Minkowski Topology

In this passage, we will study space-time, ricci tensor, and minkowski topology.

Minkowski is a well-known German Mathematician who lives in the time of Albert Einstein.  He is pretty friendly with the work of Einstein on explaining space-time curvature. He is a professor of Albert Einstein, in 21 September 1908, he delivered, alongside Einstein works, the meaning of space-time in Special Relativity and General Relativity, on the 80th Assembly of German Natural Scientists and Physician.

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

Even if they still use the cartesian diagram to profoundly map relativity, yet the Euclidian did not falter too much from the tensor mathematics and topology.  In short, as a starting, let's imagine two places in space-time, one started in New York City, and say the other one started in Bandung.  Accordingly, let's say the distance is stated in two dimensions, in which started in New York City was 1000 years ago even before the city was built, while the one in Bandung started just several years ago.  According to time reference, these two states were differentiated by the fourth dimension, especially close frame of reference yet quite different as long as quaternion has to comply.  So, the t on the first state equation is say 1000 and the second t let's commute with r is 3.  let's say that the equation is 

S² = x² + c²t² 

and

S² = x² + c²r² 

We can see that the delta S of the component would include two different time measures, in which were 1000 as t and 3 as r.  As how we see it, then S would propagate either as the square root of the first as well as the second equation.  To solve this equation and knows the real dimension of the planar, we would use the equation in differentiation to solve on each slopes and points.

Minkowski Spacetime Cone, Illustration Photograph by Spencer Sutton (fineartamerica.com)

Minkowski define several characterictics to be considered as Einsteinian-Minkowski Topology (Also with the help found in Ricci Tensor Metrices) as, first it is a flat pseudo-Euclidian diagram of space-time, second the space-time interval is described as interval ds² = c²Δt² - Δx² - Δy² - Δz² 

, third it is independent of initial frame of reference that is chosen.

Accordingly as analysis between two points in the diagram we may use Ricci Tensor to make it simpler in breaking-down each equations.  The Ricci tensor is a step to step analysis to study Minkowski Topology and pin point a dimension in space-time, quite different with Dirac Equation in which describes string theories and quantum, Ricci Tensor is more quite much to say "eligible" to be used in calculating Minkowski Topology.

The Ricci tensors as follows:

These elongation in the right hand side is the Reimann Tensor. One perhaps might ask now, where does a calculation the being able to be put in hand in the Topology?

As how we see that Minkowski Euclidian are four basis variable calculation, one may use matrix to calculate such succumbent.

In the diagram, we may simplify each basis and mount it unto an algebraic function, thus then otherwise may make us able to calculate the dimension of the event point in the other dimensional diagrams.

Therefore, Ricci-Reimann Tensor is one of Mathematical Tools in mapping points in four dimensional space-time, disregarding also its use in Black-Holes and Singularities, there would perhaps be a quite interesting foundings if we also use the disclosure of quaternion algebra and Dirac Equation, to bridge in between the examples of Membranes Theories and String Theorems.

References:

- Ricci tensor (planetmath.org)

- Einstein Relatively Easy - The Minkowski metric

- Einstein Relatively Easy - Minkowski's Four-Dimensional Space-Time

- The Dirac Equation (ucsd.edu)

- Drawing Time in Four Dimensional Graphs by Muhammad Sadhra Ali

$${\mathrm{<br>}}_{}$$$$K_x(u,v)=\frac{R_x(u,v,v,u)}{g_x(u,u)g_x(v,v)-g_x{(u,v)}^2}$$

Does time have initial energy in itself?

First, I would like to commence with you that there are three main categories of how you see the time; one, you see it as just changing moment, second, you see it as dimension, and the third you simply put as the pulse of works in changes.

All these views matter not when we only research in essence, not too deep to the benign of time itself.  Matter in space has variables and do speed just a fractal of second faster than light, called the Higgs Boson, through topologies Boson exceeds the photon.

These views are important, first in the knowing better about time, second can only time alters all forces and realities, and third how is time thought to be a singularity or even illusions.

So, for seeing Time as another form of energy, theoretically, time must have subsidiaries, as such time must be able to be counted in the time of mass.  Secondly, time needs to be also independent and both codependent with matters as also mass.

Second, that time needs to be equivocal with the Higgs Boson that intangible with the nature of time.

The hardest thing to be ever explained although yet, could we measure time without time itself?

Light Speed/delta force of Bosonic Mass Speed x Bosonic Mass Speed = £, 

£ = A Time Fluctuation Variable Constant    

•   https://www.gnu.org/licenses/gpl-3.0.html
•  https://www.mexperience.com/mexicos-time-zones
• https://sort-care.github.io/Latex-on-Blog/

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By Schlrm. Chanda Indra Purnama

Snetzel Laws (The Law of Realities)

Snetzel  Laws

1.        Every reality has to be interpreted by five senses without exceptions.

2.       There are levels of realities or impairment of dimensions in which happen to be either immaterials or matters according to physical truth.

3.       Every phenomenon always have a counter exo-phenom that creates an alternate realities

4.       Every reality cannot be fully recorded and comprehended by science.

5.       Relativity of time is only a bifurcation of progress.

Seeing through the Phenomena of three things, first is believes upon seeing creatures or other imaginative beings in other world or dimension makes us think that whether or not those are physics to be comprehended, second is the phenomenon of being incarcerated by negative energies, there are a lot of recordings upon exorcisms and conjurations, thus those actually scientifically comprehended by senses, third is that people are able to fall in love also other creatures, what is actually love in physics sense?  Does it able to be comprehended mathematically?  Can someone scientifically proof the existence of love?

From those arguments, firstly we could see that many people may imagine and create their own world creatively, thus like the Novel of Chronicles of Narnia, The Harry Potter Series, and even other imaginative believes as such the existence of Jinns and Angels.  From all these facts and arguments, may one expect that those realties actually happen through quantum phenomenon or just mere psychological creature that happens virtually in our mind?  These would be described in the discussion.

Secondly, many recording of negative energies does exist as such exorcisms, seeing ghosts, and conjuration.  Are those facts only comprehensible through mystery of meta-physic?  Or does negative energies able to make one observer split in personalities like what happened to Sybil case in Cognitive Clinical Psychologies?

Third, many people are married, some chose to have sexual activities without marriages, some conserve their virginities for husbands, and wives, but strange thing called love does startle our critical thinking.  Is it real?  Can love be describe in Physics or is it just a hormonal changes in the nature of our bodies, may one really mathematically define love?

There are several laws decoding energies, some of the were Thermodynamics, Conservation of Energies, Brownian Motions, and others, yet such Laws hasn’t comprehensively nurture us in the thinking of creative energies and beings of other dimension like aliens.  Are those realities?  By confronting the first lemma of Snetzel Law that to be scientific every reality need to be comprehended by all the five senses, we could create a formulations as such that 1/5 of every realities are described in each normal senses, so as such everything could be either 100% real or 0% real.  Mathematically, it could be derived R = X . Pr where R is realities, Pr is probabilities, and X is percentage of senses.  This could predict the existence of other senses in which could measure the happening of other realities if ever it is true scientifically.  Watching movie for instance is not a total realities but demi-realities with pseudo-characters, in which that every miniature of our stories are embedded in our mind and perspective to see an interesting movies based on our experiences.

According to the second law of Snetzel, there are impairments of dimension, these are supposedly according to Einstein Theories, Minkowskian Theories, Laws of Nature as such Newtonian, accordingly. Through the understanding of Snetzel Law, dimension could be impaired, thus this impairments may be a results of corruption in index of realities.  To count such index we may think that realities are both immaterial and physical yet still in Physics understanding.  These index maybe written as such, i+i^2=0 if and only if it comes from imaginative mind while i+i^2=1 if and only if it is a physical truth.  Therefore, if the index appear in between 0 and 1 then it is a demi realities as such that if it is found thus the variable exceeds 1 or below 0 it is called pseudo realism.

The third law state that every phenomenon of realities have a counter exo-phenomena, it means that if we found such phenomena in any realities such exo-phenomena or decode of phenomena must appear in alternate terms, this is according to Quantum Theories, String Theories, and even Multiverses.  This is decoded P=-EP, this measure that P as Matrix of Phenomena while EP are the negatives or imaginary of every Matrix of Phenomena.

Four laws stated that every reality are not always be comprehended by science.  This is the boundaries unto this law.  Snetzel cannot comprehend every reality.  As such that every human memories limited, which means, we cannot memorize every single thing that happens in these universe.  This is the boundary condition.  Scientifically, it written, every reality is hyper-paradox.  Mathematically, V R = U R^R.

The fifth law stated that relativity of time is only bifurcation of progress.  Accordingly, these maintain the norm that time is relative according to Einstein as such it is according to the frame of reference in such.  Mathematically written, T = (1/phi . r^2 .t /3) . 2 where T is time, r is euclidean length and r is boundaries of curve.  This is an exaggeration upon time relativity, in which made that relativities is bounded to space-time and realities.

Summary, the phenomena of other world, imagination, and love may be appearing in Physics as such seeing it from Snetzel Laws, making the the constant variables of motions.  Thus, the phenomena of extra-terrestrials may be comprehended that the index of realities must not be exceeding but in stable condition.

References:

- Einstein A. (1916), Relativity: The Special and General Theory (Translation 1920), New York: H. Holt and Company. 
- https://opentextbc.ca/researchmethods/chapter/phenomena-and-theories/.
- Haskell Curry, Foundations of Mathematical Logic, 2010.
- Sternberg, Robert J. (2007). "Triangulating Love". In Oord, T. J. The Altruism Reader: Selections from Writings on Love, Religion, and Science. West Conshohocken, PA: Templeton Foundation. 
- Arnold, Vladimir Igorevich. Catastrophe Theory, 3rd ed. Berlin: Springer-Verlag, 1992.

Systematical Design and "Space Crafting"

In this passage, I would like to bring us unto the Grand Design Theory, postulate of systems in Forces, and the ideas and lemmas of universe expanses thoroughly first inside our memethics.  First, the Grand Design have the idea to bring about one mathematical formulae to convey our universe and all of the Physics Theories.  Even though it is almost impossible to bring about such formulae, the attempts are still going, and firstly, we need to know the background of Grand Design, how is it different than Theory of Everything, and how the mathematics and calculus behind its calculation.  Stephen Hawking have postulated that his theory implicate that the universe is ever expanding, yet in its expansion we would see about the possibilities of mathematical crafts that releases the autonomic means of the relation to its expansion and the forces.  Secondly, we would postulate several bases to be theories at least in gedanken experiments to see whether it is possible to bring about the systems in Forces.  Algorithmic speaking, we would see whether or not there are "allegories" in between the bases postulate of the four fundamental Forces and how the Forces interacts or disintegrates.  Lastly, we would form the ideas and lemmas of universe expansion, see the mathematical implications and looked upon the memes of the whereabouts on thus creative works.  In coherence, we would see that Physics have some modules that it held creating the universe which made an architectural means in forming e.g. Nebulae, Cosmic Rays, and Black-Holes.  This meant that there are more to see Physics in its beauty on explaining the Universe and Nature Phenomenon.

Grand Design tells us the Question of Life have answers in Nature Phenomenon while Theory of Everything conveys us that M-Theory and Superstring Theory are both candidates for the unification theory of the four fundamental forces.  The mathematics behind Grand Design and TOE includes the calculus of Manifolds with deeper understanding on Minkowsky Relativity.  It also included General Relativity of Einstein and meaning of Graviton.  Yet, this gravitational scheme cannot find it standing with the other Forces Field thus create disambiguation to form Membrane Theory that satisfy the need of infinities in singularity.  We could postulate thus that M-Theory holds a specific system to glue all the theories together.  As if an architect trying to draw a design, this specific system re-modulate the mathematical functions to follow certain "universal algorithm" that we can call as "Space Crafting".  Since Big Bang, we always think that there are some kind of abstraction to the universe as it expands.  Yet, this abstraction are not known as space but virtues.  We may postulate therefore that these virtues are empty minkowskian manifolds waiting to be exerted by forces.  These crafts are totally empty and held no forces or Physical entities whatsoever.  These manifolds could be crafted to spare the empty spaces from the multiverses.  This means that all our thinking of the universe had been there from the first time, and there were postulatedly nothing new about the universe.  Only discoveries after discoveries that fills up the empty manifolds.  These manifolds all exerted are basically infinite end, whether it is closed loop or end to end.  As if an empty canvas those manifolds are exerted by space-time to create our universes.

http://www.ita.uni-heidelberg.de/research/bartelmann/grav_lens.shtml?lang=en

Secondly, we could postulate the systemic of thus saying electroweak Forces, Heterotic String Theory, and Quantum Field Theory in Klauza-Klien Theories.  As how we understood it, the system of electroweak forces are mathematics inside EM and Weak Forces.  Thus it has many intrinsic in the system of the inner products.  While, on the other hand, Heterotic String Theory uses many manipulation on implementing the manifolds.  While QFT uses many "alegories" of system like thus used in Thermodynamics; while since QFT also included spins as how electroweak theories do.  Infuses it into Klauza-Klien Theories, we might see an impending that KKT uses coordinate transformation, principle of equivalence, and spinor.  By all these knowledge, we could summarize it unto three basics view of Physical Mathematic, first it uses manifold, second it has spinors, and the third it includes Jacobian in some extent.  So, we could modulate the theory into lemmas of x, y, and z, with extra t dimension as how it is postulated by KKT.  X would stand as manifolds craft, Y as spinor craft, and Z as Jacobian craft while t are left to the constant/dimensional craft.  After this, we could put any notion and uses any mathematical methods to play a space crafting.  These modules could get us into position even with non-zero end yet we need to do gedanken first on how it would end.  E.g., a Big Bang were created in a non-zero planar on X craft, while a black-hole were formed in Y craft, and the earth moved into the lunar eclipse in the Z craft.  We could see that T as relativity of three immodular motions.  To calculate this, please refer to my previous paper Drawing Time in Four Dimensional Graphs.  Then, as X craft create a crests in Y manifold, multiverse were immersing in Z manifolds of Vega so that the T would be impending as relativity between lights and bosons.

https://physicslight.wordpress.com/2013/03/11/higgs-boson-discovery/

Thirdly, we could form ideas and lemmas on how these memes were modulated into algorithms of either C++ or C languages to find the bifurcations of such (I haven't done this myself. red).  Perhaps, excel also could help to form the initiate positioning of the graphical representation of the universe.  After that, we could put it on Matlab or Mathematica, to see how the corresponding ideas matches with the calculus we immerse.  These could help us to predict Big Bang in multiple realities.  Not only thus multiple universes exists, but our thoughts also create its own Quantum Realities.  This must have a record on the impending abstraction that bifurcate in the empty manifolds to wait for the science creating the phenomenon to thus exists.  As light and mass are in race towards one another, we would see that our universe are emanating like a distant star over another distant dwarf.

http://www.bbc.com/future/story/20130610-mind-bending-multiverse-mysteries

Discussion, what would it has to do with Physics?  It is so impending to know that Physics has basic core thinking, to know that behind it there are modules of ideas that created interpretation of many Nature Phenomenon, we would know thus that Physics are not only predictive and scientific, but fun and creative.  How can one use Systematic Design into application?  We could use it to predict the morphology of nano-structures with impending time, or we could measure the Hadrons in two different experiments at once, or else we could use it just to help us form usable formal formulae.  Why do we need "Space Crafting"?  We need this methods to help bridging the mathematics behind the fundamental Forces so that we could create an understanding that those Forces somewhat "interacts" altogether.  Also, with this method, we could see the understanding of our universe better and see another perspective of Nature.

In conclusion, GD and TOE has differences on the mathematical and philosophical background of the written theories; even though both concludes that there are one unification theory, GD are more passive unto KKT yet TOE are actively mentioning manifolds of Klauza-Klein as the immersion of thus.  This lead us to know that there is a system that govern the four fundamental forces.  This system could be predicted by using basic understanding of mind abstraction.  All the memes therein then could by applied in computerized mean to find the algorithm structure to better understand the universe.  So, Systematical Design and "Space Crafting" could be a new entrance to scientific methods on researching about Physics and Mathematics.


Bibliography

• Stephen Hawking & Leonard Mlodinov.  Grand Design, Bantam Books, 2010. New York.
• https://www.quora.com/How-is-the-Theory-of-Everything-different-from-The-Grand-Design-by-Stephen-Hawking
• http://www.damtp.cam.ac.uk/research/gr/public/qg_ss.html
• Anze Zaloznik.  Klauza-Klein Theory, University of Ljulbjana Faculty Mathematics & Physics, April 2012.  Ljulbjana.
• Michael Spivak.  Calculus on Manifolds, Addison-Wesley Publishing Company, January 1995. Massachusets.

Particles of Physics; Neutrino

Have you ever seen a Christmas Light bulbs those changes colors?  You might perhaps think of how does that work in real.  While considering complex instrumentals and coding with wiring and all that stuff on how to create a safety lamp boxes to sign your car to move forward or stop, let me not bring you to that.  The thing I wanted to emphasize here is that, the lamps changes colors, yes it does.  That brings our understanding in Quantum Physics as Particles of Neutrinos that has different flavor or lamp bulbs which changes "colors".  There are generally known to be two kinds of way to see a Neutrino which is from oscillations and/or Types.  Also, alongside with Neutrinos, we also know several other Physical Particles in such are Baryon, Boson, and Fermion and such.  We will discuss about these four Physics properties and also see the differences in between, and which is not which nevertheless.

We are going to be introduced to Neutrinos.  Just like lamp bulbs that changes in color, Neutrino changes its properties from the positional changes in the cosmos.  Types of Neutrinos are considered having many ways to be divided, one of them through quark divisions.  There are three in each types of quark; the up-type quark which are up, charm, top, and the down-type quark which are down, strange, bottom.  According to oscillation, just like other leptons, Neutrinos are divided unto Tau, Muon, and Electron.  Yet, we could only use one division at a time to properly understand the Neutrino.  Other ways to classify Neutrinos are by how the other charged leptons conveyed towards thus, now before we go too far, let me explain about leptons.  Lepton are Physics Particles that does not interact with others in strong force interaction.  Thus, there are four kind of Forces i.e. Strong, Weak, Electro-Magnetic, and Gravity.  So, to say, leptons do not interact with other lepton is strong interaction, mind that.  Let's go back to our standing point, which is the neutrino.

https://profmattstrassler.files.wordpress.com/2011/10/neutrinoclassification.png

The Neutrino in the above description are viewed through its bosonic articular, or from its mass.  So, looking from mass every muon, tau, and electron has its own antiparticles.  These are not atoms, if an atom is divided into phases and forces, we would get oscillations as such that shown in quantum as how it is.

This video would verily helps to understand Hadrons.  There are Elementary Particles and Hadrons or Composite Particles.  Fermions are leptons, antileptons, and electrons also up/down, strange/charm, or top/bottom as quarks.  Baryons and Mesons, though can be divided into quarks.  Please watch the video to deeply understand more about particle physics.

In this journal, I would like to more emphasize on Neutrino.  Neutrino start at about 15 billion years ago, soon after the birth of the universe.  Neutrino were first postulated in December 1930 by Wolfgang Pauli to explain about the spectrum of beta decays.  

Thus, we all can conjugate that Neutrinos were oscillating.  Neutrino just like other particles have duality properties that were mounted by Heissenberg.  All those neutrino-1, neutrino-2, and neutrino-3 are differentiated from its eigenstate.  They travel through space at different frequencies.  The flavor of a neutrino is the superposition of its frequencies. 

http://www.hyper-k.org/en/img/waves.jpg

Neutrino oscillation happens when a neutrino have masses and non-zero mixing.  It was discovered on 1998 in Super-Kamiokande as the basic of Standard Model Physics.  The atmospheric changes between the atmosphere and muon neutrinos generated by collision were apprehended.  The number of down Neutrinos were only half of the up Neutrinos.  This is because the rest were turning into Tau Neutrinos.  Neutrino were later observed using AI Beam and Solar Neutrinos.

In conclusion, there are many types of neutrinos and how to divided it.  Just like a Christmas lamp bulb, it changes properties as it moves atmospheric backgrounds.  There are only one division can used upon one observation.  It could release either Tau, Muon, or Electron Neutrinos.

Study Lists:

- https://icecube.wisc.edu/info/neutrinos

- http://www.hyper-k.org/en/neutrino.html

- http://www.astro.wisc.edu/~larson/Webpage/neutrinos.html

- https://www.youtube.com/watch?v=2eFvVzNF24g

Geometric Static towards Bifurcation of Movement

In geometry, we know as a study of nature's polynomials, several types of amp.  First, Geometry scalar, geometry planar, geometry dimensional, and geometry static.  In this written paper, I would like to introduce Bifurcation of Movement inwards Geometric Static.  There are several things that needed to be understood that this static geometry are general geometry at large, could be used for fractals, large polynomials, shapes, and also meta-dimensions.

Geometric Static are the state of geometry where null changes are made to its median, mode, either ranges.  In this overview, we stop fractals at certain point of changes.  Bifurcation of Movement on the other hand, receipt as spreadth of vectorials happening towards certain changes in its process of making. So, Geometric Static towards Bifurcation of Movement means the statical point in geometry explaining movement in the study of bifurcations.

There are more than three parameter in studying Geometry of Bifurcations.  First is the fractal parameter.  Second, is chaos behavior parameter.  Third is the periodic parameter of statures.

If we modified the picture above, up until parameter halt, we could see in between Period 1, Period 2, and Period 3 a shape. a triangle with triangular bisections.  This is the geometric static of such parameter of fractals, looking through the second parameter, chaos are disambiguated by furlong automatic extraction of pattern over and over again.  Seeing the third parameter, saturation of such statures my be exhibit.

The picture given are an example of Geometric Static.  This is made as such that seeing bifurcations more to the origins than patterns.  With his distinguishing pattern, one my see that much creativity is needed to creets this and make it of use.

So, short-conclusively, geometric static towards bifurcation of movement may open us to a new realm of study sturdy Geometry of Bifurcations, periods & behavior, Parameter Halt Movement, and many others. The founding of such lemma is intact with fractals study, geometry, and static movement.

Bibliography
- http://ucsmp.uchicago.edu/secondary/curriculum/geometry/demos/
- https://www.bandungfe.net/
- Kompleksitas oleh prof. yohannes surya & hokky situngkir
- Mode based parameter estimation: theory & application

02 February 2018, Friday

Comparison Analysis between Fourier Series & Mandelbrot Set 

Mathematical analysis can be very complicated especially when we see through the eyeglasses of the functions it uses in an abstract formula.  Although, abstract formula uses many lemmas on why is it being used that way and not the otherwise, we can always analyse the use of thus different functions in comparative ways.  First, we shall compare the lemmas and philosophical basis on the use of Fourier Series.  Second, how is Fourier Series stronger than Mandelbrot Emergence.  Third, the use of Fourier Series as a combination Permutation on Probabilities.

https://plus.maths.org/content/computing-mandelbrot-set

As so debated that Fourier and Mandelbrot Set are comparatively heavy, there are also foundation in such that neutrality are centered upon the argumentation's;  Fourth, the Mandelbrot Series strength upon Fourier Series, Fifth the usage upon Mandelbrot Set on algorithms and Fourier Series to strengthened mapping, and Sixth how to collaborate these two baselines, so that the use of the lemma may be widened.

Firstly, we shall compare the lemmas on properties of Fourier Series.  Fourier Series are a set of number in serial mode that expands periodic function; it is used in orthogonal proportions on sines and cosines, in computing basis it is known as harmonic analysis. Fourier Analysis uses these three functions in determining continuation:

https://www.gaussianwaves.com/gaussianwaves/wp-content/uploads/2013/05/Fourier_Series_and_Symmetry.png

Secondly, Fourier Series is stronger than Mandelbrot Emergence since on an emergence there are many more to much information can be contained unto each variables and algorithms while Fourier Series restructured overall, taking each stakes a periodically basis and serial them using specific functions to emerge the overhaul of the number synthesized.

Thirdly, the use of Permutation and Combination can be applied unto Fourier Series toward its manger in Delta Kronecker, these may compute the risks and improbabilities of failure or other things in functions.  We can apply General Carrier on Complex Fourier Function to get that Canonical Background upon hypothetical questions.

https://www.physics.ohio-state.edu/~ntg/834/notes/tensor_intro.pdf

Fourthly, Mandelbrot Set has strength of bases more than Fourier in its Analysis.  Mandelbrot can creatively make new patterns and fractilized them upon dots, while Fourier series can explain Canonical Proximity upon one's calculation.  These might seem that Mandelbrot Set won in its field upon crawling in the most speed fractal cases.

Fifthly, Mandelbrot Set can be used upon structured mapping over branched and modul them into a psychological mapping with keywords algorithms while use Fourier Series we can always expand thus to a higher dimension as such that that mapping in pictorial form in 3D to 4D.

Lastly, we can collaborate these two mathematical lemmas to create a better outcome and functions upon building them impossibles, perhaps lemma widening, holologic megastructures, or even creating a 4D images using Sketch on Windows.

Wikipedia

 
In comparative-discussion we can see that many possibilities that people would use Fourier Series for undergoing periodic researches as such weathers, time, thermodynamics and such yet many of thus Nuclear Scientists, MRI experts would rather choose to use Mandelbrot Set to equipped their grand discussion.  However neither the matter is possible.

Conclusively, Fourier Series and Mandelbrot Set are able to be collaborated through lemma exchange up to Algorithms Synergy and Structuralist Form.

Reference & Bibliography:

- http://mathworld.wolfram.com/FourierSeries.html/22:17
- https://plus.maths.org/content/computing-mandelbrot-set/22:17
- KOMPLESITAS, oleh Prof Yohannes Surya, Hokky Situngkir dan lainnya
- https://ipfs.io/ipfs/.../wiki/Kronecker_delta.html
- http://tutorial.math.lamar.edu/Classes/DE/FourierSeries.aspx