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