|From the video: Isfahan (a detail of this detail) - 3D digital still - 2005, Cristóbal Vila|
noun ( pl. -trices |ˈmātrisēz| or -trixes )
1 an environment or material in which something develops; a surrounding medium or structure : free choices become the matrix of human life.
• a mass of fine-grained rock in which gems, crystals, or fossils are embedded.
• Biology the substance between cells or in which structures are embedded.
• fine material : the matrix of gravel paths is raked regularly.
2 a mold in which something, such as printing type or a phonograph record, is cast or shaped.
3 Mathematics a rectangular array of quantities or expressions in rows and columns that is treated as a single entity and manipulated according to particular rules.
• an organizational structure in which two or more lines of command, responsibility, or communication may run through the same individual.
ORIGIN late Middle English (in the sense [womb] ): from Latin, ‘breeding female,’ later ‘womb,’ from mater, matr - ‘mother.’
|North American Wood Thrush|
“As we listen we lose the sense of time—it links us with eternity…Its tones…seem like the vocal expression of the mystery of the universe, clothed in a melody so pure and ethereal that the soul still bound to its earthly tenement can neither imitate nor describe it.”
- Anonymous Twentieth Century naturalist describing the Wood Thrush
"It was dawn and as I lay there listening to the birds w/ my eyes shut I began to see a weird pattern emerging from the darkness... an almost graphic pattern similar to computer graphics... It looked like chopped meat being criss-crossed (sic) by a rapidly moving concentric ring pattern... similar to my cyclocentric* patterns but more intricate. From this emerged what seemed like another darker dimension - again filled with cyclocentric patterns but these were made of various colors of light... and some were large and whirlpooling (sic) while smaller brighter patterns emerged... all of them moving and vibrant and living and all of them revolving and forming harmonics by which even tinier glowing patterns emerged. It was as if I was delving into a series of many dimensions... but I could only glance at certain aspects (of the patterns) for milliseconds at a time (as they were) far too complex and enmeshed for human resolution...
...In the beginning I found myself entranced, but it finally became frightening because I was awake, and when I opened my eyes I continued to see the patterns. I thought I might be going mad...that my work with the cyclocentric patterns had triggered some variety of psychedelic experience... Just then, a thrush began to sing outside my window, I willed myself to concentrate on its song which, incidentally, is my favorite birdsong**. When listened to closely, however, it is very much like a broken symmetrical pattern... unfinished in some way... as if some of it was beyond the human range of hearing. I hadn't noticed it before but there's this series of clicks at the end of some notes that sound like static - as if, had you slowed them down - they might sound quite different.*** So, in a sense, I traded one pattern experience for another and was thereby able to stop the visual patterns from firing..."
- Excerpt from a journal entry I wrote May 31, 1996, originally posted (in full) here.
* A reference to cyclohedral nets.
** Listen to the wood thrush here first. Then watch them here or here.
*** Lo and behold, I found this sample of the thrush song slowed down... but, not slow enough, I'm afraid.
Update 11/4/14: This just in... This Bird’s Songs Share Mathematical Hallmarks With Human Music - The hermit thrush prefers to sing in harmonic series, a fundamental component of human music. More slowed down thrush songs.
I rediscovered the video (above) - Nature by Numbers - by Spanish 3D artist, Cristóbal Vila - on Aeon yesterday, although a link had been languishing on this blog's sidebar for some time. It's four years old, which may be a significant number in terms of cyber-years... but, in terms of the matrix, where time is a continuum, it's no time at all. Today is yesterday. Tomorrow is now. Or, something like that.
We live in a matrix; that is, not necessarily The Matrix, but, a living, phenomenal matrix... a dense, organic fabric of geometrical relationships that rivals anything men or machines might conceive (though, admittedly, some might argue with me on this point). But, we do have myriad glimpses... in art, in science... and, sometimes, even dreams. I dreamt * once of such a fabric (recorded above) but, even in the dream the sheer complexity of the matrix was impossible to fathom without becoming certifiably insane.
Which is what, I believe, Spanish artist, Cristóbal Vila intimates in this lovely little video, where, by incorporating both the Fibonacci series, and the Golden Section (terms dear to geometers, both practical and sacred) he effectively marries a sunflower to a dragonfly wing.
Vila continues to explore the beauty of geometry in his amazingly rendered "Isfaram" (see uppermost digital still), which is a tribute to Persian architecture and the medieval artists who embellished it. Crystallographers are also inspired - or shall we say, informed - by the patterns and arabesques that decorate the remnants of the ancient Middle Eastern world. After all - in terms of "visual chemistry" - the medieval artists were there first (see this previous post). Their intricate tessellation - referred to as Girh tiling - predated Penrose (and, his tiles) as well (see Medieval Islamic patterns: Penrose, eat your heart out).
But, my favorite Vila offering is his video "Inspirations" (see still below). It is his ode to the incomparable M.C. Escher, and might be a virtual tour of Escher's studio. (If only it were mine!)
Visit Cristóbal Vila at his website, Eterea Studios, where his 3D tutorials and contact information can also be found.
* I refer here to this experience as a dream here, but, judging by the actual journal entry, this part was actually not a dream... not even a lucid one. What was it? I have no idea.
(Added note: On the other hand, considering the connection to Timothy Leary (see original document), one might say it was a type of "acid flashback". The problem with that theory is that, during the days of my teen-aged experimentation, I was one of the few people who couldn't hallucinate if my life depended upon it. This is not to say, however, that the mechanics of such an experience is unrelated...)
|From the video: Inspirations - digital still (found here) - 2012, Cristóbal Vila|
The soundtrack for Nature by Numbers is: “Often a Bird“ by Wim Mertens.
For an interesting anecdote regarding both Penrose and Escher - and Escher's last print, "Ghosts" - turn to this .pdf file: The Mathematical Side of M. C. Escher.
Interestingly, 2014 is the International Year of Crystallography.
Regarding Dr. Timothy Leary, I just found an interesting document attributed to him: The Declaration of Evolution.
I am pleased to report that the post you have just read has been cited in a fantastic essay regarding lateral vs. linear thinking, posted by the incomparable (lateral) thinker, Ms. Tam B, web-mistress of Histories of Things to Come. See: The Not-So-Discreet Charm of Lateral Thinking.