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Visualization in 3D of Dynamics of Toroidal Helical Coils

In quest of optimum designs for a Concordian Mandala

Potential merit of a toroidal helical configuration
Configuration of a toroidal helix
Deriving coordinates for a toroidal helix (helical toroid)
Dynamic possibilities of 3D visualizations of a helical toroid with multiple windings
Movement of spheres along the pathways of a toroidal helix
Potential cognitive implications of toroidal helical movement
Technomimicry, metaphors and symbolism
Category juggling reframed through visualization dynamics
Requisite controversy engendered and encoded by a counter-coil pattern?
Towards a 3D visualization of toroidal counter-coiling dynamics
Transforming vehicles of identity between global and toroidal forms
Fearful attraction of a hole
Representational challenge of the periodic table of chemical elements
Cognitive heart dynamics framed by two tori in 3D

NB: Recent document. Introduction only. Read remainder separately on Laetus site


The purpose of this document is threefold. Firstly it constitutes a further development of the possibilities of 3D visualization of the 5 nonagons previously outlined with respect to what was termed a Concordian Mandala -- in contrast with the Discordian Mandala in 2D (Three-dimensional Configuration of Nonagon Mandala, 2016). Those experiments made it apparent that a key to this development lay in helicoidal (sinusoidal) windings on a torus rather than a simple ring structure, especially in a quest for parameters which might be consistent with the pattern of a set of Borromean rings.

The second purpose is to render comprehensible for others the approach to the dynamics of 3D visualization of the helicoidal structure using readily accessible software through with the relevant mathematical formula could enable the configuration. In this sense it is intended as a guide reflecting the progressive learnings of anyone with only a modest degree of competence in the mathematics or the visualization software. The focus is to enable dissemination of such models over the web via standard web browsers. Given the time taken (by the author) to discover how to render what is indicated below, the intention is to reduce significantly the obstacles to others of exploring such possibilities further.

Thirdly, a particular purpose follows from the context of the previous experiments, namely to enable consideration of the configurations as mapping surfaces through which more integrative patterns of concepts can be held dynamically. The context has been considered previously in relation to the technical considerations which are the primary focus of the articulation here (Con-quest Aesthetically Reframed via the Concordian Mandala, 2016; Concordian Mandala as a Symbolic Nexus: insights from dynamics of a pentagonal configuration of nonagons in 3D, 2016).

Contextually the theme is of some relevance in a period when the market for virtual reality devices is about to expand significantly, when a 2016 Nobel Prize in Physics was awarded for insights into the mathematics of vortices, and when the US presidential campaign of 2016 is demonstrating the fundamental inability of democracies to transcend the primitive dynamics to which many would appear to subscribe -- for lack of any credible alternative.

Rather than proposing any new "model", one purpose of the following exploration is to enable model exploration of a new kind -- with a visual dimension enhancing comprehension in new ways, somewhat reminiscent of the explosion of interest in online gaming. The following could be understood as creating a learning pathway or bridge between the "trivial" for the few and the "obscure" for the many.

NB: Recent document. Introduction only. Read remainder separately on Laetus site