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Opus 4.6 No Skill used only the prompt and first try. Create an algorithmic art piece inspired by frost patterns on glass and snowflake crystallization. Use recursive branching structures that grow outward from a central point with radial symmetry. Each generation of branches should be thinner and more delicate...

20,008 次观看 • 5 个月前 •via X (Twitter)

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I think one of the roles we play as mathematicians in society is to help people become acquainted with the underlying secret patterns. I have been working for several years on projects in crystallography, where we study crystal structures. But few people know that such periodic patterns come with severe constraints on their symmetry. In the plane, there are 17 different symmetry types, a fact well known even to the designers of the mesmerizing patterns of the Alhambra. Here you can find and experiment with such tilings in the plane, gaining insight into the intrinsic beauty of the so-called wallpaper groups, the crystal symmetries in dimension 2. The app interactively helps you design symmetric patterns with colors and shows how changes in the structure of the unit cell propagate via symmetry. In dimension 3, if you look into International Tables for Crystallography, Vol. 1, you will find a theorem due to Schoenflies and Fedorov stating that there are 230 such symmetry types, a cornerstone of modern chemistry. Beyond that, in dimensions 4 and higher, a count can be made, but it requires a proof of the general theorem due to Frobenius and Bieberbach. This was an answer to the first part of Hilbert’s famous eighteenth problem. One of the fun consequences of such a classification is that in dimensions 2 and 3, 5-fold symmetry is forbidden in regular periodic arrangements. Intrinsically, this fact is related to the existence of matrices with a fifth-root-of-unity eigenvalue. For integral matrices, this is possible only in dimensions 4 and higher. If you generalize the square and cube tilings to dimensions 4 and 5, obtaining hypercubic tilings, the 5-fold symmetry pattern emerges. Skew projections of the 5D hypercubic tiling onto a 2-dimensional plane give rise to a quasicrystalline tiling known as the Penrose tiling. You can find such patterns in front of the Andrew Wiles Building at the Oxford Mathematical Institute. In later posts this summer, I will take a deep dive into group homology, a modern tool for studying the geometry of crystals. There are still many open questions, for example, how many symmetry types exist exactly in dimensions beyond 6. This is still largely unknown; at present, we only have asymptotic lower bounds.

Bartosz Naskręcki

44,042 次观看 • 1 个月前

🟧VIVID Gallery is launching ‘Looming Emotion’ by Shaderism | Arttu 🪞 A mesmerizing exploration of the overlooked aspects of our deepest emotions. 📅Save the Date: June 12th on Magic Eden on Bitcoin 🟧 Launchpad About the Artist 🧑‍🎨 Arttu Koskela is an algorithmic full-time artist, who uses web technologies to create real-time artwork, often incorporating aspects of audio-visuality, interactivity, and physics simulations, while exploring the themes of playfulness and self-reflection. Among his most notable works stands ‘Blinds Spots’, an Art Blocks collection curated. Through the looking-glass 🪞 Looming Emotion is an algorithmic art collection that depicts the conscious and unconscious habitual patterns distracting individuals from the unresolved emotions lurking behind them, which contribute to many of life's challenges. 🗺️ The collection style is inspired by wood carving artworks, glass distortion and Tom Patti’s sculptures. The variety of the 400-piece collection is created by the visual expression of colours in the glass and background, the noise patterns, tile configurations and different aspect ratios. Collector Benefits 💎 All Vivid Gallery and Shaderism | Arttu collectors can apply for a discounted private sale at 0.008 BTC. To participate in the private sale, complete the forms announced in our Discord Server (link in bio). In addition, every SATS holder is eligible for a free piece 🧡 Become a ‘Looming Emotion’ collector 🖼️ Around 100 pieces will be left after the private sale for a FCFS WL at 0.01 BTC. You can get a WL by filling out Vivid & Shaderism's collectors forms, engaging with our content, winning a collaboration raffle from our partner communities and participating in our upcoming spaces. Find all the info on our Discord (link in bio). Try to win a WL spot 🎁 If you'd like to take part in the WL, we're giving away 10 spots through the looking-glass. Participate in the raffle below ⬇️

Vivid Gallery

15,332 次观看 • 2 年前

ᴀ ɴᴇᴡ ᴄʜᴀᴘᴛᴇʀ — ᴊᴏɪɴɪɴɢ ᴠᴇʀꜱᴇ Over the years, I’ve worn many hats in the art world: artist, non-profit director, curator, publisher, gallerist, and advisor to collectors and institutions. Though photography has been a throughline in much of that work, my interest in contemporary art more broadly reaches far and wide, continually pulling me toward practices that stretch perception and redefine possibility. While I’ve always been drawn to physical art – painting, mixed-media, artist books, etc. – my curiosity for digital art runs just as deep, and I've long been fascinated by the evolving ways we create and engage with art. Digital art has an unexpected tactility. Even when encountered on a screen or in ephemeral gallery installations, it often carries a material presence that’s hard to explain, yet deeply felt. That sense only intensified after 2020, when I became immersed in the world of web3, and blockchain’s implications for visual art really clicked (digital authenticity, ownership, provenance). New ways to make and to be a part of art also emerged during this time. Since then, I’ve been continually challenged and inspired by this new generation of artists, like witnessing a sort of on-chain Renaissance. Naturally, I started collecting and participating when and where I could, and my perspective and appreciation have only expanded and grown. As the space has evolved over this time, so too has a clear need: a dedicated, art-focused home for digital art, one that serves both seasoned collectors and the newly curious, cutting through noise with clarity and care. Most big platforms have drifted away from this vision, where the art itself can feel like an afterthought. verse has always stood out to me with a quiet confidence and a deep commitment to a more intentional, curated, artist and collector-centered approach that continues to resonate. Over the past year, I’ve naturally gravitated to using the platform more often – first, for discovering artists through gallery releases, and more recently through the thoughtful rollout of the beta secondary marketplace (the dedicated artist portfolios and organized gallery programs are a total game changer!). There is something here that not just works, but feels necessary. Which is why I’m thrilled to share that I will be joining verse to help to shape what comes next. I’ll be leading various secondary market efforts, including auctions and art advisory, as well as contributing ideas to help refine the product and collector experience as Verse grows into THE platform for digital art. The team is full of some of the hardest-working and most passionate people in the space, and there’s a commitment to preserving a focus on art while always buzzing with the possibility of what else can be built. It’s infectious. There are too many exciting things in the roadmap and I can’t spill those (yet). But, what’s coming? Chef’s kiss. One thing I can share today is that we’re kicking things off with something very special: an upcoming secondary market auction bringing together exceptional works from across the ecosystem. Some of you are already aware, or maybe heard about it on the Verse podcast. I’d love to hear from you (DMs are open), so please feel free to reach out if you’re thinking of parting with a piece or seeking something specific at the moment. This auction will be a celebration of where digital art is today and where it’s headed – with no eye-watering buyer’s premiums and collector-friendly terms that actually make more sense for web3. It’s truly by and for the community. Learn more below ↓

Shane Lavalette

10,406 次观看 • 1 年前