Comprehension of complexity and paradox through 3D mandalas

Eliciting Insight from Mandala-style Logos in 3D (Part #4)

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Logos and mandalas endeavour to render succinct and communicable a nexus of complexity by which paradox and subtlety may be inferred. An indicative example is that chosen by the International Mathematical Union (as displayed below right). This is a representation in 3D based on the iconic  Borromean rings -- typically displayed in 2D. The configuration is especially valued in mathematics since the three topological circles are linked -- but such as removing any one ring leaves the other two unconnected. In other words, no two of the three rings are linked with each other, but nonetheless all three are linked. The images are reproduced from a separate discussion (Engaging with Elusive Connectivity and Coherence: global comprehension as a mistaken quest for closure, 2018).

Examples of 3-fold articulations of Borromean rings of relevance to coordination of political systems?
Representation of rings interlocking according to the Borromean condition
Early depiction of Christian Trinity	Common representation in 2D	Distorted representation as ellipses	3D representation	International Mathematical Union Logo
Reproduced from Wikipedia

The earlier discussion of Borromean rings included the development of 3D animations (as shown below) consistent with the focus of the argument here. It includes comments of relevance by Louis H. Kauffman (The Borromean Rings: a tripartite topological relationship. 2006).

The animation on the right bewlow shows three mutually orothogonal tori with a 3-loop helix moving over each of them (Video: mp4).

Representations of Borromean rings (with Red surrounds blue; Blue surrounds green; Green surrounds red)			Mutually orthogonal tori with 3-loop helix
As an ordered knot-set	Toroidal version	3 Möbius strips (animation)
Reproduced from Kauffman (2013)	Reproduced from Kauffman (2006)	Video (mp4); Virtual reality (x3d; wrl)	Interactive variants (x3d, wrl) .

Concordian mandala? Provoked by the multiple Borromean rings configuration of five loops -- namely the Discordian Mandala used as a symbol in Discordianism -- a question is how it might be possible to imagine and represent dynamically a comprehensible mandala of requisite complexity in virtual reality. This was the focus of separate discussionm firstly on the use of 5 nine-sided polygons, then on 5 nine-looped helical coils (shown with sphere movement around them):

• Visualization in 3D of Dynamics of Toroidal Helical Coils -- in quest of optimum designs for a Concordian Mandala (2016)
• Concordian Mandala as a Symbolic Nexus -- insights from dynamics of a pentagonal configuration of nonagons in 3D (2016)
• Con-quest Aesthetically Reframed via the Concordian Mandala (2016)
• Speculation on Potential Symbolic Relevance of the Concordian Mandala (2016)

Interactive 3D demos (click to access)	Indicative screen shots / animations (click for 3D)
Dynamics of 3D configuration of 5 nine-sided polygons as a mandala  (video; x3d)
Dynamics of a Concordian mandala of 5 nine-looped helical coils (video. x3d)

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