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Author Topic: The space time manifold tensor candidates  (Read 8360 times)
Description: Iteration statements that capture the strain tensor of Einsteins space time
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jehovajah
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« Reply #15 on: January 26, 2011, 12:22:38 PM »

e^{\frac{i*\pi*j}n} =cos(\frac{i*\pi*j}n) + i*sin(\frac{i*\pi*j}n)

Betchen sent me this.
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #16 on: April 21, 2011, 06:46:21 AM »

I love digging around in the dark, and then blue-skying with what i find, just as i feel it!

However Doug really knows what he is talking about.

Doug's metric i suddenly realised is a kind of Trochoidal matrix.

doug Explains it actually was discovered by Rosen.

Here is the metric in tensor form

g_{\mu \nu}= diag\left\{ \exp \left( -\frac{2GM}{c^{2}R} \right),-\exp \left( \frac{2GM}{c^{2}R} \right),-\exp \left( \frac{2GM}{c^{2}R} \right),-\exp \left( \frac{2GM}{c^{2}R} \right) \right\}

in quaternion form

q=\left\{ \exp \left( -\frac{2GM}{c^{2}R} \right)\hat{e}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{i}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{j}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{k} \right\}.

I have to figure out how to Quasz this, but it does remind me of a whole load of trochoid experiments i did late last year.

Here's Doug explaining what it means.

<a href="http://www.youtube.com/v/XW7CzyE6Fjc&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/XW7CzyE6Fjc&rel=1&fs=1&hd=1</a>

« Last Edit: November 23, 2011, 08:08:06 PM by jehovajah » Logged

May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #17 on: August 20, 2011, 01:07:06 PM »

Quote
Description: This was made using the following operations: inversion+rotation+scaling+translation

No "mirroring" folds used

UF5 code (iteration part):

Code:

if |z|<1
   z=z/|z|
endif
z=z*exp(1i*pi/180*@angle)*@scale+c

Kali wrote this formula, in which the scale and angle are changed throughout the iterations. This is a 2d/3d formula and i will work on a 3d form of it.

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« Reply #18 on: November 12, 2011, 09:52:04 AM »

z= (1+z+z^2)^2/z^6+20*(1+c+c^2)^2/c^6

This is my gravito electromagnetic formula.


It basically models the effect of inverse square laws and inverse laws on space. I like to toy with the idea that gravity is some fractal arrangement of electromagnetism and this is my thinking so far. This is for a 2 body system with some kind of rotational relativity, one body being 20 times as massive as the other. whatever that means! grin

Enjoy.

If you use Quasz, you can change the surface noise settings to remove a lot of clean up placed there to give control over surface output. I like to think that the system in space does not really have this option! embarrass
« Last Edit: November 19, 2011, 05:28:39 PM by jehovajah » Logged

May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #19 on: November 20, 2011, 11:47:29 AM »

I am exploring some formulae around gravity and electromagnetism using Quasz. Certain vectors and vector/tensor combinations are becoming familiar to me, and complex and quaternion vector algebras are providing models of space-time . Because the fractal generator is effectively a cutting tool the models produced are in "negative" in a sense, with surfaces and bound regions representing less volatile regions.

The models so far exhibit a big rotational vortex precedes a calmer steady state-like phase. The rotational region continues out at the edge of the universe, clearly weaker.
« Last Edit: November 23, 2011, 08:05:09 PM by jehovajah » Logged

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« Reply #20 on: November 23, 2011, 08:19:37 PM »

q=\left\{ \exp \left( -\frac{2GM}{c^{2}R} \right)\hat{e}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{i}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{j}-\exp \left( \frac{2GM}{c^{2}R} \right)\hat{k} \right\}.

This is the quaternion base of the tensor used in producing the above images
G,M,c are constants, R is a vector with 3 components, but i used a quaternion with 4 components, the 4th being a sort of radius.
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« Reply #21 on: August 24, 2012, 12:30:56 PM »

In quasz Terry has an in built function number 37 which corresponds to the second manifold tensor candidate with n set to 0 and c instead of 1/c.

1/z^2  +  c

The first sculpture is an image of a Minkowski torus with a gravity well  structure that is complex

<Quoted Image Removed>

the second looks into the gravity well structure

<Quoted Image Removed>

the third shows the torus shape followed by 2 other views

<Quoted Image Removed>
<Quoted Image Removed>
<Quoted Image Removed>

I then take a look at the gravity well structure which passes completely through the torus but not symmetrically and the structure appears to be the result of antisymmetric action from the other side of the torus

<Quoted Image Removed>

<Quoted Image Removed>


I then show the spatial structure with the wells

<Quoted Image Removed>
<Quoted Image Removed>

The sculptures are sensitive to the seed points with the real coefficient of the seed determining the toroidal shape while the i and j  coefficients seem to determine the well structure. The anti symmetry is due to rotation not reflection which is a translation in relativistic motion i am currently cogitating.

The mandelbrots are informative especially mandelbrotp but i have no cosmological referent for the mandelbrot boundary conditions yet in mind.

Each sculpture relies on the quad motion statement in quasz and the cutting boundary |z|≤4. This parameter has much to do with the eventual form and surface structures of the sculpture and i am exploring form and structures in spaciometry.

I now have a referent and that is the Van Allen radiation belts that surround the planet. The details of this model are crude, but then it is a crude inverse square law motion in a constant solar pressure field c. The two wells correspond well with the aurora borealis effects of the magnetic field effect. That electric and magnetic effects are not well differentiated is again due to the crudeness of the model.
In my blog I discuss the electromagnetic origin of gravity.
http://jehovajah.wordpress.com/jehovajah/blog/newtons-magnetic-gravity-6

I also discuss the controversial origin of the manifold concept in Die Mannigfaeltigkeit in my blog post archives.

I am currently looking at quaternions in detail to understand better how to model these relations in sculptures by Quasz
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
jehovajah
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« Reply #22 on: July 17, 2013, 08:48:17 AM »


http://jehovajah.wordpress.com/jehovajah/blog/2013/07/17/newtonian-fluid-motive-as-spacematter



This is both Newton's and Maxwell"s conception of Spacematter or the Aether. It is a fluid that is fractal and forms these corpuscular vortices.

What are they?

Our perception of the dynamic metaphysical energy all around us, the Newtonian motive which Maxwell envisaged as vortices of electic and magnetic fluids, after Faraday.

However, read my research to distinguish carefully between motive as matter and the concept of matter.
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« Reply #23 on: April 25, 2014, 05:51:10 AM »

Sometimes I frighten myself! When I look back over my blue skying and find I have written something I clearly did not understand at the time, and then when I come to note something I do understand I find I have already written it!

In this candidate post I write down basically a Fourier series  type formulation, based on my current research into Grassmann's Vorrede to the 1844 Ausdehnungslehre.

This represents the Newtonian fluid motive ie the energy plasma motive of pure space and in pure space as the electro Thermo magneto fluid element complexes of our formal subjective processing.

\sum(coshmx+ sinhnx)exp( cospx+isinqx+jsinrx+ksinsx)
For m,n,p,q,r,s as independent frequencies from 1 to N and -\pi<x<\pi
And\sum can have as many terms as feasible or desired.
In fact I do not restrict the arguments of the trig functions to x in the quaternion iteration in Quasz. More interesting results are generated using x#,y#,imaj(z), imak(z) appropriately.

The sinhx + coshx *)represents the radial extension usually associated with electrostatic energy, but Ivor Catt has shown there is no electrostatic energy! Rather this energy he says is constantly dynamic. However I do not even regard it as electric or magnetic. It is the radial expansion component of a vortex spatial dynamic, the rotational component  cospx+isinqx+jsinrx+ksinsx , usually considered as the Magnetostatic energy is in my view the rotational component of the vortices In space and of space.

Magnetism, as empirically evidenced in a wire or a lodestone is due to the organised structuring of these spatial vortices. In particular in a twisted copper wire, the induction process of the vast sea of vorticular motion rolling onto the wire organises and concentrates the vortices to stretch out along it's length. The twist is put into the wire in its manufacturing process as it is drawn.
The inductive action is by Maxwell defined as conduction, and thus conductivity and inductivity are the same measure.

Because the new science wanted to distinguish itself, and because of industrial and corporate concerns and patents we lost sight of the simple Gilbert plasma model for these Phenomena.

While this formula is just the description, I will use it to generate some sculptures of how this iterates through space in its manifold forms and constraints, both as a Julia type and as a Mandelbrot type

*) also I use coshx + i*sinhx as a direct vector form of the radius, as Grassmann derives his concept using a general trig line segment! It gives similar results but shaped differently.


* etmvar.png (15.29 KB, 320x240 - viewed 301 times.)

* etmjvar2.png (54.45 KB, 320x240 - viewed 307 times.)
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #24 on: April 26, 2014, 04:06:08 AM »

The attachments show some initial research results with Quasz and variations of the above expressiion.While these do not look like "wave" patterns  they are, and the scale at which that becomes viewable obscures these details, and the almost similarity of the large structure and some of the smaller structures in the second image.
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« Reply #25 on: April 26, 2014, 08:11:46 PM »

The posted equation does not produce an interesting julia. It is in fact a blank space until bailout 22.03 , then it is a uniform density . It represents either a cloud or an intense density.  however the mandy type produces the attached sculpture.


* etmmorig.png (86.78 KB, 320x240 - viewed 289 times.)
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« Reply #26 on: April 29, 2014, 04:11:47 AM »

This incredible formulation already produces a rich variety of sculptures applicable to all scales from the quantum to the cosmological


* etmwavfreqh3.png (77.08 KB, 320x240 - viewed 281 times.)

* etmwavfreqh2.png (20.19 KB, 320x240 - viewed 290 times.)

* etmwave.png (139.08 KB, 320x240 - viewed 286 times.)
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« Reply #27 on: April 29, 2014, 04:55:29 AM »

To place this thread in its context view this general discussion.

<a href="http://www.youtube.com/v/XDAJinQL2c0&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/XDAJinQL2c0&rel=1&fs=1&hd=1</a>

While I do not hold the same opinion as the good professor, nevertheless the empirical data does require intuitive models based on geometry and a prior Mechsnics. The results obtained by using Grassmanns analytical concepts, even partially understood are very illuminating.. I claim that thermodynamics is an incomplete theory, completed only in electromagnetodynamics, which itself is inconsistent without thermodynamics.

Further more, this complex of principles has one simplifying notion : that of rotating space dynamically dilating at all scales.

My sculptures are an attempt to show this notion has merit as a formal model .
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« Reply #28 on: April 24, 2015, 07:42:37 AM »

I merely note a whimsical notion that derives from my research into Hermann and Justus Grassmanns work. It is that the fundamental line element of space  is a trochoidal line element that spirals and twists! Fluttering and flitting away !

The Grassmanns give us a direct expressive way to describe such stringlike structures in a status matrix that can model local dynamics.

The methods give us a hands on way to study natural dynamics and set out an algebraic label that can be manipulated manually to mimic the behaviour. Then we can explore the product design of such labels to see if they provide useful calculations that capture the complexity of natural movements.

Only then can we design a computer algorithm that generates model behaviours by design.

In the past I was taught to get hot and excited by these "mathematical" algorithms, but now I realise that that is like getting excited by a sculpture of a tree and ignoring the living tree!

But, I have been searching for an explanatory label to describe fluid dynamics specifically as well as generally. Such labels can lead to a language that makes it easier to discuss fluid dynamic observations and data measurements, and thus to develop expertise.

What is a manifold? It is the span of such line element systems, however many we place in the basis structure.

String theory wants to put at mostt 11 creating elements in a trochoidal line element . 3 such trochoidal line segments should form a system that models our space from quantum o classical magnitudes?
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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« Reply #29 on: February 04, 2016, 06:18:53 PM »

http://m.youtube.com/watch?v=35Y7u_VDrww

It has been a while since I posted an update, but it has taken until now to see images published that look like the sculptures of those motion equations i was experimenting with so long ago!
It really indicates to me that iteration, rotation and fractal geometry is the most fruitful process for modelling natural phenomrena at all scales !
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May a trochoid of 去逸 iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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