On Friday, October 13, 2017 at 8:19:54 AM UTC+1, Martin Brown wrote:

Quantum mechanics is strange - things behave like a wave to decide where
to go (approximately along the path of least time) and then like a
particle when they get there to deliver a quantum of energy.



People are strange sometimes but creation isn't. Basalt like that of the Giants Causeway in Antrim, Northern Ireland form as hexagons while pyrite crystals form as cubes.

Until a few decades ago it was thought that no natural form could generate pentagonal geometry as pentagons don't fit together neatly like cubes of hexagons but an alloy of aluminium and magnesium produced a geometry that showed pentagonal traits with the trade-off being non periodicity, where the arrangement of crystals and neither ordered or random. Of course the quantum mechanic dudes spoil this by invoking their usual 'is it a bird,is it a plane' spiel but they are best left to their own devices.

https://en.wikipedia.org/wiki/Quasic...iffraction.JPG

The antecedent of the misnamed quasicrystals was Penrose tiling where 4 angles acted like geometric DNA in creating the patterns which are found in alloys and not just schematics on paper. I found a way to account for an encompassing geometry that satisfies why inanimate crystals follow a non-periodic development far removed from each other but this solution would only appeal to those who are visually enchanted by the tiling patterns -

https://en.wikipedia.org/wiki/Talk:Quasicrystal

I may as well show a picture of Elvis Presley to readers here for all the good it does them but the arrangement of the Penrose tile angles in sequence around a parent 432° geometry is a wonderful story that takes in beauty and efficiency observed throughout nature from the small crystals to stellar evolution.