Fractal Physics

[Ethan Every]

I've been exploring fractals as part of a rather long term philosophy project and have had a good deal of success modeling the simplest structures of my system with the folded geometry of the mandelbox. In addition to meeting the logical constraints I've established it seems that the geometries of the Mandelbox are capable of recreating nearly every photo and representation of quantum holography I've come across. I've also found that generating interference patterns within the fractal allows me to model dynamic processes and larger scale concepts in physics like gravitational lensing, gravitational waves, fresnel distortion and general CAS emergence. You can see all of these properties in motion at my youtube channel url deleted This video is a general preview of my work. url deleted I would love some feedback on these findings, some representations are more obvious than others and the interference based visualizations are difficult to see with youtube's compression so larger resolution representations are linked in the description. Thank you for your time, I hope you find these useful

[Strange]

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Moderator Note

Moved to Speculations

 

[swansont]

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Moderator Note

Also, the link has been removed. Discussion should take place here, and not require anyone to go elsewhere.

 

 

 

[Ethan Every]

 

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Edited November 17, 2019 by Ethan Every
I'm an early morning crank

[swansont]

30 minutes ago, Ethan Every said:

I would love some feedback on these findings, some representations are more obvious than others and the interference based visualizations are difficult to see with youtube's compression so larger resolution representations are linked in the description. Thank you for your time, I hope you find these useful

The image on the upper left - not sure how it represents an entangled photon. It looks like a higher-order gaussian mode of a beam of light.

See the 2 2 mode here:  https://en.wikipedia.org/wiki/Gaussian_beam#/media/File:Hermite-gaussian.png

 

How is it fractal?

These images can be represented mathematically, and you seem to have found that representation, or something similar.

[Ethan Every]

I'd insert the link to the article if I could

The images are of the mandelbox fractal

Thanks for the feedback btw

 

[Strange]

33 minutes ago, Ethan Every said:

I've been exploring fractals as part of a rather long term philosophy project and have had a good deal of success modeling the simplest structures of my system with the folded geometry of the mandelbox. 

Producing things that look similar is not necessarily meaningful (without, perhaps, some deeper justification or some statistical analysis of how similar the results are).

Fractals are widely used in computer graphics, for example, to model naturalistic surfaces and textures. That doesn't mean that the objects being modelled are fractals (they aren't), just that fractals are a convenient way of producing similar looking results. Other, non-fractal, methods are also employed to get similar results.

Unless you can show that there is more going on than just making pictures that look like something else, I am distinctly unimpressed.

[Ethan Every]

There are plenty of physicists arguing that the geometry of spacetime is folded. This model is largely in support of those views, being able to recreate a large variety of these properties with a single fractal is what I find interesting

1 hour ago, swansont said:

The image on the upper left - not sure how it represents an entangled photon. It looks like a higher-order gaussian mode of a beam of light.

See the 2 2 mode here:  https://en.wikipedia.org/wiki/Gaussian_beam#/media/File:Hermite-gaussian.png

 

How is it fractal?

These images can be represented mathematically, and you seem to have found that representation, or something similar.

I'm aware of the gaussian similarity, however in this case the internal view of the mandelbox fractal has orbitals that are in the same position as the representations in the entangled photon state. In addition the external view of the low iteration mandelbox fractal is capable of recreating the geometry found in the single photon hologram shown above.

[Strange]

19 minutes ago, Ethan Every said:

There are plenty of physicists arguing that the geometry of spacetime is folded.

Citation needed.

19 minutes ago, Ethan Every said:

In addition the external view of the low iteration mandelbox fractal is capable of recreating the geometry found in the single photon hologram shown above.

Do you think there is any pattern that could not be reproduced using fractals?

[Ethan Every]

1 hour ago, Strange said:

Citation needed.

Do you think there is any pattern that could not be reproduced using fractals?

Certainly. In fact I've had zero success representing any of these objects with Kalibox, mandelbulbs etc. Although I've been able to generate interference patterns in some of these large scale properties like lensing never materialized. What I find compelling about the mandelbox specifically is the simple way it models folding and the fact that 1st iteration representations of the fractal can replicate the rather specific geometries of photons from multiple perspectives.

[Strange]

6 minutes ago, Ethan Every said:

Certainly. In fact I've had zero success representing any of these objects with Kalibox, mandelbulbs etc.

That is not what I asked.

[Ethan Every]

I see. Well perhaps not. Actually what interested me in fractals in the first place was that the way they deal with infinities, I hoped they might answer some identity problems in the philosophical world . I assume there are a wide variety of fractal representations that might be useful for modeling physical objects. What I'm hoping is that the folded geometry of the mandelbox may shed some light (pun intended) on a possible structure of light, I'm exploring the idea that it's properties are perhaps emergent from a folded geometry. Thanks for the feedback, I'm getting into the nitty gritty work on it. Perhaps I got a little over excited and shared the preview prematurely

 

Edited November 20, 2019 by Ethan Every
Bad connection: multiple submissions of same paragraph

[Mordred]

Well don't give up hope. Your certainly not the first to look into fractal applications via the Mandelbrot set. If you Google a bit you can certainly find literature including some textbook references to guide you. However don't restrict yourself to image representations. Look into the graph reproductions and group representations.

The purpose of physics isn't to produce pictures but to describe interactions and physical processes.

 It's not a theorem I am too familiar with as I tend to stick to the standardized gauge groups however this may provide some direction. (Note cellular automata ) has fractal qualities.

https://www.google.com/url?sa=t&source=web&rct=j&url=https://scipost.org/SciPostPhys.6.1.007/pdf&ved=2ahUKEwimpP797_flAhUuJTQIHfklD7c4ChAWMAN6BAgIEAE&usg=AOvVaw229Pz3Qe3vKM846eMvTjgo

Edited November 20, 2019 by Mordred

[Ethan Every]

1 hour ago, Mordred said:

Well don't give up hope. Your certainly not the first to look into fractal applications via the Mandelbrot set. If you Google a bit you can certainly find literature including some textbook references to guide you. However don't restrict yourself to image representations. Look into the graph reproductions and group representations.

The purpose of physics isn't to produce pictures but to describe interactions and physical processes.

Agreed! Thanks for the feedback. I agree about the explanation being the most important part, thats a much longer process I'm working on. Among other things at this point I've noticed the Fresnel lense distortion that appears to be recreated is a direct result of the folded geometry, in fact basic diffraction/interference patterns emerge in the simplest iteration of the fractal which is encouraging. However in higher iterations it appears capable of modeling a large variety of phase diagrams. - a simple illustration of a little phase fluctuation

Aside from the the textbooks, any ideas on formulating emergence? That's the real headache... goodness

[Mordred]

59 minutes ago, Ethan Every said:

Agreed! Thanks for the feedback. I agree about the explanation being the most important part, thats a much longer process I'm working on. Among other things at this point I've noticed the Fresnel lense distortion that appears to be recreated is a direct result of the folded geometry, in fact basic diffraction/interference patt

Aside from the the textbooks, any ideas on formulating emergence? That's the real headache... goodness

 Well to be honest the first step is to learn how emergence would arise in the particular field your modelling. Ie spacetime or other. This involves how that field is quantized. Once you quantize you have a finite group.

 Here is the thing in order to develop a fractal physics representation you must first learn the physics and how it is mathematically described. Then develop your fractal equivalent.  QFT for example has emergent particle number density equations for every field that corresponds to that fields energy.

 So you will need to be clearer on what you want emergent 

[Ethan Every]

Well put, I'll continue to put some time into this and hopefully have something more substantial to offer next time. Thanks

[studiot]

First let me thank you for introducing me to the Mandelbox, which I understand was first demonstrated in 2010      +1

I would like to discuss the danger inherent in what you are doing with reference to your first picture.

On 11/17/2019 at 1:07 PM, Ethan Every said:

I've been exploring fractals as part of a rather long term philosophy project and have had a good deal of success modeling the simplest structures of my system with the folded geometry of the mandelbox. In addition to meeting the logical constraints I've established it seems that the geometries of the Mandelbox are capable of recreating nearly every photo and representation of quantum holography I've come across. I've also found that generating interference patterns within the fractal allows me to model dynamic processes and larger scale concepts in physics like gravitational lensing, gravitational waves, fresnel distortion and general CAS emergence. You can see all of these properties in motion at my youtube channel url deleted This video is a general preview of my work. url deleted I would love some feedback on these findings, some representations are more obvious than others and the interference based visualizations are difficult to see with youtube's compression so larger resolution representations are linked in the description. Thank you for your time, I hope you find these useful

 

 

 

Now here's the thing:

The sort of image you show (on the top left) of photons  is inherently different from the fractal surface you also exhibit at the top right.

The difference is the scale invariance which is a fundamental property of fractals.

If you were to enlarge the photon picture so that one blob occupied the same picture areas as the current 9, you would see just one blob.

On the other hand if you enlarged the fractal image that way you would still see 9 blobs.

 

I look forward to your comment on this difference.

 

[Strange]

On 11/17/2019 at 2:54 PM, Ethan Every said:

There are plenty of physicists arguing that the geometry of spacetime is folded.

You still haven't provided a reference to support this.

[Ethan Every]

On 11/20/2019 at 6:12 AM, Strange said:

You still haven't provided a reference to support this.

 

I’ve seen folding space most often referenced in physics regarding einstein-rosen bridge (theoretical wormholes) and more recently the ideas wormed their way (pun intended)  into some explorations of quantum tunneling and entanglement (https://arxiv.org/pdf/1604.02589.pdf for example). Tom Lowe said regarding the Mandelbox “Since escape-time fractals need some points that do not escape to infinity and some points that do, it follows that the way to provide this is to fold space on top of itself and then enlarge it”. This seemed like an intriguing way to model how information might interact with singularities, entanglement, tunneling etc. In a general sense I’m interested in the possibility that any constant in a complex system (like the speed of light in the physical universe) might be expressed as a geometry and that this structure may act as an attractor on the evolution of the system. Physics and light seem like a great domain to test these ideas because not only do we have the interaction of a constant with a complex system but advances in simulation and visual detection through quantum holography may make successful models easy to identify. Attractors in other systems are often buried under layers of abstraction and are rarely visible as isolated objects in the system as observed. 

On 11/20/2019 at 5:18 AM, studiot said:

First let me thank you for introducing me to the Mandelbox, which I understand was first demonstrated in 2010      +1

I would like to discuss the danger inherent in what you are doing with reference to your first picture.

 

Now here's the thing:

The sort of image you show (on the top left) of photons  is inherently different from the fractal surface you also exhibit at the top right.

The difference is the scale invariance which is a fundamental property of fractals.

If you were to enlarge the photon picture so that one blob occupied the same picture areas as the current 9, you would see just one blob.

On the other hand if you enlarged the fractal image that way you would still see 9 blobs.

 

I look forward to your comment on this difference.

 

The Mandelbox has an interesting relationship with scale. Unlike the mandelbrot set zoom and scale don’t replicate the geometry of the previous render. I’ve prepared some visuals to illustrate the point. Here I use the 1st iteration Mandelbox where the geometry is easiest to identify. With the software I use here it seems to have 3 distinct phases related to scale: -3 to 0, 0 to 1, and 1 to 5. 0 to 1 has some interesting properties.  0 to 1 has some interesting properties. As the scale increases the center sphere projects fringe lobes away from the center as the interference pattern in the center increases in frequency.

Throughout that transformation the center sphere extends resembling (though with obvious distinctions) a sphere with chaotic geodesic flow which is the first known example of a sphere in 3 dimensions whose geodesic flow is chaotic (Image on right created by Bryn Mawr math major Louisa Winer using Mathematica, Surface Evolver and Geomview.) At 1 beams along the axis extend and a container like object encompasses the previous state, this is reversed with rot angle 180.  

 

Specifically regarding the entangled like representation found within the object an increase in scale presents 3 successive representations of the geometry while an external view of that transformation shows a flickering interference pattern, I've uploaded videos of these transformations that contain much more information in the transformations. If there is a dm option you can ask for a link as we're not allowed to post to external links

[Ethan Every]

 

Heres the easiest way I can summarize this idea: My wording will general here.

Many physicists believe that all the forces unified in a singularity before the big bang. There's an assumption that whatever that primal state is it has some infinite dimension allowing it to avoid the necessity of an external cause as well as some finite dimension allowing for a potential non-uniform distribution of energy. Perhaps if we would like to model what’s inside that singularity we could use a unified structure with some infinite points and some finite points. If this structure could also recreate the properties we observe in our physical reality as emergent properties we might have some additional explanation for the trend toward complexity. Time escape folding fractals have some points that extend to infinity and some that do not and the mandelbox specifically is capable of replicating a number of complex properties including the geometries of photons found in quantum holography from a variety of perspectives, interference based reconstruction of fresnel lense zone plates, aberrated zone plates, gravitational lensing, diffraction and a miriad of other properties. I’m suggesting this is a model worth exploring when discussing basic structures. Thanks all for the feedback, I'll have formalized versions of all this in a few months and will update as soon as I do. Cheers