Buddy
The Living Force
Some recent research in the area of 'archetypes' has led to noticing frequent mention of the word 'fractal' as it is used to describe some general relationships. I thought I'd make this post in case anyone found it useful or interesting.
At the very small quantum scales, the sizes of the gaps between electron energy levels, the shapes of magnetic fields and particle pathways seem to be fractal[1]. At the largest scales the positions of the galaxies are apparantly fractals or multifractal across distances of at least 500 million light-years[2]. In between these widest scales, we can find fractals in the most unexpected places.
The universe seems to contain some interesting properties or complexities that give it a fractal geometry which can be found in the rhythm of the human heartbeat (and even the walking gait)[3]. Correlations are even being found between geomagnetic signal and the human heartbeat[4]. There is already general recognition of relationships between animal behavior and impending geological events, as indicated in reply number 29 and 30 of this thread.
Patterns and patterns of patterns can also be seen in relationships between seemingly unrelated things like teams of software engineers and slime molds[5]. Interestingly enough, a human aggregate being seems to be an allowable possibility in this line of thought...maybe in a different density? [Note: I'm certain I read somewhere Laura or someone mentioning something about a group of 3D people possibly functioning as a single 4D STO being but I can't find it now].
Fractal mathematics with image morphological analysis has been utilized to investigate the effect of improper lubrication in gearboxes due to wear particle generation between gear wheels.
Source: _http://www.emeraldinsight.com/Insight/viewContentItem.do;jsessionid=BCB1D612DB4602BD44AB388C7BD63F78?
contentType=Article&contentId=1520151
Fractals in music?
Benoit Mandelbrot suggested to Harlan Brothers that he undertake a mathematically rigorous treatment of fractal music. Brothers published a paper entitled "Structural Scaling in Bach’s Cello Suite No. 3," which appeared in the journal Fractals (Vol. 15, No. 1, 2007; pages 89-95). The article reveals musical structure related to the Cantor set and helps to establish a mathematical foundation for the classification of fractal music. A new article, entitled "Intervallic Scaling in the Bach Cello Suites," will appear in the journal this fall (that was in 2004 I think). The paper describes a novel and robust approach to establishing the existence of power-laws in music.
As with graphics[6], music can exhibit a wide variety of scaling behavior. In the course of exploring the role of power laws in music, Brothers has found many types of scaling including self-similarity with respect to duration, pitch, interval, motif, and structure. He has also written compositions to illustrate some of these scaling characteristics.
Source: _http://www.brotherstechnology.com/math/fractal-music.html
Then we have biologist Rupert Sheldrake thinking that there is more to the morphogenesis of living things than the execution of a program stored in DNA. He has some interesting examples, and calls the idea the "hypothesis of formative causation". He claims to detect a relationship between the developing shape of one example of a living thing, and all the other things of that kind currently alive, and alive in the past. He doesn't know what the mechanism is, and just uses the term "morphic resonance" as a conceptual bucket to refer to the mysterious communication. Some individuals have been seen to go into "automatic deny" and ad hominem attack mode with Dr. Sheldrake, and insist that formative causation does not occur, probably because Sheldrake does not yet propose mechanism.
Could this 'mysterious communication' also be connected to the reported evidence of double-stranded DNA having the "amazing" ability to recognize similarities in other DNA strands from a distance? I'm not sure of the connection between underlying fractal mathematics/geometry and Sheldrakes work. Maybe it requires a shift of focus. When I found myself drawn to Sheldrakes' work I found myself asking what does this have to do with fractals? It then occured to me not to get hung up on a word. Instead, think about what it means: formulas or equations for creating smaller copies out of a larger unit in one direction, and reconstructing a larger structure from the smaller copies in the opposite direction. Copies of copies - and everything staying connected because of the deeper relationships to the deeper structure. At that point, the Jpeg2000 wavelet technology[6] made more sense and connected with everything else. I guess this research was all about trying to see in terms of energetic connections between self-similar patterns interacting with each other - and maybe the whole simultaneously.
What about the 'soul'?
Could the individual soul of a human being or any other individual/collective soul be a fractal, self-similar copy of the 7th density One? Sort of like when you tear off a piece of a hologram image and you find that you can still see a pale but distinguishable copy of the original image inside the torn-off piece (the kingdom of God within)? What about the component energy frequencies of human beings? Could our emotions, physicality, mind and spirit, etc. be a partially encapsulated, yet still connected, quantity of the energy fields present throughout the universe in the deeper structure that appears to be empty space? If so, that would seem to suggest the idea that from an STO or universe perspective, the concept of "ownership" changes to "stewardship". Can we stand the idea of some of our most deeply held concepts crumbling?
What about other subject areas?
Maybe other forum members can contribute thoughts or discoveries in various fields that add to the process of identifying the underlying unity in the universe. The more patterns we can learn to identify and recognize now, the more advanced warning we may have in order to be prepared for anything. OSIT
-----------------------------------------------
[1]
American physicist Richard Feynman noticed that even though there are an infinite number of ways for particles to get from one place to another, some routes are much more important than others and he found a way to sort them out. Instead of particle paths being smooth, regular curves, they are fractal, i.e., 'hoppy'. The "path integral" is said to have been invented to do the tricky maths needed to make quantum mechanics useful.
_http://arxiv.org/PS_cache/hep-th/pdf/9302/9302097v1.pdf
_http://www.amazon.com/Quantum-Mechanics-Integrals-Richard-Feynman/dp/0070206503
[2]
_http://adsabs.harvard.edu/full/1994A&A...286..351D:
Title: Mixed fractal models for the distribution of galaxies
Authors: Dubrulle, B.
Journal: Astronomy and Astrophysics (ISSN 0004-6361), vol. 286, no. 2, p. 351-356
Bibliographic Code: 1994A&A...286..351D
Also:
NASA Astrophysics Data System (ADS)
200 more abstracts, starting with number 1. Total number available from this query: 1056266.
_http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?return_req=no_params&db_key=AST&text=The%20ability%20of
%20fractal%20models%20to%20reproduce%20the%20observed%20distributions%20of%0Agalaxies%20is%20explored.
%20Mixed%20models,%20made%20of%20fractal%20density%20fluctuations%0Asuperposed%20on%20a%20Poisson
%20background,%20are%20needed%20in%20order%20to%20explain%20the%0Aobserved%20large%20scale%20
cutoff%20of%20the%20number%20counts%20probabilities%20and%20the%0Apower-law%20behavior%20of%20the
%20correlation%20functions.%20The%20distribution%20of%0AIRAS%20galaxies%20is%20well%20fitted%20by%20a
%20model%20in%20which%20the%20Poisson%20component%0Ais%20five%20times%20larger%20than%20the%20
fractal%20component,%20of%20dimension%201.6.%20A%0Asimilar%20mixed%20fractal%20model%20is%20built%20
for%20visible%20galaxies%20in%20the%0ASouthern%20Sky%20Survey,%20taking%20into%20account%20some%20
dynamic%20aspects%20of%0Aclusters.%20The%20best%20fit%20is%20obtained%20for%20a%20mixed%20model%20
in%20which%20the%0APoisson%20component%20is%20as%20large%20as%20the%20fractal%20component,%20of%20
dimension%202.%0AThe%20fit%20is%20however%20not%20good%20at%20large%20scales.%20These%20results%20
illustrate%0Athe%20complexity%20of%20the%20matter%20distribution%20in%20the%20Universe,%20and%20prove
%20the%0Anecessity%20of%20considering%20multifractal%20models.%20They%20also%20suggest%20that%20the
%0Amultifractallity%20is%20confined%20only%20to%20small%20scales.%0A+COSMOLOGY,%20FRACTALS,%20
GALACTIC%20EVOLUTION,%20GALACTIC%20STRUCTURE,%20POISSON%20DENSITY%20FUNCTIONS,%20SPATIAL
%20DISTRIBUTION,%20STATISTICAL%20DISTRIBUTIONS,%20UNIVERSE,%20INFRARED%20ASTRONOMY%20
SATELLITE,%20MANY%20BODY%20PROBLEM,%20SKY%20SURVEYS%20(ASTRONOMY)+&title=Mixed%20fractal%20
models%20for%20the%20distribution%20of%20galaxies
[3]
Clinical Utility of Fractal Heart Rate Analysis
_http://www.physionet.org/tutorials/fmnc/node10.html
Multiresolution Wavelet Analysis of Heartbeat Intervals Discriminates Healthy Patients from Those with Cardiac Pathology
_http://www.citeulike.org/user/simonpoglitsch/article/4214421
Abstract:
We applied multiresolution wavelet analysis to the sequence of times between human heartbeats ( R - R intervals) and have found a scale window; between 16 and 32 heartbeat intervals; over which the widths of the R - R wavelet coefficients fall into disjoint sets for normal and heart-failure patients. This has enabled us to correctly classify every patient in a standard data set as belonging either to the heart-failure or normal group with 100% accuracy; thereby providing a clinically significant measure of the presence of heart failure from the R - R intervals alone. Comparison is made with previous approaches; which have provided only statistically significant measures.[Note: The term "wavelet" refers to the patterns used in data construction/deconstruction with little or no data loss. For an introduction to wavelets, see _http://www.amara.com/IEEEwave/IEEEwavelet.html]
[4]
Similarities between the dynamics of geomagnetic signal and of heartbeat intervals
_http://www.iop.org/EJ/abstract/0295-5075/80/5/50006
Abstract: We analyze the dynamics of a widely used measure of geomagnetic activity —the Dst index— and compare our findings with those found in healthy human heartbeat dynamics. We show that the Dst index belongs to a special class of complex signals, exhibiting long-range temporal correlations, multifractality and scale-invariant distribution. Specifically, we find that i) Dst series and magnitude series of Dst increments are long-range correlated while the sign series of Dst increments is anti-correlated; ii) the scaling exponents that govern these temporal correlations increase with geomagnetic activity; iii) Dst series exhibit multifractal behavior; iv) the multifractal spectra that characterize Dst series are practically independent of the geomagnetic activity; and v) the distribution of Dst increments exhibits scale invariance at a wide range of time scales. These results are in surprising agreement with those found in the study of heartbeat intervals. Our findings are consistent with the concept of universality in complex systems and may contribute to a better understanding of the mechanisms that govern geomagnetic activity.
These findings might be useful to add to the discussion here.
[5]
Consider that the GNU/Linux operating system, and all the applications that run on it, is freely available with all source code, without cost, and has been constructed by volunteer software engineers/programmers from all over the world, collaberating over the internet - many in the form of a co-operative human jelled team and without any management whatsoever. GNU/Linux is the main operating system used by serious academic science sites and Internet Service Providers.
Now consider the slime mold: unicellular organism with multiple nuclei.
Slime molds spend much of their time living as collections of single celled organisms. They wander around their territories, finding food like any other amoebas do. Then suddenly, when conditions become difficult, huge numbers of these little organisms start to get co-operative and congregate in one place. They zoom up the ladder of evolution, and literally start climbing on top of each other. As they do so their cells blend into each other (although each cell's nucleus remains distinct), and the collection of similar individuals, each freely following its own amoeba desires, forms a single plant-like organism!
_http://catalogue-of-organisms.blogspot.com/2008/09/diversity-of-slime-moulds.html
_http://pandasthumb.org/archives/2008/01/those-amazing-s.html
_http://en.wikipedia.org/wiki/Slime_mold
_http://www.gnu.org/
[6]
In addition to the familiar vector art formats like .emf, there's the Jpeg2000 format that uses wavelet algorithms for compression/decompression. While there is a modest increase in compression performance of JPEG2000 compared to JPEG, the main advantage offered by JPEG2000 is the significant flexibility of the codestream. The codestream obtained after compression of an image with JPEG2000 is scalable in nature, meaning that it can be decoded in a number of ways; for instance, by truncating the codestream at any point, one may obtain a representation of the image at a lower resolution, or signal-to-noise ratio.
_http://en.wikipedia.org/wiki/JPEG_2000
_http://www.jpeg.org/jpeg2000/
_http://www.jpeg.org/apps/index.html
At the very small quantum scales, the sizes of the gaps between electron energy levels, the shapes of magnetic fields and particle pathways seem to be fractal[1]. At the largest scales the positions of the galaxies are apparantly fractals or multifractal across distances of at least 500 million light-years[2]. In between these widest scales, we can find fractals in the most unexpected places.
The universe seems to contain some interesting properties or complexities that give it a fractal geometry which can be found in the rhythm of the human heartbeat (and even the walking gait)[3]. Correlations are even being found between geomagnetic signal and the human heartbeat[4]. There is already general recognition of relationships between animal behavior and impending geological events, as indicated in reply number 29 and 30 of this thread.
Patterns and patterns of patterns can also be seen in relationships between seemingly unrelated things like teams of software engineers and slime molds[5]. Interestingly enough, a human aggregate being seems to be an allowable possibility in this line of thought...maybe in a different density? [Note: I'm certain I read somewhere Laura or someone mentioning something about a group of 3D people possibly functioning as a single 4D STO being but I can't find it now].
Fractal mathematics with image morphological analysis has been utilized to investigate the effect of improper lubrication in gearboxes due to wear particle generation between gear wheels.
Source: _http://www.emeraldinsight.com/Insight/viewContentItem.do;jsessionid=BCB1D612DB4602BD44AB388C7BD63F78?
contentType=Article&contentId=1520151
Fractals in music?
Benoit Mandelbrot suggested to Harlan Brothers that he undertake a mathematically rigorous treatment of fractal music. Brothers published a paper entitled "Structural Scaling in Bach’s Cello Suite No. 3," which appeared in the journal Fractals (Vol. 15, No. 1, 2007; pages 89-95). The article reveals musical structure related to the Cantor set and helps to establish a mathematical foundation for the classification of fractal music. A new article, entitled "Intervallic Scaling in the Bach Cello Suites," will appear in the journal this fall (that was in 2004 I think). The paper describes a novel and robust approach to establishing the existence of power-laws in music.
As with graphics[6], music can exhibit a wide variety of scaling behavior. In the course of exploring the role of power laws in music, Brothers has found many types of scaling including self-similarity with respect to duration, pitch, interval, motif, and structure. He has also written compositions to illustrate some of these scaling characteristics.
Source: _http://www.brotherstechnology.com/math/fractal-music.html
Then we have biologist Rupert Sheldrake thinking that there is more to the morphogenesis of living things than the execution of a program stored in DNA. He has some interesting examples, and calls the idea the "hypothesis of formative causation". He claims to detect a relationship between the developing shape of one example of a living thing, and all the other things of that kind currently alive, and alive in the past. He doesn't know what the mechanism is, and just uses the term "morphic resonance" as a conceptual bucket to refer to the mysterious communication. Some individuals have been seen to go into "automatic deny" and ad hominem attack mode with Dr. Sheldrake, and insist that formative causation does not occur, probably because Sheldrake does not yet propose mechanism.
Could this 'mysterious communication' also be connected to the reported evidence of double-stranded DNA having the "amazing" ability to recognize similarities in other DNA strands from a distance? I'm not sure of the connection between underlying fractal mathematics/geometry and Sheldrakes work. Maybe it requires a shift of focus. When I found myself drawn to Sheldrakes' work I found myself asking what does this have to do with fractals? It then occured to me not to get hung up on a word. Instead, think about what it means: formulas or equations for creating smaller copies out of a larger unit in one direction, and reconstructing a larger structure from the smaller copies in the opposite direction. Copies of copies - and everything staying connected because of the deeper relationships to the deeper structure. At that point, the Jpeg2000 wavelet technology[6] made more sense and connected with everything else. I guess this research was all about trying to see in terms of energetic connections between self-similar patterns interacting with each other - and maybe the whole simultaneously.
What about the 'soul'?
Could the individual soul of a human being or any other individual/collective soul be a fractal, self-similar copy of the 7th density One? Sort of like when you tear off a piece of a hologram image and you find that you can still see a pale but distinguishable copy of the original image inside the torn-off piece (the kingdom of God within)? What about the component energy frequencies of human beings? Could our emotions, physicality, mind and spirit, etc. be a partially encapsulated, yet still connected, quantity of the energy fields present throughout the universe in the deeper structure that appears to be empty space? If so, that would seem to suggest the idea that from an STO or universe perspective, the concept of "ownership" changes to "stewardship". Can we stand the idea of some of our most deeply held concepts crumbling?
What about other subject areas?
Maybe other forum members can contribute thoughts or discoveries in various fields that add to the process of identifying the underlying unity in the universe. The more patterns we can learn to identify and recognize now, the more advanced warning we may have in order to be prepared for anything. OSIT
-----------------------------------------------
[1]
American physicist Richard Feynman noticed that even though there are an infinite number of ways for particles to get from one place to another, some routes are much more important than others and he found a way to sort them out. Instead of particle paths being smooth, regular curves, they are fractal, i.e., 'hoppy'. The "path integral" is said to have been invented to do the tricky maths needed to make quantum mechanics useful.
_http://arxiv.org/PS_cache/hep-th/pdf/9302/9302097v1.pdf
_http://www.amazon.com/Quantum-Mechanics-Integrals-Richard-Feynman/dp/0070206503
[2]
_http://adsabs.harvard.edu/full/1994A&A...286..351D:
Title: Mixed fractal models for the distribution of galaxies
Authors: Dubrulle, B.
Journal: Astronomy and Astrophysics (ISSN 0004-6361), vol. 286, no. 2, p. 351-356
Bibliographic Code: 1994A&A...286..351D
Also:
NASA Astrophysics Data System (ADS)
200 more abstracts, starting with number 1. Total number available from this query: 1056266.
_http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?return_req=no_params&db_key=AST&text=The%20ability%20of
%20fractal%20models%20to%20reproduce%20the%20observed%20distributions%20of%0Agalaxies%20is%20explored.
%20Mixed%20models,%20made%20of%20fractal%20density%20fluctuations%0Asuperposed%20on%20a%20Poisson
%20background,%20are%20needed%20in%20order%20to%20explain%20the%0Aobserved%20large%20scale%20
cutoff%20of%20the%20number%20counts%20probabilities%20and%20the%0Apower-law%20behavior%20of%20the
%20correlation%20functions.%20The%20distribution%20of%0AIRAS%20galaxies%20is%20well%20fitted%20by%20a
%20model%20in%20which%20the%20Poisson%20component%0Ais%20five%20times%20larger%20than%20the%20
fractal%20component,%20of%20dimension%201.6.%20A%0Asimilar%20mixed%20fractal%20model%20is%20built%20
for%20visible%20galaxies%20in%20the%0ASouthern%20Sky%20Survey,%20taking%20into%20account%20some%20
dynamic%20aspects%20of%0Aclusters.%20The%20best%20fit%20is%20obtained%20for%20a%20mixed%20model%20
in%20which%20the%0APoisson%20component%20is%20as%20large%20as%20the%20fractal%20component,%20of%20
dimension%202.%0AThe%20fit%20is%20however%20not%20good%20at%20large%20scales.%20These%20results%20
illustrate%0Athe%20complexity%20of%20the%20matter%20distribution%20in%20the%20Universe,%20and%20prove
%20the%0Anecessity%20of%20considering%20multifractal%20models.%20They%20also%20suggest%20that%20the
%0Amultifractallity%20is%20confined%20only%20to%20small%20scales.%0A+COSMOLOGY,%20FRACTALS,%20
GALACTIC%20EVOLUTION,%20GALACTIC%20STRUCTURE,%20POISSON%20DENSITY%20FUNCTIONS,%20SPATIAL
%20DISTRIBUTION,%20STATISTICAL%20DISTRIBUTIONS,%20UNIVERSE,%20INFRARED%20ASTRONOMY%20
SATELLITE,%20MANY%20BODY%20PROBLEM,%20SKY%20SURVEYS%20(ASTRONOMY)+&title=Mixed%20fractal%20
models%20for%20the%20distribution%20of%20galaxies
[3]
Clinical Utility of Fractal Heart Rate Analysis
_http://www.physionet.org/tutorials/fmnc/node10.html
Multiresolution Wavelet Analysis of Heartbeat Intervals Discriminates Healthy Patients from Those with Cardiac Pathology
_http://www.citeulike.org/user/simonpoglitsch/article/4214421
Abstract:
We applied multiresolution wavelet analysis to the sequence of times between human heartbeats ( R - R intervals) and have found a scale window; between 16 and 32 heartbeat intervals; over which the widths of the R - R wavelet coefficients fall into disjoint sets for normal and heart-failure patients. This has enabled us to correctly classify every patient in a standard data set as belonging either to the heart-failure or normal group with 100% accuracy; thereby providing a clinically significant measure of the presence of heart failure from the R - R intervals alone. Comparison is made with previous approaches; which have provided only statistically significant measures.[Note: The term "wavelet" refers to the patterns used in data construction/deconstruction with little or no data loss. For an introduction to wavelets, see _http://www.amara.com/IEEEwave/IEEEwavelet.html]
[4]
Similarities between the dynamics of geomagnetic signal and of heartbeat intervals
_http://www.iop.org/EJ/abstract/0295-5075/80/5/50006
Abstract: We analyze the dynamics of a widely used measure of geomagnetic activity —the Dst index— and compare our findings with those found in healthy human heartbeat dynamics. We show that the Dst index belongs to a special class of complex signals, exhibiting long-range temporal correlations, multifractality and scale-invariant distribution. Specifically, we find that i) Dst series and magnitude series of Dst increments are long-range correlated while the sign series of Dst increments is anti-correlated; ii) the scaling exponents that govern these temporal correlations increase with geomagnetic activity; iii) Dst series exhibit multifractal behavior; iv) the multifractal spectra that characterize Dst series are practically independent of the geomagnetic activity; and v) the distribution of Dst increments exhibits scale invariance at a wide range of time scales. These results are in surprising agreement with those found in the study of heartbeat intervals. Our findings are consistent with the concept of universality in complex systems and may contribute to a better understanding of the mechanisms that govern geomagnetic activity.
These findings might be useful to add to the discussion here.
[5]
Consider that the GNU/Linux operating system, and all the applications that run on it, is freely available with all source code, without cost, and has been constructed by volunteer software engineers/programmers from all over the world, collaberating over the internet - many in the form of a co-operative human jelled team and without any management whatsoever. GNU/Linux is the main operating system used by serious academic science sites and Internet Service Providers.
Now consider the slime mold: unicellular organism with multiple nuclei.
Slime molds spend much of their time living as collections of single celled organisms. They wander around their territories, finding food like any other amoebas do. Then suddenly, when conditions become difficult, huge numbers of these little organisms start to get co-operative and congregate in one place. They zoom up the ladder of evolution, and literally start climbing on top of each other. As they do so their cells blend into each other (although each cell's nucleus remains distinct), and the collection of similar individuals, each freely following its own amoeba desires, forms a single plant-like organism!
_http://catalogue-of-organisms.blogspot.com/2008/09/diversity-of-slime-moulds.html
_http://pandasthumb.org/archives/2008/01/those-amazing-s.html
_http://en.wikipedia.org/wiki/Slime_mold
_http://www.gnu.org/
[6]
In addition to the familiar vector art formats like .emf, there's the Jpeg2000 format that uses wavelet algorithms for compression/decompression. While there is a modest increase in compression performance of JPEG2000 compared to JPEG, the main advantage offered by JPEG2000 is the significant flexibility of the codestream. The codestream obtained after compression of an image with JPEG2000 is scalable in nature, meaning that it can be decoded in a number of ways; for instance, by truncating the codestream at any point, one may obtain a representation of the image at a lower resolution, or signal-to-noise ratio.
_http://en.wikipedia.org/wiki/JPEG_2000
_http://www.jpeg.org/jpeg2000/
_http://www.jpeg.org/apps/index.html
