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 CristÃ³bal Vila.
Go to 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 twodimensional 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?
Nice CG movie.
ReplyDeletePersian architecture seems to evoke some kind of wafting allmost memory when I see it. It's been responsible for my superficial attraction to Gurdjieff.
Has nothing to do with Gurdjieff.
ReplyDeleteThe
most important archetype of all is the self. The self is the ultimate
unity of the personality and is symbolized by the circle, the cross, and
the mandala figures that Jung was fond of painting. A mandala is a
drawing that is used in meditation because it tends to draw your focus
back to the center, and it can be as simple as a geometric figure or as
complicated as a stained glass window. The personifications that best
represent self are Christ and Buddha, two people who many believe
achieved perfection. But Jung felt that perfection of the personality is
only truly achieved in death
I think you missed the point about the Intent in Actualization. Thatwhether it's theobjectie reality where one finds these symbols metaphrs is talking about structures much wider o the platform Tom showed. Looking at the diagram of the tiling at first glance....is to understand this represents something I discovered in the dream world. Lives are built upon it. Tibetans build them and then take them apart. Really not superficial at all but have enormous depth.
"...underwriting the form
ReplyDeletelanguages of ever more domains of mathematics is a set of deep patterns
which not only offer access to a kind of ideality that Plato claimed to
see the universe as created with in the Timaeus; more than this, the
realm of Platonic forms is itself subsumed in this new set of design
elements and their most general instances are not the regular solids,
but crystallographic reflection groups. You know, those things the
nonprofessionals call . . . kaleidoscopes! * (In the next exciting
episode, we'll see how Derrida claims mathematics is the key to freeing
us from 'logocentrism' then ask him why, then, he jettisoned the
deepest structures of mathematical patterning just to make his name...)
* H. S. M. Coxeter, Regular Polytopes (New
York: Dover, 1973) is the great classic text by a great creative force
in this beautiful area of geometry (A polytope is an ndimensional
analog of a polygon or polyhedron. Chapter V of this book is entitled
'The Kaleidoscope'....)"
To clarify, the Gurdjieff, is my subjective correlation  didn't mean to
ReplyDeletesuggest it was objective. It's a correlation i have yet to sort out.
Since using this blog/Disqus I'm noting more inconsistencies. I use Firefox, so I've yet to confirm that is the 'cause' or not. In my experience IE may/may not provide solution but I stay away from it as much as I can, due to it's nonstandardization.
"I think you missed the point about the Intent in Actualization."
ReplyDeleteVery likely, as I tend to actually ignore such observations at that level unless they connect to me deeper than the intellectual level.
Mandala's, in general, don't get me at the deeper level. They, however, are aesthetically pleasing in the intellectual mode, for me.
Yes thanks RBM for clarification. Still experimenting within Diqus format parameters, and I understand.
ReplyDeleteAgain thanks for your clarification.
ReplyDeleteI just wanted to point out that this sits in the same realm and aside from the intellectual. An internal exploration does in dreaming not deviate and represent the intellectual but fully empowers the observer about discovery.