I have been studying your video(s) about "Fractal Toroidal Moments" and "Fractal Magneto-Hydrodynamic Structures" and, although I have some idea about why you use the "Fractal" adjective, I am not sure how rigorously it applies here.
Yes, Toroidal Moments and Magneto-Hydrodynamic Structures have an intuitive Fractal-like nature about them in that, as we zoom into them, they, at least partly, regenerate. But, again, that is not a rigorous definition of "Fractal" in this context. Can you supply it?
Predominantly because it is (1) self-similar and has (2) essentially infinite detail - scale invariant, however, if we are to say the following about fractals.
A fractal is defined by these five main points:
1. Self-Similarity: Parts of the fractal resemble the whole, at different scales.
2. Infinite Detail: Zooming into a fractal reveals more detail, with no limit to the complexity.
3. Non-Integer Dimension: Fractals often have a fractional dimension, not fitting into traditional geometry's integer dimensions.
4. Recursive Generation: Many fractals are created through recursive processes where a simple rule is applied repeatedly.
5. Complex from Simple: From simple rules, fractals generate highly intricate structures, often appearing chaotic or naturalistic.
4 and 5 are easy to see as being present, though, the recursive nature of the structure is at each level orthogonally arranged, which is part of the the 'simple rule'
3 is not intuitive, however, when you understand that it does not fractally arrange on the NRB (which are regular spheres) but in the apple, which is replete with golden ratio and I believe is the reason for this ratio appearing in natural forms, it makes sense. Whilst scaling with φ does not define a fractal, when it is combined with self-similarity and essentially infinite detail due to scale invariance, in the round I believe it qualifies as fractal.
I showed these aspects for the first time on 5th Feb 2025
Another excellent presentation/abstract, together producing a forensic analysis of the underlying collaborating mechanisms to produce a well reasoned and readily understood framework to accurately describe a whole range of hitherto apparently disparate “mysterious” phenomena and experimental observations. Brilliant in its revelations of the profound nature of the “fractality of nature and its building blocks” of the cosmos from which all else emerges. 💖👍🌟
One of two, other one already published
Hello Bob,
I have been studying your video(s) about "Fractal Toroidal Moments" and "Fractal Magneto-Hydrodynamic Structures" and, although I have some idea about why you use the "Fractal" adjective, I am not sure how rigorously it applies here.
Yes, Toroidal Moments and Magneto-Hydrodynamic Structures have an intuitive Fractal-like nature about them in that, as we zoom into them, they, at least partly, regenerate. But, again, that is not a rigorous definition of "Fractal" in this context. Can you supply it?
Thanks
Regards,
Phillip Power
Predominantly because it is (1) self-similar and has (2) essentially infinite detail - scale invariant, however, if we are to say the following about fractals.
A fractal is defined by these five main points:
1. Self-Similarity: Parts of the fractal resemble the whole, at different scales.
2. Infinite Detail: Zooming into a fractal reveals more detail, with no limit to the complexity.
3. Non-Integer Dimension: Fractals often have a fractional dimension, not fitting into traditional geometry's integer dimensions.
4. Recursive Generation: Many fractals are created through recursive processes where a simple rule is applied repeatedly.
5. Complex from Simple: From simple rules, fractals generate highly intricate structures, often appearing chaotic or naturalistic.
4 and 5 are easy to see as being present, though, the recursive nature of the structure is at each level orthogonally arranged, which is part of the the 'simple rule'
3 is not intuitive, however, when you understand that it does not fractally arrange on the NRB (which are regular spheres) but in the apple, which is replete with golden ratio and I believe is the reason for this ratio appearing in natural forms, it makes sense. Whilst scaling with φ does not define a fractal, when it is combined with self-similarity and essentially infinite detail due to scale invariance, in the round I believe it qualifies as fractal.
I showed these aspects for the first time on 5th Feb 2025
https://www.youtube.com/live/ltV3--jlALg?si=Txy2hKee6xDPsJ8n&t=4018
For me, Hyper and Super - Toroidal Moments just don't cut it.
Another excellent presentation/abstract, together producing a forensic analysis of the underlying collaborating mechanisms to produce a well reasoned and readily understood framework to accurately describe a whole range of hitherto apparently disparate “mysterious” phenomena and experimental observations. Brilliant in its revelations of the profound nature of the “fractality of nature and its building blocks” of the cosmos from which all else emerges. 💖👍🌟
Is this the abstract you sent? Nice!
Yes