Welcome to Fractal Forums

Hello to all fractal freaks in the crowd. I am known as FractalWoman on the internet and on YouTube. I am a Fractal Cosmologist and believe that the universe is fractal AT ALL SCALES. I have been developing my own cosmology based on the Mandelbrot Set/Buddhabrot Set mathematical construct. I think you may find this interesting. You can find it here:

http://www.butterflyeffect.ca/Close/Pages/Introduction.php

I'm excited to be a part of this forum and I hope I meet some interesting people along the way. Peace. FW

Hello and Welcome!

I'll have to give your stuff a read later on when time allows, sounds interesting.

A Fractal Cosmos has been proposed by a few different sources, and it's always fun to explore the possibilities   O0

Glad to have you aboard...

hello and welcome to the forums, i think i stepped over your site some time ago
have fun!

Greetings, and Welcome to this particular Forum (again) !!!    :)

There are definitely several "interesting people" that are Members.  Hope they are what you are looking for.
 

Hello.  (clicks on cosmology link) Looks very interesting.  :) :)

Welcome, Lori :embarrass:
As one newbe to another, I'm glad to find another fractal cosmologist in the crowd. From your web address, I surmise that you're in Canada. I'm in western Washington. Maybe we're practically neighbors.

I do appreciate the beauty of the Mandelbrot set, but I don't see any similarity between it and E = mc². There are, of course, an infinite number of equally simple fractal formulas—any one of which could be the key to the universe. I hope you are still in school, so you can acquire the skills you will need to unlock the fractal secrets of the universe.

I'm afraid it's too late for me to learn anything new, but I'm just beginning to use what I have learned to create something new. I wish I could reduce my own Fractal Foam Model of Universes (http://home.comcast.net/~fractal_cosmology/Articles/Fractal_Foam_Model_of_Universes.html) to a simple formula. Z = Z² + C is about all the math section of my feeble brain can handle. Well, actually, I'm okay at integral calculus, but what I need is for someone to invent a new branch of chaos theory.

My own fractal starts with expanding foam. That leads to a self-organizing random chaos. After about 60 orders of magnitude, it generates another expanding foam. Everything in between is our universe. If that can be reduced to a simple math formula, great!  

@phractal phoam
This is a Quote from your website.

From it i learn one important thing which is that solid as a phase refers to a rigid lattice structure and not to an impenitrable mono substance. The phase changes that occur then relate to the dissolution of this lattice structure and the increasing improbability of any two given regions being associable by any linear rule. Those regions that do remain associable reflect a electrostatic /gravitational relationship that also inhere certain chemical and physical properties. However at even greater phase change conditions these associations become improbable and regions are involved in an electrostatic/gravitational plasma dynamic which may be amenable to gas law /thermodynamic principles.

While these phase changes may seem random or chaotic i have ahunch that they are linked to what i call conic sectional curves/motion ands that general wave motion may be linked through conic sections to vorticular motions in general.

Whereas i see no particular need for the term ether seeing it as congruent in every way with the term space i have no objection to it and recognise its historical significance and the information earlier scientists have encoded with it.

So if i understand what you describe by it : our universe is a foam filled bubble within a foam filled super bubble?

I don't want to take over Lori's "Meet&Greet" thread to discuss my own model, so I have started my own "Let's collaborate on something!" thread entitled Fractal Foam Model of Universes (http://home.comcast.net/~fractal_cosmology/Articles/Fractal_Foam_Model_of_Universes.html). Any further discussion of my model should be taken there. I will respond, here, to one comment on my model.


I prefer to believe that every universe in the scale-wise succession is infinite in spacial extent. Whether universes come and go in a finite time seems less certain. A bubble in our cosmic foam consists of a void, perhaps 10^24 meters across, surrounded by walls made of hundreds or thousands of galaxies. There are perhaps one million such bubbles within our observable universe (Hubble sphere) which is about 10^26 meters across. I think that hubble shpere is an infinitessimally small part of what I call our universe. A super-universe electron is about a trillion times wider than our Hubble sphere.  

The purpose of my fractal cosmology is to demonstrate an "isomorphism" between the Mandelbrot set and black holes (and our universe). An isomorphism shows a relationship between the properties between two "objects" or systems. So I'm not saying that the Mandelbrot set is equal to a black hole but that there properties in one that match similar properties the another. So E = mc² means nothing to this isomorphism because the M-Set has no concept of mass per say. Another way of looking at it is, E = mc² really says that E = E. So I can talk about E in my model without talking about mass. In my model, the number of iterations is isomorphic to E.


I truly hope this wasn't meant as an insult. I had some horrible experiences in a physics forum where my "level of education" was questioned incessantly . I am almost 50. I have a university degree in computer science and have been working in a university research environment for 25 of those 50 years. Ten of those years I worked in the field of Astronomy. Currently, I build medical devices for cancer biopsy and treatment therapies. I have many papers and patents with my name on it. I spend most of the rest of my spare time studying physics, fractals and cosmology. This is fun for me but that doesn't mean that I don't take it very seriously.


Yes, I agree, I have studied All the fractals, but non are as interesting than the Mandelbrot set. No other fractal can create the infinite variations that the Mandelbrot set is capable of. It is the most complex mathematical object in 2+ dimensions. In other words, z = z cubed + c is actually less complex than the lower order version.

I have developed some of my own fractal patterns that seem to show a correlation between fractals and the way our universe works.

It is my contention that space-time, matter, black holes and event horizons are all fractals. The space-time is expanding because it "dividing" which is equivalent to what you said about your fractal foam model:


When space-time divides, what is really happening is the measuring stick is shrinking. So the "universe" isn't really expanding (as you suggested) but it does kind of look that way from our perspective. Also, as the universe expands (or appears to expand), black holes are contracting which increase the gravitation effect, the warping of space-time around them. This is why black holes appear to get "heavier" as time goes on. This is not because they are "eating" and destroying matter however. I don't think that it is even possible for matter to breach the event horizon of a black hole. Black holes get "bigger" (smaller really) because space-time is dividing. Why? Because entropy demands it.

Event horizons are also affected by space-time division. The event horizon is the "interface" between expansion and contraction. As space-time divides, event horizons "complexify" and so we have the complex shapes of the galaxies that we see today. In my model, a galaxy, the whole galaxy, is the event horizon of it's central black hole.

Alright; you got me there. I’m no mathematician. In particular, number theory leaves me cold. I wish you luck proving this isomorphism.  


I truly did not mean that as an insult. Like Einstein and Newton, I have Asperger syndrome, which prevents me from anticipating how my words might be interpreted on a personal level. I didn’t do well in school, and I’m too old now (64) to make a mark in the academic world, so I’m sowing my seeds of philosophy among those who might be destined to earn PhDs and Nobel prizes after I’m gone.


Really!? All the fractals? You must have been at it for trillions of years! I’d be interested in seeing what happens with z = z^x + c where x is irrational. E.g., z = z^√2 + c.
 

I would put it differently: particles, atoms, molecules, planets, solar systems, galaxies, cosmic foams, and even universes, are strange attractors within a single all encompassing fractal. I leave it to mathematicians to discover the numerical representation of that fractal.


I think it’s irrelevant which is “really happening”. If you define distance in terms of the separation of two very distant galaxies, then we are shrinking, but it makes better sense from our perspective to define distance in terms of material things. I believe the present standard is the speed of light and the wavelength of a particular emission line. In my model, I speculate that a cubic meter contains a constant number of ether-foam bubbles (approximately 10^105 of them). As the number of bubbles increases, the new bubbles bleed out of objects and end up in the great voids.


I don’t think astrophysicists use the term “event horizon” that loosely. The term is used in regard to black holes and the Hubble limit, but not to galaxies. When a black hole “eats” additional mass, that mass approaches the old event horizon but never crosses it; a new event horizon forms at a slightly greater radius, engulfing at least some of the new matter. The greater the mass, the larger the radius of the event horizon.

Yes, I know several "Asperger's" and they do seem to have this "disconnect" from the personal perspective. You're lucky in many ways. Personal connections can cause alot of suffering so without that you can focus on your higher mind. Don't give up on being able to learn even at 64. I personally will never give up.


Wow, you really do have Asperger syndrome. Of course, what I really meant to say is that I have programmed, played around with and/or studied and most if not all of the "mainstream fractals" that one might find while researching fractals.


This is in fact how I word it in webthesis:

http://www.butterflyeffect.ca/Close/Pages/StrangeAttractors.html

http://www.butterflyeffect.ca/Close/Pages/DarkMatter.html

and my crazy idea about DNA

http://www.butterflyeffect.ca/Close/Pages/DNA.html


Yes, this would be interesting, however I still think there's something special about the squared version. After we all, we do live in a universe that has inverse 'squared' laws and energy seems to be equal to mass times the speed of light 'squared'. Why squared and not cubed?  That's my question.

Maybe even powers are more interesting that odd powers. Perhaps you have not let the calculations run long enough to see structure developing in the other fractals. In my model, an electron is about a trillion times wider than a median size ether-foam bubble. If that is a first order strange attractor, you could simulate the mix of s-waves and p-waves for ages on a PC and swear nothing is there. Besides, the distances between strange attractors in our universe tend to be about 100,000 times the size of the attractors. Would you recognize a real-world object which fills one cube out of 10^15 cubes? It's possible we haven't yet invented a computer capable of simulating the fractal that runs our universe.  

The Mandelbrot construct (strange attractor) generates phenomenon very much like our universe.

Gravity:

http://www.butterflyeffect.ca/Close/Pages/Gravity.html

Radiation:
http://www.butterflyeffect.ca/Close/Pages/Radiation.html

Stars and Galaxies
http://www.butterflyeffect.ca/Close/Pages/FullOfStars.html


Not only that, but a 64-bit computer has a "planck limit" very similar to that of our universe at ~10 -33

http://www.butterflyeffect.ca/Close/Pages/Significant%20Digits.html

So, in my humble opinion, I believe that we do have computers that are perfectly capable of simulating our universe, at least in theory.

Also, the current standard model of the universe requires many dozens of equations and dozens if not hundreds of parameters in order to model it correctly. It is my opinion (humble again) that the best unified model of the universe will be the result of ONE equation with NO parameters. All forces become emergent properties of this ONE equation or process (feedback loop).

The Mandelbrot construct, meaning complex points (quaternions in 4D space) iterated through the function z = z squared + c, is a good example of what I see as the perfect "unified model" where just ONE equation/process with zero parameters generates a multitude of phenomenon (not unlike what we see in our universe).

This is what I expect "the unified equation of our universe" to look like and how I expect it to behave.

Fractalwoman:

I've followed your inspirational work for quite some time.

The psychological desire for one unified theory or principle to explain everything appears to transcend scientific agendas. My guess is that it contributes to the religious impulse as well. The search for unity amongst the seemingly endless diversity of phenomena we perceive around us has certainly yielded amazing insights with regard to the underlying commonalities involving that which can be measured. 

When I zoom into certain fractals I experience the same emotions as when I gaze at the succession of astonishing Hubble pictures which have revealed ever deeper glimpses into the universe. In addition, I don't consider fractal patterns to be mere Platonic abstractions, but rather manifestations of the physical universe, no less real than anything else which can be physically measured. The essential question, as you've implied, is to what extent fractal dynamics actually do reflect an underlying cosmic organizing principle.

From the start, analogies have played a fundamental model building role in scientific exploration. However certain analogies may be more useful as metaphors than actual models. For example, attempts have been made to apply the principles of Quantum Mechanics to classical situations which may be far too complex to operate according to those principles. Still, the application of QM metaphors can lead to fertile insights, even if misapplied in some technical sense.

Though I'm not quite ready to say that I expect the "unified equation of our universe" to be fractal in nature, I certainly hope it can be shown to be so, especially from the perspectives of parsimony and the more poetic "Truth is beauty." 

In particular, I'm not yet convinced that the full extent of self-referentiality apparently required for consciousness, can be fully captured in the context of fractal dynamics as presently formulated. Any "Theory Of Everything" would seem incomplete without being able to describe the dynamics underlying what we experience and describe as consciousness. However, if we consider the fractal patterns we generate to be the product of a kind of metafractal co-creation between ourselves and the outcomes of iterating various complex valued equations, then that might point the way to some kind of unified fractal based TOE. However, I cannot presently conceive of any way of formalizing this "co-creative metafractal" idea in such a way as to render it amenable to scientific testing, since there exists such a wide chasm between the algorithms involved in iteratively recomputing the outputs of complex valued equations, and the vastly more complex iteratively recursive models which may be required to characterize the action/reaction loops which describe our behavior in the world.

Fractex,

Consciousness is a unified field...

Here's funny story. A few years ago I had someone contact me about using one of my Buddhabrot images in their magazine. The magazine is called "Light of Consciousness". I was happy to oblige and gave then a nice high rez Buddhabrot called Golden Buddha. The reference to the issues can be found here:

http://light-of-consciousness.org/back-issues/LOC_CurrentArticles_18_1.htm

As you can see, the article that they associated my Buddhabrot image with was called: "Consciousness is the Unified Field" by John Hagelin. Now John Hagelin is one of the physicists from The Secret and What the Bleep. I was really surprised because I knew about Dr. Hagelin and was totally tickled to have my image associated with the idea of a unified field. Buddhabrot is in essence a unified field.

Here is what Dr. Hagelin has to say about this unified field:

The unified field is the fundamental field of unity, the field of peace.
Coherence, unity, peace, is communicated through the field of consciousness.
The field of consciousness is a field that we share.

Stuff like that.




 

So, the Buddhabrot set, the set of all points from the outside of the Mandelbrot set sometimes referred to as the anti-Mandelbrot Set, generates a unified field (of points) which happens to look a lot like a seated buddha figure. This I do not believe is a coincidence. Buddhism is all about consciousness and getting to the "center" which I like to think of singularity. Buddhism talks about a "voidness that is all inclusive". They talk about infinite possibilities. The universe can be infinitely vast or infinitely small depending on the scale of measurement. They see the universe as larger structures embracing lower ones in a structure extending ad infinitum in both directions to the infinitely large or the infinitely small. This is referred to as the "view of realms-embracing-realms". Sounds a lot like a fractal hierarchy to me.

When I look at Buddhabrot closely I see an "all-embracing" figure, arms stretch out embracing all the lower realms. Buddhabrot embraces all realms and therefore represents the meta-realm.

Hummm...

The buddhabrot show the orbit of all point that are outside of the mandelbrot set.
If you see "arms" or "paths", it is because exactly what you're supposed to see when you track an orbit, it was programmed to do that (and it does) :)
The anti-buddhabrot is the same thing, but for plot that are inside of the mandelbrot set (and not "outside", that why it's called "anti"). and is really borring to explore  :sad1:

It also work with other formula, not only z=z²+c

BTW, here at fractalforums we already know the answer to the great question about life, universe, and everything... and it's not z=z²+c

Edit : never heard about the "anti-mandelbrot"

The Mandelbrot Set is the set of all points that don't reach escape velocity, ie. the inside points only. The Buddhabrot set is generated using points that DO reach escape velocity, ie. the outside points.

So, the Buddhabrot set is the Anti-Mandelbrot set and the Mandelbrot set is the anti-buddhabrot set.

I guess I'm the only one that says anti-mandelbrot but what I am saying is technically correct (regardless of what algorithm we are using to render images).


??? Not sure what you mean by this. We are just following trajectories that are inherent in the system. It wasn't "programmed to do that" it just does it. The orbits or trajectories are emergent properties of the iteration process. These orbits are both deterministic and unpredictable (at least the first time you run the algorithm). Deterministic in the sense that the next position in the orbit is directly determined by the previous point. Unpredictable in the sense that we can never know what the next value is going to be exactly until we run it through the equation.


Please enlighten me. I'm all EARS... and please don't say 42!!! Because I know for a fact that it is the irrational number 42.83712038127394837129...

A Buddhabrot rendering is basically 2D histogram of the orbits, could be thought of as a probability density, the brighter points having a higher probability and the darker points having a lower probability of getting "hit" by one of the trajectories. So in that sense, it is a unified field in that you need ALL the points (outside points) or at least a good number of them in order to render the complete Buddhabrot image.