Visualization in 3D of Dynamics of Toroidal Helical Coils


Anthony Judge | Laetus in Praesens – TRANSCEND Media Service

… in Quest of Optimum Designs for a Concordian Mandala


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.

To continue reading Go to Original –


Share this article:

DISCLAIMER: In accordance with title 17 U.S.C. section 107, this material is distributed without profit to those who have expressed a prior interest in receiving the included information for research and educational purposes. TMS has no affiliation whatsoever with the originator of this article nor is TMS endorsed or sponsored by the originator. “GO TO ORIGINAL” links are provided as a convenience to our readers and allow for verification of authenticity. However, as originating pages are often updated by their originating host sites, the versions posted may not match the versions our readers view when clicking the “GO TO ORIGINAL” links. This site contains copyrighted material the use of which has not always been specifically authorized by the copyright owner. We are making such material available in our efforts to advance understanding of environmental, political, human rights, economic, democracy, scientific, and social justice issues, etc. We believe this constitutes a ‘fair use’ of any such copyrighted material as provided for in section 107 of the US Copyright Law. In accordance with Title 17 U.S.C. Section 107, the material on this site is distributed without profit to those who have expressed a prior interest in receiving the included information for research and educational purposes. For more information go to: If you wish to use copyrighted material from this site for purposes of your own that go beyond ‘fair use’, you must obtain permission from the copyright owner.

Comments are closed.