AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal

Come along this simple journey into the mathematics of numbers to see how Nature might use a simple cookie-cutter template approach to express the richness and harmony of her forms. We are talking about the simple whole numbers of quantities, and, the irrational, infinity-based fractions π, √2 and ϕ. The latter group act as fractals of proportion…that is, they inform the former group of simple whole numbers as to the proportions that they should aggregate about so as to form a harmonious and resonant unity of the larger Universe. And, as their fractional decimals run to infinity…linking the finite with the infinite…they are also known as fractals of infinity. The math is simple stuff, too! The journey is in seeing how these relationships we all learned in grade school may actually point to a much deeper connection in Nature!

The distillation of Nature…for our purpose…down to biology, chemistry, physics and mathematics…with each of the above a subset of the one below…on one hand…and, really, the arts on the other…is an attempt…as futile as it may seem…to know and understand ourselves.

And while the seemingly subjective side of the arts to know, feel and express that nature is an implied task, in science we think we really know something about Nature if we can describe and ultimately predict.

And yet, you don’t really know Nature…at the core…until you know her numbers…her real numbers…and not simply the mathematical constructs fabricated to describe her numbers. Her numbers are about quantities. Quantities from every possible…imaginable or unimaginable…source…when juxtaposed with so much of this here and that there…give us the expression and esthetic we call Nature.

Brooks (Base) Square, BBS, was born in an attempt to find the numbers…the “numbers of inevitability” as it was later to be called…that define, describe and elucidate the Inverse Square Law, ISL.

The ISL describes the space-time behavior…that is, the architecture…governing gravity, electromagnetism, light, sound, etc., as the density…concentration…of their essence…force/energy…falls off inversely with the square of the distance of separation from the source.

The BBS matrix itself was initially and conceptually derived from the simple geometry of the circle/sphere and square/cube (and other simple forms). Later it took on a form and life of its own.

In re-visiting the earlier work on the geometric relationships between the circle and square (and others)…that is, their numbers…π, √2 and ϕ…all irrational numbers whose decimals run to infinity…led to the provocative and highly charged idea…presented here…that these numbers of infinity were acting as fractal templates of proportion…the juxtaposition of certain numbers…at the gates, or portals, of creation…ensuring both the inherent harmony of all forms and forces of energy expressed, and, the umbilical tie-back to the mother infinity below. Fractals of infinity.

This is one of three videos on AFPOP. The others being: AFPOP Intro and AFPOP

white papers:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/Gomas/gomas09.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/BBS-ISLsplashpage.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/AFPOP/AFPOP-60.html

new media net.art projects:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/netart85.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/netart95.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/AFPOP/AFPOPnetart13.htm

artwork:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/olddraw4.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/newpai11.htm

Thanks for viewing!

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sidebar:

Essay on "AFPOP: A Fresh Piece of Pi(e)...and the √2, too...Fractal - Fractal - Fractal"

You are Nature…you are infinity. Within your infinite symmetry everything is neat and tidy. Nothing is out of place. Nothing is amiss. Trouble is…and since you are all knowing you know this…it’s boring.

Excitement comes from the simple act of breaking one of your symmetries. And that’s because havoc quickly follows this break unless you break another symmetry to balance the first. But the new symmetry of two balancing asymmetries amongst the overall symmetry is hardly worth getting out of bed for.

The alarm rings. You wake up with a new resolve to break another symmetry…your third, now…and, of course, another balancing symmetry…your fourth. Hum.

The next day, and then the day after that, and the day after that…you do the same so that after one week’s worth of your days you’ve got quite a little mix going. It’s getting a little more exciting. And you are getting excited…but hold on…you have to keep a grip on it…your emotions, that is…because all these asymmetries…and the number keeps growing…are forcing you to keep tract. You’re turning into a frick’n accountant. Quantities! Changes in quantities! How the frock are you going to keep track? After all, if too much of your core symmetries become broken and/or disengaged, you will end up like the other deranged infinities, disappearing into the vapor museum…a.k.a. asylum…of unfulfilled promise.

So what do you do?

Well, you said you’ve become an accountant, so you do what accountants do, you account…you account for things. Well, hell, there are getting to be an awful lot of things…what, with all theses breaks in the symmetries…to account for. And what do you mean “account for,” anyway? Are we talking specifics; like qualities, like the who, what, when, where, how and why? And for each asymmetry? Hey, remember, while you may b formally known as “infinity,” the name itself drives from “infinite simplicity” which got transformed to “infinitely simple” along the way to “infinity,” while your nickname “beautiful” never fails to get your metaphorical blood running whenever you metaphorically hear it from a metaphorical admirer…”hey, beautiful!”

Back to reality. Your simple answer is to quantitate all change…all flux. Be it beans, sprouts, spins, energy densities…you will count…and account for…it all. They call it enumeration…assigning a number, as a symbol…to represent the quantity. The quantity is real. The change in quantity is real. The symbol…the number…is in its strict 1-to-1 correspondence to the quantity…equally as real. Others can change the symbol, manipulate the symbol, or even believe and/or lay claims they are responsible for creating the symbol, but underlying it all, at the root of enumerating quantity…the original symbol-quantity abstraction…the number…remains real. It is part of Nature.

Wow! The excitement continues…especially now that the recognition of numbers…that had been there all along…is giving you a fantastic power. A little of this, a little of that…and before you know it, the symphony of all your well-calculated symmetry breaks has given birth…birth! Who’s the father?…to a new form…a new, expressive form of you. It’s like a dream. A reoccurring dream. It’s there when you sleep, gone when you awake, there when you sleep, gone when you awake. Pulsing in and out, on and off, there and not there. The rhythm is not only intoxicating…and it’s very alive…it’s also extremely important…for your dreams while asleep are but manifestations of the symmetries/asymmetries that you have allowed…by counting the numbers…while awake.

Cool! But within this new field of energy…manifested during the pulse wave of dream sleep…you want more. More, more, more!

You know that manipulating the numbers…the quantities…of the symmetry/asymmetry ratio is the way to do it, yet there must be a simple, elegant way to do so such that resonance and harmony of your growing dream-space perfectly reflects the intentions of your wake-space…that includes an all-encompassing, everlasting reference to your core identity…infinity.

It dawns on you that ratio…that is, proportion…is what you have been doing all along and taking this idea…specific ratios of proportion…and applying it as a portal control for the emergence of all quantities…numbers…will instill those same ratios of proportion to all the forms…as open fields of energy and/or as condensed, concentrated fields of energy (a.k.a. matter) presented in the dream-space.

Thus the idea of the self-similar, re-iterative fractal was born. And while there are certainly a number of these infinite fractals…or fractals of infinity…around, some of the most important are those that would form The Architecture Of SpaceTime (TAOST). The irrational numbers π, √2 and φ (φ), fit the bill…as they are infinity-based, with their decimal endpoints going to infinity, and, as they are fractal ratios of proportion…building the simple, core geometric shapes of the circle, triangle, square, rectangle, pentagon, etc…all manifesting the dictates of structure and growth as embodied in the Inverse Square Law (ISL) as fully elucidated in the Brooks Base Square (BBS) matrix.

So let the fun being. As your infinite wake-time omniscient self plays a pulsing, flickering dream-time movie, you have purpose fulfilled…you are creative! And to add to the excitement, to keep the dream-state interesting, you have given the partially sentient products of your creation just enough of the magic to keep them wondering, too!

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Brooks (Base) Square, BBS, was born in an attempt to find the numbers…the “numbers of inevitability” as it was later to be called…that define, describe and elucidate the Inverse Square Law, ISL.

The ISL describes the space-time behavior…that is, the architecture…governing gravity, electromagnetism, light, sound, etc., as the density…concentration…of their essence…force/energy…falls off inversely with the square of the distance of separation from the source.

The BBS matrix itself was initially and conceptually derived from the simple geometry of the circle/sphere and square/cube (and other simple forms). Later it took on a form and life of its own.

In re-visiting the earlier work on the geometric relationships between the circle and square (and others)…that is, their numbers…π, √2 and ϕ…all irrational numbers whose decimals run to infinity…led to the provocative and highly charged idea…presented here…that these numbers of infinity were acting as fractal templates of proportion…the juxtaposition of certain numbers…at the gates, or portals, of creation…ensuring both the inherent harmony of all forms and forces of energy expressed, and, the umbilical tie-back to the mother infinity below. Fractals of infinity.

This is the second of three AFPOP videos: Introduction. The others are AFPOP and AFPOP-Intro-animation

white papers:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/Gomas/gomas09.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/BBS-ISLsplashpage.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/AFPOP/AFPOP-60.html

new media net.art projects:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/netart85.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/netart95.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/AFPOP/AFPOPnetart13.htm

artwork:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/olddraw4.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/newpai11.htm

Thanks for viewing!

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``` Aren't you simply stating the obvious?
~"hopefully...yes! But, what do you mean?"

Aren't you simply taking a part...a fraction...of the circle/square to make a new set of circles/squares...?
~"yes!"

And then, relating the differences across the sets and between the sets...?
~"yes!"

And then, pointing out how those differences all relate back to the original part...a fraction...of the circle/square?
~"yes...you're getting it! Keep going."

Isn't that obvious...that they would relate? It's like inbreeding!?"
~"yes, exactly...but keep going!"

You're starting to bug me!
~"yes, exactly...if that is a question...good, if not. Keep going!"

How does inbreeding...passing on the same genes, without the obvious benefit of diversity...help us?
~"do you really think Nature ever seriously considered giving a unique genetic code to every species?
Why not just tweak the master code here and there. It's all that is needed to establish the species,
inter-relate the species back to one, yet allow for some variation...some diversity...within.

Same goes for the building blocks of spacetime...the numbers...and the quantities they represent."

Get outta 'ere! What do numbers have to do with genes?
~"it must be tough living in your body...no, really, try this.

Everything is quantitative...even the subjective notion of quality. It's all about the numbers, baby!

Numbers of inevitability.

But getting back to your question. Genes are like biological fractals...conceptually, not so much visually.
As expressed over time, a self-similar, re-iterative expression of a fundamental pattern whose larger
expression...generations over time...reflect, mimic...indeed...can be shown by deconstruction...to reveal
that initial fundamental pattern, i.e. a group of genes...is a biological fractal."

So I am part of someone else?
~"naturally, yes...we all know that...as, too, the parts of your parts are all recycled stardust."

Numbers? Quantities? Geometry? Circles/squares? Spheres/cubes? Spacetime?
~"in order for spacetime to hold and be a manifestation of all energy...as the fields and matter...it
has to quantitate the spacetime...the total spacetime energy. Every quantum unit of spacetime must be
enumerated as to quantity and distribution...a.k.a. density...and be relatable back to the whole...
the one...in order to make sense of it all. You know, little things like the conservation of energy,
charge, spin, momentum, must all be accounted for."

Ok, but that's still pretty broad...kinda out there!?
~geometry...the quantitation and proportional arrangement of shapes and forms...doesn't just
describe the quantum unit of spacetime...it is The Architecture Of SpaceTime (TAOST). Numbers,
quantities, geometry, circles/squares, spheres/cubes...they are the real spacetime...and as fractals
...fractals of infinity...they create it all...including us!

Sounds like you're on a role, dude. Do continue.
~"again, Nature is incredibly, sublimely beautiful in her expression as well as the means.
A fractal template of proportions that will fundamentally inform...at the core...all expressions
...manifestations...of her energy provides not only the built-in resonance and harmony of the parts
to the whole, it also allows for the accounting...the how much, how often, the who, the what,
the why...and the how!"

Whoa! Got any examples of that in mind?
~funny you mentioned it! The fractal templates of proportion are pi (π), the square root of two (√2)
and the golden mean/proportion (ϕ). They are all irrational numbers whose decimal fractions never resolve,
instead go to infinity. They are all intimately involved with defining and expressing the Euclidean
geometry of circles, triangles, squares, rectangles, pentagons, and so on. All three fractals have one
foot in the infinity pool and the other in the ideal Platonic shapes and forms...and π and √2 are
intimately related both in the transformation of one to the other, but perhaps most importantly, built
into their very geometry is the basis of the Inverse Square Law (ISL), as formally presented in the
Brooks (Base) Square (BBS) matrix. As we know, from light to sound to gravity to energy/force distribution,
the ISL defines The Architecture Of SpaceTime (TAOST). And now, we see that this geometry is informed
and accounted for by the fractals of proportion...the fractals of infinity...π, √2 and ϕ.

~yes...you are really getting it!

Seems to me most things out there are NOT ideal...hey?
~that's exactly right! Diversity, evolution, richness, uniqueness...every form of expression is tweaked
...altered by a multitude of factors, some big, some small...into what seems more like a Riemann
non-Euclidean form of geometry in which parallel lines meet giving us...in the larger picture...the
curved spacetime of Einstein's General Theory of Relativity. For us, it just may mean your nose is
this way, someone else's is that way...but there is no getting around it is a nose.

So fractals of infinity...fractal of proportion...that's where it's at!?
~yes...you are a beast!

Circles and squares...as well as other geometric forms...have always been inter-related. Inherent in their geometry is the relationship of their linear elements to their areas...forming the basis of the Inverse Square Law (ISL), as formally presented in the Brooks Base Square (BBS) matrix. At their core, these geometric forms are based on three irrational, infinity-based numbers of proportion...π, √2 and ϕ...pi, the square root of two, and the golden mean. These core proportion-based relationships suggest that they may be acting as fractals in the formation of The Architecture Of SpaceTime (TAOST). Fractals of infinity.

white papers:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/Gomas/gomas09.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/BBS-ISLsplashpage.htm

new media net.art projects:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/netart85.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/ISL/Brooks_(Base)_Square/netart95.htm

artwork:
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/olddraw4.htm
http://www.brooksdesign-ps.net/Reginald_Brooks/Code/Html/newpai11.htm

Thanks for viewing!

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Brooks (Base) Square

by

Reginald Brooks

A Brief Introduction

TOAST-The Architecture of SpaceTime

TCAOP-The Conspicuous Absence of Primes

Interconnectedness

Conclusion

References

Appendix A

Appendix B

NOW online

@

brooksdesign-ps.net