com/watch?v=DU3TaKPhPac

Snowflakes: a chapter from the book of nature by Israel Perkins Warren - published in 1863 - with beautiful illustrations
https://publicdomainreview.org/collection/snowflakes-a-chapter-from-the-book-of-nature-1863/
https://archive.org/details/snowflakeschapte00warriala/page/n3/mode/2up
hat tip:  boingboing.net
A global classification of snow crystals, ice crystals, and solid precipitation based on observations from middle latitudes to polar regions
https://www.researchgate.net/publication/257132993_A_global_classification_of_snow_crystals_ice_crystals_and_solid_precipitation_based_on_observations_from_middle_latitudes_to_polar_regions which found that snowflakes can be divided into thirty-nine categories, further divisible by 121 subtypes.

Simone Conradi drawings "using mathematics and Python, no generative AI"
https://bsky.app/profile/sconradi.bsky.social

Geometric and other art, some intriguing ideas
https://lovid.org/

Unfold Form - origami reusable concrete form that reduces the need for both concrete and steel
https://ethz.ch/en/news-and-events/eth-news/news/2025/01/zigzags-for-greener-construction.html
https://www.core77.com/posts/135375/Architecture-Student-Invents-Brilliant-Formwork-that-Reduces-Concrete-n-Steel-Usage

Robert Obier’s sculptures and art
https://www.obierstudios.com/portraits
https://www.core77.com/posts/135547/Architect-Industrial-Designer-and-Sculptor-Robert-Obiers-Creations

"The go-to source for physical puzzles"
https://www.puzzlemaster.ca/
hat tip:  https://kk.org/cooltools/

Geometric cakes for Ramadan
https://www.bbc.com/travel/article/20240406-kek-lapis-the-most-beautiful-cake-for-ramadan

Animation of the three-body problem
https://mastodon.social/@infobeautiful@vis.social/114155933549054103

Smoke ring geometries
https://x.com/stonersvilla/status/1901635534721605898

Geometry Links - January 10, 2025

 Mathematicians discover new universal class of shapes to explain complex biological forms

https://www.ox.ac.uk/news/2024-09-12-mathematicians-discover-new-universal-class-shapes-explain-complex-biological-forms
The paper itself:  Soft cells and the geometry of seashells
https://academic.oup.com/pnasnexus/article/3/9/pgae311/7754698?login=false
hat tip boingboing.net

Structural modeling kit - magnets and springs
https://molamodel.com/
https://www.core77.com/posts/133959/Architecture-Student-Develops-Structural-Modeling-Kit-Now-Sells-Them-Worldwide

The Geometry of Concepts: Sparse Autoencoder Feature Structure - geometric structure in LLM-learned concepts
https://arxiv.org/abs/2410.19750

First coherent picture of atomic nucleus made of quarks and gluons
https://press.ifj.edu.pl/en/news/2024/10/15/

Online collection of plaid patterns
https://plaid-patterns.com/
hat tip boingboing.net

Kelli Anderson’s imaginative pop-up books
https://www.kellianderson.com/books/

Geometry of tides and rivers
https://www.instagram.com/p/DAEvhs1ynYD/
More at https://www.instagram.com/geometriasagrada.en/
hat tip:  boingboing.net

Alhambra Palace and Crystallographic Groups
https://structures.uni-heidelberg.de/blog/posts/2023_01_palace_crystallographic/index.php
hat tip Howard Rheingold

The vault organelle
https://en.wikipedia.org/wiki/Vault_(organelle)
hat tip Massimo @Rainmaker1973

"The Steampunk Whirling Wonder Fidget (Gear Ball)” 
https://www.grynalor.com/products/the-steampunk-whirling-wonder-fidget-gear-ball

Maze Generator
https://mazegenerator.net/
hat tip kk.org/cooltools

Moving Geometry from Vera Viana
https://veraviana.net/

Geometry Links - September 19, 2024

 Labyrinth Locator - find labyrinths all around the world

https://labyrinthlocator.org/
hat tip:  boingboing.net

Abu Dhabi real-time data sculptures of brain waves
https://twitter.com/SCDabudhabi/status/1793232852454351293

"A majestic visualization of the toroidal structure and flow of a smoke ring"
https://twitter.com/Rainmaker1973/status/1804085910763364836

What if we could see spacetime?
https://www.youtube.com/watch?v=YNqTamaKMC8
hat tip:  boingboing.net

Simulating Extreme SpaceTimes:  black holes, neutron stars, and beyond
https://www.black-holes.org/
Their videos are very good if you’re into spacetime dynamics on the cosmic scales
https://www.youtube.com/c/SXSCollaboration

Aleks Melnyk’s extensive metal stencil products
https://www.amazon.com/stores/AleksMelnyk/page/9D4534FA-EB02-45F9-A5EF-294E88E8A552
hat tip core77.com at https://www.core77.com/posts/132925/Aleks-Melnyks-Pyrography-Stencils

Lunar gravity simulator
https://www.core77.com/posts/133036/Acrobatic-Artist-Bastien-Dausses-Incredible-Low-Gravity-Invention

OCD Art
https://www.core77.com/posts/133324/Fighting-Through-Mental-Struggles-Incredible-Renderings-Created-with-Only-a-Pencil

Bridges Math Art Conference papers online
https://archive.bridgesmathart.org/2024/#gsc.tab=0
hat tip Gwen Turner

3D printed clear radiolaria from Jessica Rosenkrantz
https://mastodon.social/@nervous_jessica/112997128650862037
https://www.instagram.com/nervous_jessica/
https://n-e-r-v-o-u-s.com/
and
Bismuth crystal jigsaw puzzles
https://n-e-r-v-o-u-s.com/shop/product.php?code=410
hat tip:  https://www.core77.com/posts/133615/Experimental-Design-Lab-Nervous-Systems-Bismuth-Crystal-Puzzles

Elastic Grid - online interactive Op Art
https://elasticgrid.pinkus.link/
hat tip:  boingboing.net

Geometry Links - June 16, 2024

 Optical illusions illuminate neural pathways

https://scitechdaily.com/demystifying-vision-optical-illusions-illuminate-neural-pathways/

Peter Lu on Islamic Geometry
Quasicrystals in Medieval Islamic Architecture
https://www.youtube.com/watch?v=rldnu9rNpH8
Girih Tiles: Decagonal Geometry in Seljuq Architecture
https://www.youtube.com/watch?v=6AJx8IVcL_c
hat tip Eleftherios Pavlides

Most detailed (so far) 3D map of the Cosmos
https://news.ucsc.edu/2024/04/desi-universe-mapped.html
Video fly-through
https://www.youtube.com/watch?v=jRYUt9nE9b0

Kirby Urner’s slide deck on tetrahedral tessellators, Bucky Fuller's esoteric geometry of the B, E, A, S and T modules
https://docs.google.com/presentation/d/13QLfgKo6kyX0j0K0RJ7W0uisB0ZyeBiK-_qbzytipck/edit

Ancient Egyptian Calligraphy: A Beginner's Guide to Writing Hieroglyphs by Henry George Fischer
https://books.google.com/books?id=rWlk49hUmDIC&printsec=frontcover#v=onepage&q&f=false
hat tip Dr. Kirsten D. Dzwiza  https://youtube.com/@antikemagie, https://www.instagram.com/antikemagie/, https://www.antikemagie.com/
Editorial Comment:  a beautifully clear primer

Bacterial art
https://www.theguardian.com/artanddesign/gallery/2024/may/18/beautiful-bacteria-encounters-in-the-microuniverse-tal-danino

Twisted Torque Tensegrity
https://pretenst.com/construction/2024/04/23/torque

Rinus Roelofs' sculptures
https://www.facebook.com/photo?fbid=10233940204345848&set=pcb.10233940206985914
https://www.facebook.com/photo/?fbid=10234067851536948&set=pcb.10234067854537023

The Playful Eye: An Album of Visual Delight by Julian Rothenstein, Mel Gooding (Chronicle Books 2000):  "a virtual feast of games and visual tricks gathered from around the world.”
hat tip kk.org/cooltools

Daniele Barresi, champion carver
https://www.danielebarresi.net/carving
https://www.instagram.com/danielebarresi_artist/

Folding Camping Table, with a tensegrity element
https://www.core77.com/posts/132550/A-Nifty-Folding-Camping-Table

Custom rotating nozzles for 3D printing different textures in clay
https://www.core77.com/posts/132566/Producing-Crazy-Textures-by-3D-Printing-Clay-With-Custom-Rotating-Nozzles
https://www.instagram.com/piotr_wasniowski/

Geometry Links - May 4, 2024

 The marble floors of the Florence cathedral

https://www.reddit.com/r/ArchitecturePorn/comments/13dkqmy/the_16th_century_optical_illusion_of_florence/
https://www.reddit.com/r/ArtefactPorn/comments/qgsl9u/the_marble_mosaic_floor_of_the_florence_cathedral/
hat tip Monica Raymond

The Splash of a Drop - an 1895 study of drops of water splashing on a flat surface and the forms they make
https://publicdomainreview.org/collection/the-splash-of-a-drop-1895/
hat tip boingboing.net
Editorial Comment:  I bet Doc Edgerton knew this work and, if you don’t know Doc Edgerton, you should.

The New Mathematical Coloring Book:  Mathematics of Coloring and the Colorful Life of Its Creators by Alexander Sofer
https://link.springer.com/book/10.1007/978-1-0716-3597-1
hat tip Edmund Harriss

Souper Connect - A modular human-shaped block that can interlock and connect in endless ways
https://www.kickstarter.com/projects/hbb/hbb-human-building-blocks
hat tip core77.com

Cella - a Bauhausian Toy
https://www.youtube.com/watch?v=E7y9_rHrBnc
https://www.core77.com/posts/131781/Cella-A-Bauhausian-Toy

Stable torqued tensegrities from Gerald De Jong
https://www.facebook.com/photo/?fbid=10161035601318948&set=a.10150243650853948

Collaborating for Comprehensivity by CJ Fearnley, one of the founders of the Synergetics Collaborative
PDF version: https://drive.google.com/file/d/1bapsUhFtRDSPdAW6zRBe7omBlcghz-yi/ 
Amazon Kindle: https://www.amazon.com/dp/B0CW1K18B5/k

One painting, youth to age, depending upon perspective
https://www.instagram.com/reel/C5cfny9Mjc8/
hat tip Joan Mokray

Kagen Sound’s wooden puzzle boxes
https://www.youtube.com/watch?v=_NreYBwzRQk
hat tip boingboing.net

Root systems drawings
https://images.wur.nl/digital/collection/coll13/
hat tip http://kk.org/cooltools

Roman dodecahedron theories
https://www.washingtonpost.com/world/2024/04/30/roman-relic-norton-disney-dodecahedron-theories/
hat tip Amy Edmondson 

From Art to Math:  The Polymorphisms of the Polymorphic Elastegrity

https://drive.google.com/file/d/1nOIO3S0wxSSyINLFCU9CU2DedcSMAfnI/view

Geometry Links - March 22, 2024

 Rinus Roelof’s small exhibition at TEC, Oldenzaal the Netherlands

https://www.facebook.com/photo/?fbid=10233355533329438&set=pcb.10233355537849551

Mathematical patterns of Bach’s music
https://www.scientificamerican.com/article/secret-mathematical-patterns-revealed-in-bachs-music/

Sacred Geometry shop
https://www.geometrycode.com/shop/

Fynn Jackson, Origami sculptor 
https://www.instagram.com/jacksonsorigami/
https://www.etsy.com/shop/jacksonsorigami/
hat tip Vinay Gupta

Zellij, a style of North African mosaic work
https://twitter.com/BaytAlFann/status/1765319198996037662

Math Encounters: "Realizing Abstractions: what can mathematics do for art?" Edmund Harriss Nov. 2023
https://www.youtube.com/watch?v=KD9ujxO9D-I

How to fold the Miura ori
https://www.youtube.com/watch?v=ufA1Yvdq_kk
hat tip https://boingboing.net/2024/03/09/how-to-fold-a-piece-of-paper-like-a-satellite-solar-panel.html
More from the Fold Factory
https://www.youtube.com/@foldfactory/videos

NERVOUS Systems has been doing generative design since 2007
https://n-e-r-v-o-u-s.com/projects/
https://www.core77.com/posts/130027/Incredible-Sculptures-and-Fixtures-by-Experimental-Design-Studio-Nervous-System

Simulation of convection on the surface of Betelgeuse 
https://www.mpa-garching.mpg.de/1094283/hl202403

Naguri jig for wood patterning
https://www.core77.com/posts/130115/A-Clever-Jig-for-Producing-the-Naguri-Pattern-in-Wood

Hexabranchus sanguineus or the Spanish dancer
https://twitter.com/MikeHudema/status/1768840123020353998
hat tip Mike Udema: "Nature is amazing. Protect it.”

Penrose tilings and quantum information
https://www.quantamagazine.org/never-repeating-tiles-can-safeguard-quantum-information-20240223/
hat tip to Vinay Gupta

Geometry Links - February 15, 2024

 Music box Moëbius strip of Erik Satie’s Gymnopedie 1

https://wolfliving.tumblr.com/post/736992332742852608/mo%C3%ABbius-gymnopedy-transposition-de-la-1%C3%A8re
hat tip to Cory Doctorow

Bradford Hansen-Smith’s new book, the Circle: a wholemovement perspective, is now available, documenting is further explorations of geometry in folding the circle
https://www.amazon.com/Circle-wholemovement-perspective-Bradford-Hansen-Smith/dp/0976677350/ref=sr_1_21

Geek Mom’s LED light
https://mastodon.social/@geekmomprojects/111604449708190756

Trace Loops paper animation
https://www.instagram.com/p/CwYdu43q1cJ/
hat tip boingboing.net

Greek village where every house is decorated with geometric figures
https://www.bbc.com/reel/video/p0h2sy22/the-greek-island-of-geometrical-wonders

National Museum of Mathematics has online courses:  for instance, topological crochet
https://momath.org/onlinecrochet/

Lanny Smoot’s omnidirectional floor
https://boingboing.net/2024/01/18/disney-imagineer-showcases-a-new-holotile-floor-on-which-you-walk-without-going-anywhere.html

Golden Ratio Tetra Spiral
https://www.youtube.com/watch?v=WRw6asdcpow
hat tip David Brian Koski

Some geometric models from Rinus Roelof
https://www.facebook.com/photo/?fbid=10233200136004602&set=pcb.10233200139444688

Sponge spicules - a biologist friend mentioned them on Facebook and I took a look.  Very interesting structural component system(s)
https://en.wikipedia.org/wiki/Sponge_spicule
Hat tip to Manda Clair

Armenian alphabet also a numerical system for mathematics
https://www.bbc.com/travel/article/20240208-how-a-1600-year-old-alphabet-shaped-armenian-identity

Improved one corner balancing cube
https://willempennings.nl/balancing-cube/
hat tip boingboing.net

From Geometry Links:  https://geometrylinks.blogspot.com/2016/10/geometry-links-compendium-2011-october.html

Cubli - a cube that can balance, jump, and walk
http://youtu.be/n_6p-1J551Y

Geometry Links - December 17, 2023

 Matt Brand’s specular holography - specular holography and rhombiyurts

https://www.zintaglio.com/
hat tip https://www.wcvb.com/chronicle 10/4/23

Tawa portable wood art game
https://www.kickstarter.com/projects/woodas/tawa-the-portable-wood-art-game-for-traveling

Stained Glass Smash - online app that creates geometric art by simulating smashing glass
https://glass.funwebsite.fun/
hat tip:  http://kk.org/cooltools

Siena Galaxy Atlas 2020
https://sga.legacysurvey.org/

Pisano quilts
https://observablehq.com/@tesseralis/pisano-quilts
Editorial Comment:  Any Peano curve quilts?

Following Albrecht Dürer’s 1525 geometric net:  snubcube and its dual
https://www.facebook.com/photo?fbid=10232826009691678&set=pcb.10232826014291793

Slow motion splash geometries
https://twitter.com/BrianRoemmele/status/1713704757838127226

Pull-up patterned polyhedra: Platonic Solids for the classroom
http://buff.ly/3W65iLU
printable templates: http://buff.ly/3BuY3DZ
hat tip Karl Thidemann

Nepali mokha art on the verge of disappearing
https://globalvoices.org/2023/12/01/as-nepali-villages-modernize-mokha-art-is-on-the-verge-of-disappearing/

Optical illusion - illusory yellow
https://twitter.com/AkiyoshiKitaoka/status/1730166843753800087

Heartbreaking: Local quadratic polynomial as a function of x struggling to fit constantly rotating data
https://mastodon.social/@acegikmo/111541524766320445

Ncube - generalized hypercube visualizer
https://ncube.ndavd.com/
hat tip boingboing.net

Geometry Links - October 4, 2023

 Pneuhaus - inflatable sculpture

https://www.pneu.haus/
https://www.instagram.com/pneuhaus
hat tip boingboing.net

Antique book patterns of front or end papers from 1890-1930, ordered by theme, by Bergen Norway Public Library
https://www.flickr.com/photos/bergen_public_library/albums/72157633827993925

Minimalist movie posters
https://www.michalkrasnopolski.com/#/classic-movies/
hat tip core77.com

Spectrolite is a Mac app which does color separation, halftoning, posterizing, layouts for art prints, zine and booklet imposition, and a bunch of other fun things
https://spectrolite.app/
hat tip boingboing.net

Early [1.4 million years ago] human ancestors turned stones into spheres on purpose, study suggests
https://www.theguardian.com/science/2023/sep/06/early-human-ancestors-turned-stones-into-spheres-on-purpose-study-suggests

Daniel Agdag’s cardboard sculptures
https://www.theguardian.com/artanddesign/gallery/2023/sep/16/fragile-fantastical-designs-in-cardboard-in-pictures

Octet_8_in_1 by Joe Clinton
https://vimeo.com/863331197

Thomas Burgess’ adventures in geometry
https://thomasburgess.github.io/

InfiniteX Dodecahedron programmable art light
https://trivlo.co/products/color-art-light

Indian Tribal Tattoos
https://globalvoices.org/2023/09/28/documenting-indian-tribal-tattoos-before-they-disappear-forever/
Aipan Art
https://www.instagram.com/p/CsGYW8AIpfv/

Disaster relief bed - simple geometry that may have a deep impact
https://www.core77.com/posts/125913/Industrial-Designer-Invents-Vastly-Superior-Disaster-Relief-Bed

Ancient Egyptian mathematics and geometry
https://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus