BIM-MPS_Details-IV

As one can see, the color bands that make up the PN can form all three "generations" withing the MPS space. They do so in a completely fractal manner, based on the exponential power of 2. They do so in a repeating NPS template that is exactly the same for each MPS, with only the relative numbers being different.

As an overview, let's look at a half a dozen examples before diving in to a more detailed look. To note: only the y values listed are illustrated within the much larger x+y=z central column shown.

Yet another advanced section. And it will be addressed in the Appendix I in Book VI. Here is just a little bit.

The MPS on the BIM (BIMMPS)

Bringing it all together: Parts I - II - III - IV

The Perfect Numbers may be expressed as the sequential running sums (∑) of the cubes of the sequential ODD numbers as 1³ + 3³ + 5³ ... and we have the genesis of the Butterfly Fractal~3~.

In the Butterfly Fractal~1~ and Butterfly Fractal~2~, we find the MPS parameters based around the EVEN numbers, especially within the exponential power of 2. When we look at their summations, we find it delivers the ODDs we are looking for that inform the MPS directly.

This gave the x and z=Mp directly and the y, xz=PN and xy=CR indirectly by calculation.

Now, in the Butterfly Fractal~3~, we find the MPS parameters based around the ODD numbers, especially the Running Sums (∑) of the ODD numbers sequence of 1,3,5,… giving the MPS and the ODD³ sequence of 1³, 3³, 5³,… giving the PN!

NEXT: BOOK III: An Artist, Mathematician and Choreographer...Oceans of Numbers (Part II)

Back to Part I of the BIM-Goldbach_Conjecture.

Back to Part III of the BIM-Goldbach_Conjecture.

BACK: ---> PRIMES Index on a separate White Paper

BACK: ---> Periodic Table Of PRIMES (PTOP) and the Goldbach Conjecture on a separate White Paper (REFERENCES found here.)

BACK: ---> Periodic Table Of PRIMES (PTOP) - Goldbach Conjecture ebook on a separate White Paper

BACK: ---> Simple Path BIM to PRIMES on a separate White Paper

BACK: ---> PRIMES vs NO-PRIMES on a separate White Paper

BACK: ---> TPISC_IV: Details_BIM+PTs+PRIMES on a separate White Paper

BACK: ---> PRIME GAPS on a separate White Paper

Reginald Brooks

Brooks Design

Portland, OR

brooksdesign-ps.net

KEYWORDS TAGS: BMP, BIM-MersenneSquare-PerfectNumber, Mersenne Primes, Mersenne Prime Square, Perfect Number, Perfect Square, MPS, Mp, PTOP, Periodic Table Of PRIMES, PRIMES vs NO-PRIMES, algebraic geometry, BIM, TPISC, The Pythagorean - Inverse Square Connections, Pythagorean Triangles, DNA, Zika virus, pentagon, decagon, double pentagon, composite axial DNA double-helix, Pythagorean Triples, primitive Pythagorean Triples, non-primitive Pythagorean Triples, Pythagorean Theorem, Pythagorus Theorem, The Dickson Method, BBS-ISL Matrix, Expanded Dickson Method, r-sets, s-set, t-sets, Pair-sets, geometric proofs, MathspeedST, leapfrogging LightspeedST FASTER than the speed of light, Brooks (Base) Square- Inverse Square Law (ISL), BBS-ISL Matrix grid, The Architecture Of SpaceTime (TAOST), The Conspicuous Absence Of Primes (TCAOP), A Fresh Piece Of Pi(e), AFPOP, Numbers of Inevitability, LightspeedST, Teachers, Educators and Students (TES), number theory, ubiquitous information, FASTER than the speed of light, primes, prime numbers, fractals, mathematics, Universe, cosmos, patterns in number, DSEQEC, Double-Slit Experiment-Quantum Entanglement Conjecture, CaCost, Creation and Conservation of SpaceTime.

Art Theory 101 / White Papers Index

PIN: Pattern in Number...from primes to DNA. | PIN: Butterfly Primes...let the beauty seep in. | PIN: Butterfly Prime Directive...metamorphosis. | PIN: Butterfly Prime Determinant Number Array (DNA) ~conspicuous abstinence~. | GoDNA: the Geometry of DNA (axial view) revealed. | SCoDNA: the Structure and Chemistry of DNA (axial view). | The LUFE Matrix | The LUFE Matrix Supplement | The LUFE Matrix: Infinite Dimensions | The LUFE Matrix: E=mc² | Dark Matter=Dark Energy | The History of the Universe in Scalar Graphics | The History of the Universe_update: The Big Void | Quantum Gravity ...by the book | The Conservation of SpaceTime | LUFE: The Layman's Unified Field Expose` | GoMAS: The Geometry of Music, Art and Structure ...linking science, art and esthetics. Part I | Brooks (Base) Square (BBS): The Architecture of Space-Time (TAOST) and The Conspicuous Absence of Primes (TCAOP) - a brief introduction to the series | more White Papers...

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BIM-MPS Details, Part IV

The MPS on the BIM (BIMMPS)

The MPS on the BIM (BIMMPS)

Background

Yet another advanced section. And it will be addressed in the Appendix I in Book VI. Here is just a little bit.
The MPS on the BIM (BIMMPS)

Bringing it all together: Parts I - II - III - IV

NEXT: BOOK III: An Artist, Mathematician and Choreographer...Oceans of Numbers (Part II)

Back to Part I of the BIM-Goldbach_Conjecture.

Back to Part III of the BIM-Goldbach_Conjecture.