Is the universe a Fractal?

Benj96

If the universe is a fractal of repeating patterns on ever larger scales, for example: hierarchies, cycles, the golden ratio, structures that we see throughout human academic disciplines - the study of things and/or nature, in essence, if physics and chemistry is geometric, then, it should also be synchronic. Right?

By that I mean that any change at any level in the fractal will impact the entire fractal. Synchronicity and continuity between ALL actions. The whole premise of a fractal is that it is the same, the rules, the grammar, the coding, the geometry, apply the same way on all levels.

But it's not. It's not synchronic. If it was there would be no individual personalities, no information exchange, nothing that can act in contrast to anything the rhythm of all else (asynchronosity) . And everything would all happen at once like the cogs of a machine all trying to move the same direction. It would be like constant déjà-vu.

It's either a great irony that such a highly organised and simple set of rules, a basic pattern, a fractal, "appears" chaotic, messy, disorganised, unpredictable.

OR

The universe is not a fractal. There are no rules. Or infinite rules. Both can be argued reasonable convincingly.

I think personally, the universe being a fractal with simple rules seems more intuitive because from that one can derive easily many things: the butterfly effect, newton's third law of motion, the ability of language to construct analogies (describing a principle using another example from an "unrelated topic").

"Chaos" in a fractal would be a product of magnitude and time. If you could freeze frame ever second, everywhere, at all times, everything can be predicted. But we cannot do that and that is why I believe a perfectly organised construction/design fundamentally, can bring about huge chaos and unknowns, superficially.

Also as a side note, its neat to point out how psychedelics show us fractals when we alter our consciousness.

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jgill

The universe is not a fractal. There are no rules — Benj96

I don't think the universe is fractal, but I do think there are some rules. "Fractal" began as a mathematical notion that arises from simple iteration of a single function ("rule") in the complex plane. But as time progresses you may have noticed things change. Why not such rules? Instead of a single function perhaps there should be an infinite sequence of functions that are iterated, one after the other. (Confession: this is my mathematical area of research).

Fractals and chaos and everything in between can result from simple iteration of a single function. But when you use a sequence of functions you might be surprised at what comes forth. Look at my icon on TPF.

L'éléphant

Instead of a single function perhaps there should be an infinite sequence of functions that are iterated, one after the other. — jgill

↪Benj96

In fractal dimensionality, as posited in the chaos theory in biochemistry, there is indeed an underlying foundation (as in stable foundation) that supports the nonlinear complexity. Researchers use fractal analysis in, say, fractal surface to show that we don't have to go to another methodologies entirely to accommodate unpredictability . (What these methodologies are is a separate discussion).

What do you think @jgill?

jgill

What do you think jgill? — L'éléphant

One of the reasons I stay on this forum is that I learn things about math. Fractals, for me mostly means fractal art. Fractal analysis of phenomena it seems uses approximations to repeated patterns in skilful ways. From Wikipedia:

Unlike theoretical fractal curves which can be easily measured and the underlying mathematical properties calculated; natural systems are sources of heterogeneity and generate complex space-time structures that may only demonstrate partial self-similarity.[17][18][19] Using fractal analysis, it is possible to analyze and recognize when features of complex ecological systems are altered since fractals are able to characterize the natural complexity in such systems.[20] Thus, fractal analysis can help to quantify patterns in nature and to identify deviations from these natural sequences.

What has happened to fractals is similar to what happens to interesting concepts in math: everyone takes off in all kinds of directions with it. I haven't followed these developments with fractal theory because they didn't interest me much. I've been more concerned with what happens when infinite sequences of functions are composed. It's virtually all nonlinear in the mathematical sense.

Thanks for bringing this to my attention.

Agent Smith

Newton's law

$F = G\frac{m_1m_2}{r^2}$

Coulomb's law

$F = k_e\frac{q_1q_2}{r^2}$

:cool:

Benj96

Look at my icon on TPF. — jgill

It looks like the anatomical structure of the brainstem.

Pantagruel

By that I mean that any change at any level in the fractal will impact the entire fractal. — Benj96

Except that the universe is a collision between law-governed and non-law-governed events. So if a fractal structure evolves as a result of its fractal nature, then the changes will permeate. If it alters as a result of some locally contingent force, then not. It seems like your post assumes that everything must unfold according to a set of underlying laws, all or nothing. In fact, reality as we experience it is simultaneously law-governed and exceptional.

Fractal attractors are a common feature of complex systems, so most likely fractals do represent a significant feature of the universe.

Benj96

It seems like your post assumes that everything must unfold according to a set of underlying laws, all or nothing. — Pantagruel

Well the issue for me is that my concept of "law" is something that cannot be violated in any instance. Something fundamentally delineating the possible from the impossible.

If there are exceptions, then I wouldn't consider it a law I would consider it the most likely case at most times/instances, but not the absolute definitive case. If you get me.

So for me it's hard to imagine a universe with some parts obeying laws and other parts being lawless. As that wouldn't be universality.

I think, emergence, is a good way to navigate how new properties can arise from simple strict laws. And how these properties may seemingly contradict certain laws or act as an "exception" to the rule. But I suspect they don't violate them just as many perpetual motion machines that have been invented are very convincing but ultimately stop, or have a concealed energy source. A gimmick that doesn't violate thermodynamics for example.

There are a lot of illusory phenomenon that arise from just the sheer complexity of variables that are at work within them. I suspect they can be broken down and fully predicted with enough/fast enough computing power.

Pantagruel

There are a lot of illusory phenomenon that arise from just the sheer complexity of variables that are at work within them. I suspect they can be broken down and fully predicted with enough/fast enough computing power. — Benj96

The crux. Laws by their very nature are highly specific - they apply only to a certain type of state of affairs. Boyle's law has nothing to do with Lavoisier's law. And there is a lot of ground in between, and around them. Are there an infinite number of unique laws? Or is there a general underlying Law?

jgill

Fractal attractors are a common feature of complex systems, so most likely fractals do represent a significant feature of the universe — Pantagruel

I wasn't familiar with "fractal attractors", and found only this paper using that terminology. I suspect what you mean is "strange attractors", which have been studied extensively. But thanks for piquing my curiosity. :cool:

jgill

It looks like the anatomical structure of the brainstem. — Benj96

You might find the images in this entertaining: A Space of Semi-coupled Contour Integrals

Pantagruel

I wasn't familiar with "fractal attractors", and found only this paper using that terminology. I suspect what you mean is "strange attractors", which have been studied extensively. But thanks for piquing my curiosity. :cool: — jgill

You're welcome. Fractalness is basically a property of a strange attractor within the phase space of a system - viz. "strange attractors, which are described by a fractal structure in phase space"

L'éléphant

What has happened to fractals is similar to what happens to interesting concepts in math: everyone takes off in all kinds of directions with it. — jgill

:sweat: I think you're right.

Agent Smith

If I were God ( :grin: ), to minimize me workload, I would definitely use fractals in me work, one of which would be the universe.

Benj96

The crux. Laws by their very nature are highly specific - they apply only to a certain type of state of affairs. Boyle's law has nothing to do with Lavoisier's law. And there is a lot of ground in between, and around them. Are there an infinite number of unique laws? Or is there a general underlying Law? — Pantagruel

Ah yes now I understand what you're saying. Yes I agree some laws are extremely specific that they only apply to certain variables under rigid conditions. I would say they are constant and universal (in the sense that boyles law likely applies to any part of the universe and can be repeatkt demonstrated again and again).

But not universal in scope. What they apply to. Boyles law doesn't apply to dna reproduction in any closely associated sense. It may apply indirectly from afar in that it dictates temperatures, pressures and chemical property dynamics that go to make biological systems possible.

So if there are many specific and defined laws which are not directly connected to one another, perhaps there is one vague, ill-defined law that connects all things together.

It seems the more general and vague something is the more applicable it is to larger sets but also less informative to individual cases. And the more specific and defined something is obviously imparts more info about limited things.

Maybe the fundamental law would be so general, so broad, that it is hardly recognisable as anything we could say is a law, or even prove as a law.

Pantagruel

It seems the more general and vague something is the more applicable it is to larger sets but also less informative to individual cases. And the more specific and defined something is obviously imparts more info about limited things. — Benj96

Like statistics. I often think about this in terms of cosmology. The unfolding of the various phases of the early universe was essentially statistical in nature, based on relative densities and dispersions of whatever entities coincided with a given energy-state. The transition from a stochastic to a material cosmos is interesting.

PhilosophyRunner

↪Benj96

I don't think there is a universal law that require the universe to be composed of fractals. Rather I would put forward some parts of the universe are fractals as a consequence of other laws (current laws of physics, or some kind of unified law we don't know of yet, or something else).

Pantagruel

I think fractals are a kind of encapsulation of holism - i.e. a general underlying universal characteristic.

Benj96

I don't think there is a universal law that require the universe to be composed of fractals. Rather I would put forward some parts of the universe are fractals as a consequence of other laws (current laws of physics, or some kind of unified law we don't know of yet, or something else). — PhilosophyRunner

That's quite potentially the case. I could see how laws could interact in such a way as to repeat patterns in a fractal manner. Rather than the other way around. It's a good point.

If so, what dictates the end to the fractal so that only parts of the universe behave in this way? For example I couldn't conceive of a reason why a fractal based on pi, for example, would ever end, or derived from any irrational number or recurring number sequence for that matter, like 3.33333333'

What would make a fractal finite? And secondly is a fractal really a true fractal if its pattern ever comes to a stop, if the scale of repetition is ever limited?

jgill

What would make a fractal finite? And secondly is a fractal really a true fractal if its pattern ever comes to a stop, if the scale of repetition is ever limited? — Benj96

Mathematically, a fractal (that is not finite) is generated by iterating a rather simple function in the complex plane an infinite number of times. So, a "finite" fractal would result from iterating a finite number of times. Then it's not "turtles all the way down".

In common usage, fractal means just repetitive patterns at various scales. Ideally, all scales.

Benj96

↪jgill

ah I see okay. So in essence the big elephant in the room here is the age old discussion of whether true infinities occur practically. If the universe could ever be infinite or is definitively finite.

PhilosophyRunner

↪Benj96

Take some practical examples of fractals - snow flakes, or the center of some flowers. They are not infinite.

Now as to your previous question of why fractals occur at all, I'm not sure. I would guess it is something to do with how things form. Say a branch forms 1/3 the way off another branch (due to genetics, let's say). Then off the new branch another branch forms 1/3 the way, and so on. Hence the fractal. But it is not infinite, and it won't be exactly 1/3 of the way every time - sometimes it might be slightly more or less. It will only be an approximation of a fractal.

Benj96

Take some practical examples of fractals - snow flakes, or the center of some flowers. They are not infinite. — PhilosophyRunner

That's a good point. A snowflake is definitely a fractal and a finite one.

Now I'm thinking that given the right conditions a snowflake could keep growing outwards infinitely no? If it it was given a stable environment with no wind/turbulence to destabilise and fracture it, a cold enough temperature and enough water.

In essence it would no longer be a "snowflake" really because we define them specifically and by a certain size. It would be more just ice freezing outwards.

So we come to crystallisation as a general process. Crystallisation could be infinite no? And its a fractal of repeating molecular structure aggregating on the outer edge, be it salt or ice or any other molecule.

So if crystallisation can continue endlessly as a fractal, the only preventative variables are the lack of space, substrate or adequate temperature. The conditions that are ripe for crystal growth.

So a fractal is as large as the set of conditions that create it are in duration.

I think thats something significant and worth a bit more exploration especially when talking about fundamental rules/constants, the universe and fractality.

PhilosophyRunner

↪Benj96

True, if the conditions for a snowflake to grow infinitely large were present, it could grow infinitely large. This is if there was infinite water, infinite space at the perfect temperature, etc.

But the same is not true going smaller. As you zoom in, and get to the molecular level and smaller, the snowflake will not look like a snowflake even with infinite water, infinite space at the perfect temperature, etc. Thus it can never be an actual fractal.

But I think that is beside the point as the universe is not a giant snowflake - i.e in our observable universe there are no true fractals, just approximations. In a perfect mathematical universe, there may be.

Nickolasgaspar

If the universe is a fractal of repeating patterns on ever larger scales, for example: hierarchies, cycles, the golden ratio, structures that we see throughout human academic disciplines - the study of things and/or nature, in essence, if physics and chemistry is geometric, then, it should also be synchronic. Right? — Benj96

-What "fractal" means to you. Fractal is a label we use on structures with specific characteristics.Chemisty and Geometry are tools we use to descibe qualities of these structures.
Again I think you are committing a fallacy of composition. You are arguing from the specific to the general. What about those structures in the Universe that do not display the characteristics of a fractal?

if physics and chemistry is geometric, then, it should also be synchronic — Benj96

Define Geometric and synchronic please.

I am not sure calling the Universe "fractal" offers us any additional understanding for this Phenomenon.

Changeling

(Rogan goes a bit nazi in this though)

Is the universe a Fractal?

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