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is the universe fractal





zaxacongrejo
hello
ive been listen about fractal maths, fractal sculps, fratal paiting for years now
a because of that i have a couple of questions

are we fractal ?

is the universe fractal ?

are the basic shapes of nature related with fractal?

what about the the 6 dregrees of separation?

can the 6 dregrees of separation be a concequence of a fractal universe?

it my brain factal?"sometimes it looks like" haha

can fractal maths explian the begining of everything included the universe?

can fractal numbers save the world?

will fractal stop war?

can fractal maths produce power to suply a city?

help us to understand how fractal are realated
Bikerman
Fractal;s are patterns which, no matter what scale you use, appear similar. The word 'fractal' is actually short for 'fractional dimension' - this is because a more accurate definition would be a pattern with a fractional dimension - ie not a normal integer dimension - 1,2,3 etc. In practice this means that fractals are potentially infinite within a bounded area.
Confused yet?
Simple example - what is the length of the UK coast?
If you use a large scale map you will get a value by dragging a piece of string around the shape and then measuring it.
Now, our normal thought is that changing the scale shouldn't matter. Surely you are (say) 6ft tall whatever height I am and however far away you are? But not so.
Now, consider the coastline, but this time measured on foot with a surveying tool. It will be longer, yes?
Now, we go in further and use a piece of string. Now we have to bend the string around every rock and pebble and the coastline gets longer still.
Now we go really small and use microscopic measures - now we have to bend around much more tiny particles and the coast gets longer again - and the smaller we zoom in, the bigger our measurement gets.

Follow me?

Now let's step it up with a real fractal - the Koch Curve.
We start with a triangle: then we repeatedly draw a new triangle on each side....as follows:





And keep going.....looks something like this:



Every iteration (repeat) makes the total line 4/3 times longer - and if we continue for ever then the line will be infinitely long, even though it will never get any 'bigger' on the page. Even more weird - the area of the shape also increases each time - if you do some simple sums you should be able to calculate how much the area increases each time - yet the shape does not get any bigger to our eyes.........

The fractional dimension is calculated as follows:
Since there are 4 identical line segments that are each 1/3 long, the dimension is log 4 / log 3, which is approximately 1.26.
Afaceinthematrix
Bikerman wrote:
Fractal;s are patterns which, no matter what scale you use, appear similar. The word 'fractal' is actually short for 'fractional dimension' - this is because a more accurate definition would be a pattern with a fractional dimension - ie not a normal integer dimension - 1,2,3 etc. In practice this means that fractals are potentially infinite within a bounded area.
Confused yet?


Yes. But I think that it's because you're incorrect.

I don't think that the word "fractal" is short for "fractional dimension."

A fractal is a mathematical set that has a fractal dimension that usually exceeds it's topological dimension. This is a definition introduced by Mandelbrot that he never liked because it only works most of the time.

Dr. Lapidus and Dr. Frankenhuijsen gave a better definition* but I do not remember the exact definition. I think that it was something along the line of "An object is a fractal if its complex dimension contains a non-negative real part."

Also, what do you mean with a "normal integer dimension?" I think that you mean Hausdorff dimension - which will usually be less than the fractal dimension.


*The book that they introduced it in is:
http://books.google.com/books/about/Fractal_Geometry_Complex_Dimensions_and.html?id=bV_TM3lAdQUC
Bikerman
You got me - and you are quite right. I was lazy in the explanation (I sort of knew is wasn't quite right, and I should have checked it, but I thought it might then get too complex and boring so I took the easy option).
The basic point is right, but badly put and factually wrong on the definition.
By dimension I mean the normal euclidean/topological dimension. So 1 for sets of lines, 0 for sets of points, 2 for sets of surfaces and 3 for sets of volumes - hence integer.
Fractal shapes (lines, areas, volumes), as you say, have a fractal dimension greater than the integer topological dimension.
zaxacongrejo
the universe can be explained with fractal numbers because is fractal

all complexity comes from simplicity thats why all natural shapes seam to have a logic and an evolution
and that can be explained with fractal maths Mandelbrot

The word "fractal" often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. The mathematical concept is difficult to formally define even for mathematicians, but key features can be understood with little mathematical background.

If a rule or principle of law is conceptualized as defining a two-dimensional "area" of conduct, conduct within which should be legal and conduct outside of which should be illegal, it has been observed that the border of that area must be a fractal, because of the infinite and recursive potential exceptions and extensions necessary to account appropriately for all variations in fact pattern that may arise
Bikerman
For a moment I thought you had made a deep and interesting point, until I read it back a couple more times - now I think otherwise....
However, just in case I am missing some deep meaning, perhaps you could explain further.
You are saying, I think, that in some boundary situations (presumably involving humans to give the complexity, since most physical situations seem to me to be fairly binary at anything but an extreme microscopic scale - and then I doubt very much whether quantum behaviour can be modelled fractally - though I could of course be wrong) then the boundary itself is fractal in nature. You give the example of legal-illegal and assert that the border MUST be fractal because there are an infinite number of exceptions which can also be recursive.....Have I understood you correctly?

If so then I think it is wrong. I cannot see how you go from having a very large number of possible states along a notional boundary to then declaring that this makes it fractal. There are an infinite number of possible numbers between the boundary of 1 and 2, but I'm pretty sure the real-number continuum is not intrinsically fractal. Nor can I see how there can be any large degree of recursion.
If one were to plot a set of behaviours along the notional legal-illegal boundary then I predict you would get a pretty random spread, not a self-similar pattern which scales....
Maybe, as I said, I'm missing something - in which case I'll be happy to be educated....
JoryRFerrell
zaxacongrejo wrote:
hello
ive been listen about fractal maths, fractal sculps, fratal paiting for years now
a because of that i have a couple of questions

are we fractal ?

is the universe fractal ?

are the basic shapes of nature related with fractal?

what about the the 6 dregrees of separation?

can the 6 dregrees of separation be a concequence of a fractal universe?

it my brain factal?"sometimes it looks like" haha

can fractal maths explian the begining of everything included the universe?

can fractal numbers save the world?

will fractal stop war?

can fractal maths produce power to suply a city?

help us to understand how fractal are realated



zaxacongrejo wrote:

are we fractal ?

is the universe fractal ?

Life and everything else in the universe are at least highly abstract fractals. The basic physics and rules which allow for the formation of stars/planets, are fractal in nature. They are simple rules which create a pattern of reaction and formation. While they may not be classic patterns, the fact that a star begins fusion after enough mass is gathered, and then explodes when it's burned all available fuel, is a higher level pattern. It doesn't have to be a lock-step, visual pattern in order to be a pattern, and therefore a fractal.


zaxacongrejo wrote:

are the basic shapes of nature related with fractal?

Every shape/object in the universe is absolutely based on fractals. The physics behind snowflake formation are fractal.
Some animals, like butterflies for example, display certain colors because of the shape of micro-structures formed by fractal logic. Those structures wouldn't exist if the basic rules of physics didn't build on top of one another to form a more complex system, that in turn combines with other patterns to form a deeper fractal. The electrical forces behind an atom are fractal in nature and stack
with the interactions of neutrons and protons. This is a small fractal already. Those atoms join together to form amino acids, which work together to form DNA. So a "basic shape"/object, responsible for life, is a confirmed fractal, but this fractal gets larger/deeper still: These strands of DNA/Amino Acids/Atoms all work together to form animals which are a type of pattern. We humans are usually equipped with a pair of, generally symmetric, arms, legs, eyes, etc. We typically have a nose and hair. These all form a pattern or blueprint, which is a fractal. Then these fractals called humans, made from fractal DNA composed of fractal Amino Acids formed from fractal Atoms, go on to form fractal cities. Fractal cultures (culture breaks down in to subroutines and patterns so it's a type of fractal) are present in these fractal cities. So are fractal-based small arms and nuclear warheads. These are all on our fractal planet which is one among many.These form a fractal solar system which joins with others to form a fractal galaxy. Every galaxy you go to is self-similar, with every body in it conforming to basic rules. Every galaxy is fractal, containing stars, planets, asteroids, comets, etc. They may even contain life, as long as the fractal-rules required are present.

zaxacongrejo wrote:

can the 6 dregrees of separation be a concequence of a fractal universe?

I am unfamiliar with the theory behind "6 degrees of separation", but I'll read some on it.

zaxacongrejo wrote:

it my brain factal?"sometimes it looks like" haha

Your brain is self-similar, yes. All your neurons link together in a semi-predictable way (axons reach out to connect with dendrites, neurons release chemicals to "communicate", neurons have the ability to make new connections, etc.), due to rules which govern their formation and use. They are fractal in nature. Again, it may not be a clear cut visual pattern, but it's a logical fractal all the same.

zaxacongrejo wrote:

can fractal maths explian the begining of everything included the universe?

Everything is self-similar. It would seem impossible for the universe to exist without everything being self-similar. If atoms and the particles that make them up, didn't share properties so they could interact, then matter wouldn't form objects, and we wouldn't be here to think about fractals in the first place. Also, because fractals are patterns, and not completely random noise(absolutely no pattern shared, other than the fact that each part is truly random, which is a pattern of sorts),
that means we can use that to our advantage in determining what came before and what might come later. So maybe fractals will allow us to determine how everything started. Then again, just because fractals allow for this in theory, does not mean it's practical. Look up Lawrence Krauss. He has talked about the fact that because of a radiation "curtain", we can only see so far. This means certain observable phenomenon are no longer actually visible to us. So we can theorize about some of the farthest reaches of space, but we can't observe what is actually out there, lending more substantial backing for the theories. As a result, we may be missing key bits of info we need to work backwards and figure out certain things. Basically, we showed up to the party late with our intelligence, and now all the sophisticated party tricks we know may do us no good, because all the data left for a better party... Neutral

zaxacongrejo wrote:

can fractal numbers save the world?

Fractals place an important role in medical science, engineering of all sorts of life-saving tech, agriculture, etc., etc. Fractals are such an intuitive part of everything, that we have been relying on them the "whole time" (we...as in the universe and everything in it). It's like the muscles under your skin. You use them from birth. But you never think about them. one day, you may learn some science about how they work and become interested in manipulating them directly with that knowledge by say, body building....or something more practical. Razz Same principle here with fractals.
We have always used "them", but now we are conscious of them, and so we can make better use of them.

zaxacongrejo wrote:

will fractal stop war?

Yes. We can use fractals to examine the self-similarity of the events leading to wars, and so take steps to avoid the typical "war-fractal" sub-pattern.

zaxacongrejo wrote:

can fractal maths produce power to suply a city?

Again, we have always used fractals, especially in the generation of power. The most basic generation of power (potential energy between particles and..."empty space"...now...possibly O_o)
takes place without you realizing. Again, it's all due to the fractal nature of of our universe at it's basic level. Basically, if something is made from rules, it's a fractal. Also, anything made from that fractal is now a fractal itself...because it inherits the self-similar properties of it's parent building blocks. So if logic/physics are a fractal, then the atoms made from those fractal rules are as well.
This means water is a fractal. Water, being self-similar, has generally predictable traits (it flows to the lowest possible position if left to it's own devices) which allow us to create dams that harness it as a form of energy. We are already taking advantage of fractals to generate power. Smile
But, as with everything, we can improve upon stuff. "Base fractals" can be manipulated to create new fractals with more efficient patterns/power-output.


zaxacongrejo wrote:

help us to understand how fractal are realated


Fractals are self-similar patterns. So, anything that exists is a fractal really. The rule behind Non-existence and existence is simple. For something to exist, it can't NOT exist at the same time.
This creates two states and a basic rule for being one of those two states. Anything that exists is automatically a fractal, because it is self-similar because it complies with this basic rule, a pattern for things which exist, and those that do not. All objects that exist must therefore share this property and so everything by default, is similar to EVERYTHING ELSE which exists in this respect. That includes other fractals. All objects (or ideas even) which exist, and those which don't, form a pattern of simple "On or Off" pattern. Just like you have some fractals which have a really deep, hidden pattern, which is seemingly 100% random, they are still be based off a few simple rules which produce insane complexity.

Fractals are similar to all other fractals for the simple fact that they describe patterns formed by things that either exist, or do not exist. They describe "0" and "1". That's the lowest level I can think of....




Razz
JoryRFerrell
Afaceinthematrix wrote:
Bikerman wrote:
Fractal;s are patterns which, no matter what scale you use, appear similar. The word 'fractal' is actually short for 'fractional dimension' - this is because a more accurate definition would be a pattern with a fractional dimension - ie not a normal integer dimension - 1,2,3 etc. In practice this means that fractals are potentially infinite within a bounded area.
Confused yet?


Yes. But I think that it's because you're incorrect.

I don't think that the word "fractal" is short for "fractional dimension."

A fractal is a mathematical set that has a fractal dimension that usually exceeds it's topological dimension. This is a definition introduced by Mandelbrot that he never liked because it only works most of the time.

Dr. Lapidus and Dr. Frankenhuijsen gave a better definition* but I do not remember the exact definition. I think that it was something along the line of "An object is a fractal if its complex dimension contains a non-negative real part."

Also, what do you mean with a "normal integer dimension?" I think that you mean Hausdorff dimension - which will usually be less than the fractal dimension.


*The book that they introduced it in is:
http://books.google.com/books/about/Fractal_Geometry_Complex_Dimensions_and.html?id=bV_TM3lAdQUC


Yeah, there are fractals created without "fractional numbers" as describe by formalized human math, or integers in other words.
But, fractals occupy space. They are pieces, either mentally or physically. They have dimensions. Taken as a whole, they form an abstract "integer", but separately, they are pieces. 1 may be an integer in a formal math class, but in the end, one is part of the whole. It's not really whole by ITSELF. It need other pieces to describe a abstract "whole". I think whole numbers are more of a human creation because we are more comfortable with the idea of finite "thing's" which either ARE or ARE NOT. As time went along, we needed to expand on whole number math, and so fractional math was born. We were inherently using fractional math, but restrictions in our idea of the world prevented us from thinking about it right from the get-go. Quantum mechanics actually tears apart the idea of "whole particles" and seems to be describing everything as more of a proportional continuum within...uhm...more continuums... Razz That's a great physical example.

They have to be fractional in order to be a "piece" which repeats. Everything is fractional.
JoryRFerrell
Afaceinthematrix wrote:
Bikerman wrote:
Fractal;s are patterns which, no matter what scale you use, appear similar. The word 'fractal' is actually short for 'fractional dimension' - this is because a more accurate definition would be a pattern with a fractional dimension - ie not a normal integer dimension - 1,2,3 etc. In practice this means that fractals are potentially infinite within a bounded area.
Confused yet?


Yes. But I think that it's because you're incorrect.

I don't think that the word "fractal" is short for "fractional dimension."

A fractal is a mathematical set that has a fractal dimension that usually exceeds it's topological dimension. This is a definition introduced by Mandelbrot that he never liked because it only works most of the time.

Dr. Lapidus and Dr. Frankenhuijsen gave a better definition* but I do not remember the exact definition. I think that it was something along the line of "An object is a fractal if its complex dimension contains a non-negative real part."

Also, what do you mean with a "normal integer dimension?" I think that you mean Hausdorff dimension - which will usually be less than the fractal dimension.


*The book that they introduced it in is:
http://books.google.com/books/about/Fractal_Geometry_Complex_Dimensions_and.html?id=bV_TM3lAdQUC


...IGNORE MY LAST POST Laughing
I failed to read your post properly. I skimmed over and thought you were saying that fractals are not fractional. Now I realize you were saying that the word "fractal" does not stand for "fractional dimension".
capricornis
what if the whole thing is just a simulation? how would we ever know? http://www.slate.com/articles/health_and_science/new_scientist/2012/12/simulated_universe_testing_the_laws_of_physics_to_determine_whether_we_re.html
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