"A fool's guide to everything..." by a fool.
What I try to share by this is how the toroidal field could explain existence as viewed from different lenses and how many sacred geometric figures could emerge from the same. Hope it helps in your journey.
P.S: this is a personal interpretation, hence calling it a fool's guide.
I have now open-sourced the fractal-torus generator from the "Tortoise" project because I feel this could help other explorers. The generator also has the feature to create an image based on any pose/iteration of the torus, so that you can generate anything from sacred geometry blueprints to products to architecture with the same structure; although this requires an API key from Stability (details in the app).
Please feel free to use it for your research (and would be kind of you to credit me or my website)
Link: https://nurecas.com/tortoise_generator
Github: https://github.com/nurecas/tortoise_generator
(Best viewed in desktop)
P.S: This will be my last post from this project. I appreciate all your support and thanks for bearing with me while iterated the same.
Lattice- connecting the intersections with lines and vertices create these beautiful lattices. Somewhere in there could be Platonic solids, the cuboctahedron jitterbug or the E8 lattice
Details: https://nurecas.com/tortoise
The "Tortoise" work I posted previously is more of a geometric representation. In actuality, I am imagining the fractal torus to look something like this... a field....
After the overwhelming response to the last post, I sat with the Tortoise work longer, thinking about how it connects to the human psyche. Many people from the community shared about the work that (to paraphrase):
This is what they saw the universe as in altered states
This is how reality works
This is the holographic universe
But something still felt missing to me: the subjective factor. The reports pointed to similar structures, yet not the same ones. They varied from person to person. Of course, I could change the parameters of the fractal torus to get different configurations, but how would that explain the faces, deities and beings people meet in non-ordinary states of consciousness?
What I realized is that the structure of the universe and the felt, phenomenological experience of it need not be the same thing. Two people can meditate on one structure and see two different beings, and both could still be pointing to the same underlying form, or to its fractal repetitions.
So I decided to add a phenomenological layer on top of the structure. I used an AI model (Controlnet+Stable Diffusion via Stability AI) to pose and render the fractal torus from different angles, each with its own prompt. The blueprint underneath stays the same, but everything from psychedelic art (the segment at the end of the video) to physical objects, natural forms and architecture are visualized on top of it.
I might not be accurate here, but something about these creations felt profound.
Details of project: Tortoise
Music by EVGENY from Pixabay
Ive shared some of the different visualisations of the fractal torus titled ["Tortoise"](https://nurecas.com/tortoise?o) here before. Here I am trying out the Tortoise on a projector at home...the visualiser which shows the connections to different symbols and myths is operated via an iPad
Many many vortices... many many toruses... a net of all beings
The sema-tawy is the Egyptian sign for the union of the Two Lands. At its center is a hieroglyph, a windpipe rising into a pair of lungs, which the Egyptians used to write "to unite" because the organ is itself a unification, two lungs drawing breath through one throat. Around that central column the stems of two plants are knotted, papyrus for Lower Egypt and lotus for Upper Egypt, so that political unity is stated as a single physiological fact. The sign is carved on thrones, temple walls and furniture, and the lungs-and-windpipe amulet was laid on the chest of the dead. The Tortoise correspondence is structural. The artwork consists of two fiber families wound in opposite senses about a shared central axis and meeting at regular intervals, which is the arrangement the sign describes: paired opposites bound to one column, their crossings the points at which the binding is made. The comparison belongs with Ida, Pingala and Sushumna, where the same organizing principle appears in a different tradition. The sema-tawy is a flat heraldic sign rather than a three-dimensional form, and the correspondence is to its logic, not necessarily its appearance.
This video is part of the Tortoise project which connects a multitude of symbols and myths from around the world to a specific fractal toroidal structure.
Link: nurecas.com/tortoise
Continuing to share specific variations of the fractal torus work, Tortoise. This one is the connect to Ezekiel's Wheels. The wheel are described by Ezekiel as "a wheel in the midst of a wheel" with high, "awesome" rims filled with eyes, appearing to sparkle like beryl stone
Check the visualiser in my previous post for details:
https://www.reddit.com/r/SacredGeometry/s/wLMvVCnnDn
Continuing to share specific variations of the fractal torus work, Tortoise. This one is the connect to Indra's net (https://en.wikipedia.org/wiki/Indra's\_net)
Check the visualiser in my previous post for details:
https://www.reddit.com/r/SacredGeometry/s/wLMvVCnnDn
A field of connected toruses...
Check the visualiser in my previous post for details:
https://www.reddit.com/r/SacredGeometry/s/wLMvVCnnDn
A few weeks back, after many iterations of the fractal torus model, I created an algorithmic artwork called Tortoise, made in tandem with AI. As part of the Nameless framework, I had landed on the Hopf fibration as an important structure for defining physical reality. I took an artistic leap after this... overlaying two oppositely rotated Hopf fibre bundles, then repeating the whole structure again and again at the interstices formed by their intersections, to form a fractal torus. This differs from other torus visualisations I've seen, not only in its use of Hopf fibres, but in the fractal arrangement, which produces that "many, many eyes" quality or the "wheels within wheels" quality.
Studying it from different angles, I realised, to my shock, that this structure had many many connections to scientific concepts, myths and symbols across the world and across history:
Science: the black hole and white hole paradigm, wormholes
Sacred geometry: Flower of Life, Lotus of Life, Triskelion, Yin Yang
Religious symbols: Sri Yantra on Kurma, Shatkona, Swastika, Tree of Life, Thousand Petalled Lotus, Reclining Vishnu, Samudra Manthan, Shivlingam, Avalokiteshvara, Ezekiel's Wheel, the Celtic Cross
Sacred architecture: Muqarnas and Islamic geometric patterns, Rose windows
Visionary art made in altered states, such as Alex Grey's
Contemporary design: even the OpenAI logo
To show how all these might derive from one source, I built a system that varies the parameters of the same root Tortoise artwork until it matches each symbol. Then I made a visualiser where you can click any symbol, read about the connection, and study the match visually.
I'm not claiming these are all derived from this single structure. Each connection is pattern-matched at this stage, and the scientific ones especially are speculative. I claim only the visual match, not an actual connection. But there are too many to ignore. Perhaps what the ancients meditated upon is the same structure science is reaching towards, and the same structure seen in altered states of consciousness. If the universe is sound based, perhaps the wave-structure formed by the primordial sound corresponds to a similar fractal torus structure?
Many of these connections already exist in literature and in esoteric theory. Some were abstract, some pointed directly to a torus, though not, as far as I know, to this particular variation. This is therefore a synthesis of many people's work over millennia, seen through the lens of my own. I'm assembling it with humility and respect, hoping we notice that we are all telling the same story through different lenses.
I have made 26 connections so far, and I hope to add more. I'm giving equal weight to each tradition, so if you spot flaws or biases in the text or visual, they aren't intentional, and I hope to improve these over time.
Artwork “Tortoise” and the visualiser at: https://nurecas.com/tortoise?o
Iteration of this work titled TOR , but animated.
As always, the live, interactive build available here. (It is a very heavy build, so might be slow to run.)
Iteration of this work titled TOR , but animated.
As always, the live, interactive build available here. (It is a very heavy build, so might be slow to run.)
Oppositely chiral Hopf fibers generate a lattice of interstitial sites. At each site, a tangent-aligned copy of the complete construction is recursively inserted and scaled by the site’s exact distance from the parent fibers. A support bound ensures that every descendant nest remains contained within its generating interstice.
Built in Threejs with Chatgpt.
Live interactive version available. Play with it here.
Oppositely chiral Hopf fibers generate a lattice of interstitial sites. At each site, a tangent-aligned copy of the complete construction is recursively inserted and scaled by the site’s exact distance from the parent fibers. A support bound ensures that every descendant nest remains contained within its generating interstice.
Live interactive version available. Play with it here .
Two opposite-chirality Hopf fiber bundles, superimposed. The gaps between the fibers fill into diamond gems, each with a dark eye at its centre. Watch till the end..interactive version available here:
https://tb45bmx5xeestjcrriuq2yb2tqmajn66hg73l6ywqxq7dteei2xa.arweave.net/mHnQsv25CSmkUYopDWA6nBgEt945v7X7FoXh8cyERq4
P.S: these links are on arweave, hence the long URL. They are safe nevertheless.
Sharing the video of the interactive artworks too. You can try it out at:
https://nurecas.com/nameless?rddmrl
https://nurecas.com/source?rddmrl
For anyone interested in the live, interactive art of my previous shares: "Source" and "Lattice", these are available for viewing at the top and bottom of this page on my website. Thanks for all the support.