This image depicts the interaction of nine plane waves—expanding sets of ripples, like the waves you would see if you simultaneously dropped nine stones into a still pond. The pattern is called a quasicrystal because it has an ordered structure, but the structure never repeats exactly. The waves produced by dropping four or more stones into a pond always form a quasicrystal.
Because of the wavelike properties of matter at subatomic scales, this pattern could also be seen in the waveform that describes the location of an electron. Harvard physicist Eric Heller created this computer rendering and added color to make the pattern’s structure easier to see. See: What Is This? A Psychedelic Place Mat?
See Also: 59. Medieval Mosque Shows Amazing Math Discovery
A CG movie inspired by the Persian Architecture, by Cristóbal Vila. Go to http://www.etereaestudios.com for more info.
In 1941, Escher wrote his first paper, now publicly recognized, called Regular Division of the Plane with Asymmetric Congruent Polygons, which detailed his mathematical approach to artwork creation. His intention in writing this was to aid himself in integrating mathematics into art. Escher is considered a research mathematician of his time because of his documentation with this paper. In it, he studied color based division, and developed a system of categorizing combinations of shape, color and symmetrical properties. By studying these areas, he explored an area that later mathematicians labeled crystallography.
Around 1956, Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher’s interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher’s works Circle Limit I–IV demonstrate this concept. In 1995, Coxeter verified that Escher had achieved mathematical perfection in his etchings in a published paper. Coxeter wrote, “Escher got it absolutely right to the millimeter.”
|Snow Crystal Photo Gallery I
If you have never studied the structure of Mandala origins of the Tibetan Buddhist you might never of recognize the structure given to this 2 dimensional surface? Rotate the 2d surface to the side view. It becomes a recognition of some Persian temple perhaps? I mean, the video really helps one to see this, and to understand the structural integrity is built upon.
So too, do we recognize this “snow flake” as some symmetrical realization of it’s individuality as some mathematical form constructed in nature?
I previous post I gave some inclination to the idea of time travel and how this is done within the scope of consciousness. In the same vein, I want you to realize that such journeys to our actualized past can bring us in contact with a book of Mandalas that helped me to realize and reveals a key of symmetrical expressions of the lifetime, or lifetimes.
Again in relation how science sees subjectivity I see that this is weak in expression in terms of how it can be useful in an objective sense as to be repeatable. But it helps too, to trace this beginning back to a source that while perceived as mathematical , shows the the mathematical relation embedded in nature.
See: Nature = Mathematics?