Animation of interaction and interlocking between cognitive patterns

Middle East Peace Potential through Dynamics in Spherical Geometry (Part #3)

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Rather than introducing the visualization with a verbal explanation, this is presented immediately through the following screenshots of phases in the animation accessible here. A commentary is given below.

Screenshots indicating phases in SVG portion of animation sequence [click for separate SVG animation -- right-click on active animation for options -- improvements welcome NB: Animation works in Firefox and Opera; effects do NOT work properly in Google Chrome, Internet Explorer or Safari]
Early stage in animation	Late stage in animation

The animation progressively "populates" a space (a "territory") in two dimensions with instances of either a hexagon or a pentagon -- as "vehicles" for the Star of David and the Islamic Star respectively. The polygonal vehicles are also usefully understood as jigs or templates enabling appropriate positioning -- as in many processes for manufacturing objects which need to be held accurately in place and ensure pattern replicability. The final pattern reinforces the point that the two sets of polygons cannot be "fitted" into any coherent design -- even though some edges between the two different shapes can be established as common, as "joining".

The seemingly arbitrary pattern can, as a whole, be "folded" into a spherical form in three dimensions, as indicated by the following screen shots and the accompanying animation.

Animation sequence subsequent to the SVG phase screenshots showing extremes of the folding (and unfolding) process on a green background (animation generated using Stella Polyhedron Navigator)

The screenshots above, and the animation below, are suggestive of the challenge and possibility of getting the contrasting 5-fold and 6-fold patterns to "fit together" in three dimensions. The subsequent commentary endeavours to clarify some of the implications.

Animation sequence subsequent to the SVG phase screenshots showing extremes of the folding (and unfolding) process on a green background (animation generated using Stella Polyhedron Navigator)

The stages of the animation are suggestive of an intuitive relation between the Star and Crescent of Islam. Disposed together otherwise, the elements of the unfolded net could well be indicative of either the 5-fold or 6-fold stars.

An association football is constructed by stitching together 32 panels of waterproofed leather or plastic: 12 regular pentagons and 20 regular hexagons. As noted, the 32-panel configuration is the spherical polyhedron corresponding to the truncated icosahedron; it is spherical because the faces bulge from the pressure of the air inside. The basketball and volleyball are not constructed in this way. Reference is often made to the football design, when describing carbon buckyballs or the root structure of geodesic domes, as an illustration of the truncated icosahedron.

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