PES Tiles, v0.02.20170113

PES Tiles, v0.02.20170113

(20170210 note: This is not the latest most complete start version. The current PES_Tiles start is baunic-movie.blogspot.com/2017/01/pes-tiles-v00420170121.html, should you have reached this place through outdated links on forums and messages.  When an official destination will  be the latest and most complete version, a link will point to it also. This draft and its variants will remain here, because core values of the Fictioniverse based on #BAUniC)

Premises:

* Every exponential, even the lowliest exponential, will overtake every parabola, even the highest power parabola short of infinity, based on the same grid orientation.

* A parabola cannot touch the exponential from up. The exponential touching the parabola will always be over the parabola at the point of their meeting.

Part1: PES Tiny

We take the lowliest of exponentials (eg. 1.00000....00001^x; it should look like a flat line of value almost 1), and an even powered parabola (eg. x^2).

We displace the exponential to the parabola origin.

From this displacement we see the positive part of the exponential going over the x axis, and the negative part going under (fig001).

fig001

We rotate the exponential so that the x axis is tangential to the exponential (fig002). We see the exponential with both its 'up' side (the part with the knee of the curve) and 'down' side (the part that approaches x) pointing up in comparison to the grid of the parabola.

fig002

The rotation is finitesimaly small.

Zooming in to the junction point we are going to see a point where the parabola, being flatter than the exponential, goes under it (fig003, and exaggerated in fig004).

fig003

fig004

The junction in fig004 has 3 points of touching between the exponential and the parabola, 2 crossing and 1 touching (with the exponential up)

If we displace the exponential down, we see the middle touch splitting into 2 crossings, for a total of 4 (fig005).

fig005

Further displacement has the crossings on either side come closer to 'annihilate' each other. At their most touch-like point we are met with a similar situation to the one we started with: a parabola trying to touch the exponential from up.

At the 4 point crossing (fig005) we take the liberty to change the parameters (vertical/horizontal stretch+displacement, and a bit of rotation adjustment) so that we end up with 'segments' of the desired size. We start with segments of size 1, 1 and 2 (fig006).

fig006

Here we can overlay a sinusoid of desired specifications to match this gap (fig007).

fig007

This structure we call PES Tiny (para-expo-sin at the finitesimaly small)

Part2: PES Tunnel

The 'flat' exponential at fig001 will grow bigger than the parabola (fig008, fig009 and fig010).

fig008

fig009

fig010

Within the confines of the PES Tiny and the adjustments we allow with a sufficiently finitesimally small gap, we can fit the quality of exponentials overtaking parabolas.

Here we can fine tune the PES Tiny parameters to achieve a few resonating combinations of parabolas, exponentials and sinusoids at the point where the exponential overtakes the parabola. For example a spiral-like form.

We can craft an exponential to pass through any finite gap in between 2 displaced parabolas, matching the PES Tiny parameters.

This combination we call PES Tunnel.

While all parabolas will be overtaken by the exponential on the same grid rotation, any rotation, even the tiny ones, will void that. For the chosen rotation, we get fig011 & fig012. We could get a rotation of no tunnel for the same rotation, or the exponential crossing the other arm of the parabola (along with the grid oriented for the parabola) for a rotation on the other side (fig013, fig014 & fig015).

fig011

fig012

fig013

fig014

fig015

These rotations and displacements will be important in the combination of various PES Tiles, displacements, and parabola powers. Especially the x^odd and x^even for powers of +-1 and +-2, and their +- infinity along the x axis of the base grid.


Part3: PES Tiles
For a quasi-identical PES Tiny segment, we can rotate the parabola/expo to each other so that the corresponding PES Tunnels are adjacent based on the sinusoid and tempo in PES Tiny, with minor horizontal or vertical displacements (base grid horizontal and base grid vertical displacements, since displacements could be relative to the parts, eg. up/down the PES Tunnel following the parabola or the exponential). fig016, fig017, fig018 and fig019.

fig016

fig017

fig018

fig019

For ease of communication we will assume the exponential y growing on the positive x axis, clockwise rotated parabolas (CRP?) having 1 crossing with the exponential on the PES Tunnel with no further interceptions on that arm up (their 6th point of interception would be on the other arm; 4 points on the PES Tiny + 1 point on the PES Tile + 1 point on the other arm), and anticlockwise rotated parabola (ARP?) having its 6th point further up on the same arm as the 5th crossing on the PES Tunnel.

-Work in progress.-
Expectation: Between the PES Tunnel and the infinity upward, there are vibrational resonances that can be representative of electron field, photon (omniphoton), space/distance (black hole), branes (as in membranes in M theory), Sheppard tones representing eternal fall, a self-emergent grid of 3+1 dimensions of the micro-macro collapse-expansion of a form similar to "1.2.3:4.8.12:16.32.48:64.128.192:256.512.:..:..". The size of these graphs is enough to contain all Feynman diagrams for not only our cosmos folded at spacetime quants, but a multiverse of such cosmoses in familiar and unfamiliar physics.

Taking inspiration from nature, looking to find patterns we are familiar with (eg. t or -t, force, distance, lightspeed, etc.) within the vibrations of PES Tunnels in bigger grids composed of PES Tiles, filled with what could be seen as paradoxes from the point of view of the regular grid, but perfectly consistent within the limitations we are choosing.

Part4: The physics dimensional structure;

Part5: The physics multiverse crystal;

Part6: The physics universe, the emergence of time;