Eliciting Insight from Mandala-style Logos in 3D (Part #2)
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The technical problem with respect to interactive web dissemination has been the constraint (notably for the author) of enabling representation in virtual reality rather than simply presenting videos or animated gifs. This is despite being able to generate such interactive 3D models locally with other software protocols (
X3D,
VRML).
Such interactivity can however be offered over the web in some cases by embedding such displays using X3DOM technology (Anestis Koutsoudis, Bring Cultural Heritage 3D Content on the Web Using the X3DOM Framework, Connecting ARchaeology and ARchitecture in Europeana / Athena Research and Innovation Centre).
Access to a number of dynamic centro-symmetric displays is offered below. Some derive from the design metaphors and themes illustrated in 2D animations/projections in the imagery below. Some may not work, depending on the speed of the internet connection, especially for the more complex. Conventional video alternatives are indicated for convenience in the event of difficulty, although that option is not the purpose of this presentation.
Mereon trefoil knot: Some possibilities are discussed separately (Minimal knot of requesite complexity, 2022)
| Interactive 3D demos | Indicative screen shots / animations (click for 3D) |
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| With nested Platonic polyhedra | (click for 3D) |
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Crown chakra (Sahasrara): The possibilities and significance are discussed separately (Global Insight from Crown Chakra Dynamics in 3D? Strategic viability through interrelating 1,000 perspectives in virtual reality, 2020) namely the so-called "1,000 petalled lotus", for which a variety of dynamic 3D models are presented and discussed in Crown chakra as circular configuration of rotating heart-patterns; Construction of crown chakra in 3D using a twisted torus; Crown chakra embodying gimbal dynamics to frame the Axis Mundi (2020). Arguably this is an extreme variant of the mandala-yantra metaphor. That shown below has the configuration of 20 concentric rings of 50 petals rotating in the plane of the page.
| Interactive 3D demos | Indicative screen shots / aAnimations (click for 3D) |
| 20 Rings flat and mutually rotating |
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| 20 Rings stacked and mutually rotating | (click for 3D) |
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| 20 Rings stacked with additional dynamics | (click for 3D) |
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| Complex possibility: gyroscopic movement of selected rings | (click for 3D) |
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| Complex possibility: movement of 20 rings through a torus | (click for 3D) |
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Framing ring dynamics in relation to symmetrical polyhedra:
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Interlocking tori with complementary rotations:
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Further possible insights are discussed in relation to the crown chakra (Global Insight from Crown Chakra Dynamics in 3D? Strategic viability through interrelating 1,000 perspectives in virtual reality, 2020)
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Mnemonic aid to "location" of metasphere?
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Circle of 64 hexagrams of  Shao Yong: For which a variety of configurations are presented and discussed in Toroidal constraint -- nuclear fusion as metaphor of cognitive fusion (2019). That shown below is a configuration of 3 mutually orthogonal rings of hexagrams each rotating within a drilled truncated cube -- a toroidal polyhedron with 64 edges.
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Symbols of Abrahamic religions: As an exercise in projective geometry, a mutually orothogonal rendering can be explored (Reconciling Symbols of Islam, Judaism and Christianity, 2017; Mutually orthogonal Abrahamic symbols from the perspective of projective geometry, 2017). With respect to the Star of David, various dynamics of "cognitive cycles" can be speculatively rendered in a 3D development as the Merkabah (Cognitive implication in Merkabah as configuration of cycles essential to systemic viability, 2017)
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Ten Oxherding Images of Zen: The value of displaying the classic set of images in a torus can be explored, as explained separately (Zen of Facticity: Bull, Ox or Otherwise? Herding facts and their alternatives in a post-truth-era, 2018; Phases in the "Re-cognition" of "Bull" according to Zen? Experimental attribution of significance to traditional distinctions, 2017). The design metaphor is also discussed there in relation to the Chinese BaGua mirror pattern of 8 trigrams, especially in the light of reference to an 8-fold ox herding set (The Eight Ox Herding Pictures, 2012; The Eight Ox Herding Pictures: a Chan/Zen allegory) -- as illustrated below.
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Ouroboros: As an ancient symbol depicting a serpent or dragon eating its own tail, the Ouroboros entered western tradition via Greek magical tradition and was adopted as a symbol in Gnosticism and Hermeticism and most notably in alchemy. It continues to be recognized as the most fundamental symbol of eternal return -- inviting exploration in 3D (Experimental animations in 3D of the ouroboros pattern, 2017).
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
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Tao / Ying-Yang symbol: As one of the most fundamental symbols indicative of the transcendence of dualism, conventionally displayed in 2D, there is a case for exploring the possibilities of interacting with it in 3D (Exploring Representation of the Tao in 3D: virtual reality clues to reconciling radical differences, global and otherwise? 2019). As noted and indicated in the latter, an early draft of the 3D models encouraged the elaboration of models using far more professional techniques -- as presented below. They were prepared by Sergey Bederov of  Cortona3D, -- to whom thanks are due for permission to include them in this document. Provocatively it could be said that forms appropriate to the reconciliation of opposites in society call for some kind of "Parametrization of the Tao", or perhaps the "Parametrization of Yin-Yang". The economy of the coding required for the models is suggestive in that respect -- to the extent that the mathematics is comprehensible.
Interactive 3D demos (click to access)
| Indicative screen shots / animations (click for 3D) |
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| Experimental animations of paired elements of 3D Tao symbol (solid and wireframe renderings) |
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| Using "droplets" extruded according to the model of Sergey Bederov (above) |
Lauburu symbol of Basque culture: The symbol, and the possibility of configuring it significantly in 3D, is discussed in the following:
| Interactive 3D demos (click to access) | Indicative screen shots / animations (click for 3D) |
- Single-plane lauburu framework: 8-voice dynamics
Video (mp4). Virtual reality (x3d, wrl) |  |
- Double-plane lauburu framework: 16-voice dynamics
Video (mp4). Virtual reality (x3d, wrl) |  |
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