Is The Universe A Fractal?

March 16, 2007

A recent article in New Scientist tells of a small number of cosmologists who believe in the theory that the universe is a fractal (i.e it's made of a number of number of bits which is each a smaller copy of the whole - like a fern leaf or a broccoli). This can be proven to a certain size (200million light years or so) but over this size things get a bit big and unobservable.

This kinda goes againsn't Einstein's craic as he believes in a more homogeneous dispersion theory (that everything is more or less evenly spread across the place). Einstein's theory has some kinda knock-on effect with space-time and gravity and the like, allowing us to make universal assumptions using the general theory of relativity.

This puts into question a canny bit about the universe and how things fit into it. It's all very exciting!

I am of the belief that perhaps things are a bit fractal; it's a repeating pattern in nature and it has been shown to happen in space to a certain extent. Also that although he was some cool dude, even Einstein couldn't know everything, if only because science wasn’t as developed then. And I like the thought of different laws of physics to our own.

Anyway... I was just reading about it and thought I would ask you all your opinions? It effects us all. I'm bored with favourite pets and pretend Bedlingtonites now...

Sw@lnalla · March 16, 2007

Has CK screwed your theory missvic?

March 16, 2007

Has CK screwed your theory missvic?

I posted it first. It was my question. The Colonel is a cheater!

Sw@lnalla · March 16, 2007

I posted it first. The Colonel is a cheater!

I get the impression he's pissed and hasn't a clue.A typical toony. Even his minions are proving pathetic.

Re. your topic missvic.

I see fractal design as using mathematics to design pictures, that's how I use them. Linking them to 'Intelligent Design' just doesn't work, but then, some people are just becoming desperate.

Joe Rooney · March 17, 2007

I get the impression he's pissed and hasn't a clue.A typical toony. Even his minions are proving pathetic.
Re. your topic missvic.
I see fractal design as using mathematics to design pictures, that's how I use them. Linking them to 'Intelligent Design' just doesn't work, but then, some people are just becoming desperate.

This whole conversation is way beyond my comprehension. But I find the topic fascinating, first because you can discuss it with such aplomb, and secondly, how on earth did CK manage to hijack Missvic's opinions

There may be more to the man than I might have ever have guessed! Cunning old codger!

But please carry on folks. I am interested in seeing where this carries us.

Regards, Joe

Pencil_Neck · March 17, 2007

I get the impression he's pissed and hasn't a clue.A typical toony. Even his minions are proving pathetic.
Re. your topic missvic.
I see fractal design as using mathematics to design pictures, that's how I use them. Linking them to 'Intelligent Design' just doesn't work, but then, some people are just becoming desperate.

I believe the retired officer has some charm & character. You must have minions in life who know their

place...... :huh:

For Joe:

Fractals - Beautiful Mathematics

Fractals are mathematically generated shapes which have some special properties. The most common types of fractal, which you may have encountered before on snazzy postcards or on the Internet, are the Julia sets and the Mandelbrot set. These are both named after the mathematicians who discovered them, Gaston Julia (1893 -1978) and Benoit Mandelbrot (1924- ).

The word fractal stands for 'fractional dimensions' because a fractal does not have an integer (whole number, eg 1, 2, 56, 12 but not 1.63 or 1/2) number of dimensions. To try and clarify this a bit, recall that a line is one-dimensional (1-D), a plane is 2-D and a cube is 3-D. A fractal line, however, can be 1.675-D or 1.0032-D. If this sounds a bit odd, that's because it is. Basically it's a mathematician's way of describing how crinkly a line is.

The origins of fractals lie in the work of Lewis Fry Richardson (1881 - 1953), who asked the seemingly simple question, 'How long is the coastline of Britain?'. If you measure this quantity from a globe of the Earth, with a poorly printed outline of Britain, you might get the answer of a few thousand kilometres. If you measure it from an accurate map with a higher resolution, you would get a greater answer because of all the extra crinkles that show up with a more precise line. However, if you took a metre rule and walked around Britain measuring the coast, the answer arrived at would be bigger again, because a metre stick at that scale would fit into a lot more of the crinkly bits than showed up on the map. If you used a 10cm ruler, again your answer would be bigger, and so on ad infinitum. This leads us to conclude that the coastline of Britain has an infinite length - it is a fractal. The edge of any fractal is in fact infinite, and no matter how small a piece of the line you examine is, it will also be infinite. In effect, since you can make a crinkle as tiny as you like, you can fit an infinite number of crinkles into a tiny space.

The Extremely Complex Bit

Fractals are generated by iterations (repetitions) of a simple formula - for a Mandelbrot fractal z = z2 + c, where z and c are complex numbers. A complex number is a number made by adding a real number (any normal number you can think of is a real number, eg 1, 2.342, pi, -34.232323) to an imaginary number (a real number multiplied by the square root of minus one, this equals i). z begins at 0 + 0i (basically zero) and c is given by the complex plane mapped1 to the screen, so to generate the pixel in the very middle of the screen, c = 0 + 0i. The initial z is squared, and c is added, and again, and again, until the magnitude of z goes above a certain number - generally about four gives good results. The number of iterations required for this to happen is taken as the colour of the pixel. If z never goes above the value, the pixel is given the value 0.

Fractals were originally regarded as nothing but a mathematical curiosity, but now they are being used in computer generated imagery and in image compression technology. Fractals are at the heart of chaos theory, which tries to describe how a tiny initial change in conditions can produce entirely different end results. It is interesting to note how pixels close to each other on a fractal image can have completely different colours. Chaos theory can be used to describe the motions of planets or analyse population changes, so fractals are at the heart of a lot of modern science.

And I have still have a Simple Simon :blink:

Monsta® · March 17, 2007

I believe the retired officer has some charm & character. You must have minions in life who know their
place......
For Joe:
Fractals - Beautiful Mathematics
Fractals are mathematically generated shapes which have some special properties. The most common types of fractal, which you may have encountered before on snazzy postcards or on the Internet, are the Julia sets and the Mandelbrot set. These are both named after the mathematicians who discovered them, Gaston Julia (1893 -1978) and Benoit Mandelbrot (1924- ).
The word fractal stands for 'fractional dimensions' because a fractal does not have an integer (whole number, eg 1, 2, 56, 12 but not 1.63 or 1/2) number of dimensions. To try and clarify this a bit, recall that a line is one-dimensional (1-D), a plane is 2-D and a cube is 3-D. A fractal line, however, can be 1.675-D or 1.0032-D. If this sounds a bit odd, that's because it is. Basically it's a mathematician's way of describing how crinkly a line is.
The origins of fractals lie in the work of Lewis Fry Richardson (1881 - 1953), who asked the seemingly simple question, 'How long is the coastline of Britain?'. If you measure this quantity from a globe of the Earth, with a poorly printed outline of Britain, you might get the answer of a few thousand kilometres. If you measure it from an accurate map with a higher resolution, you would get a greater answer because of all the extra crinkles that show up with a more precise line. However, if you took a metre rule and walked around Britain measuring the coast, the answer arrived at would be bigger again, because a metre stick at that scale would fit into a lot more of the crinkly bits than showed up on the map. If you used a 10cm ruler, again your answer would be bigger, and so on ad infinitum. This leads us to conclude that the coastline of Britain has an infinite length - it is a fractal. The edge of any fractal is in fact infinite, and no matter how small a piece of the line you examine is, it will also be infinite. In effect, since you can make a crinkle as tiny as you like, you can fit an infinite number of crinkles into a tiny space.
The Extremely Complex Bit
Fractals are generated by iterations (repetitions) of a simple formula - for a Mandelbrot fractal z = z2 + c, where z and c are complex numbers. A complex number is a number made by adding a real number (any normal number you can think of is a real number, eg 1, 2.342, pi, -34.232323) to an imaginary number (a real number multiplied by the square root of minus one, this equals i). z begins at 0 + 0i (basically zero) and c is given by the complex plane mapped1 to the screen, so to generate the pixel in the very middle of the screen, c = 0 + 0i. The initial z is squared, and c is added, and again, and again, until the magnitude of z goes above a certain number - generally about four gives good results. The number of iterations required for this to happen is taken as the colour of the pixel. If z never goes above the value, the pixel is given the value 0.
Fractals were originally regarded as nothing but a mathematical curiosity, but now they are being used in computer generated imagery and in image compression technology. Fractals are at the heart of chaos theory, which tries to describe how a tiny initial change in conditions can produce entirely different end results. It is interesting to note how pixels close to each other on a fractal image can have completely different colours. Chaos theory can be used to describe the motions of planets or analyse population changes, so fractals are at the heart of a lot of modern science.
And I have still have a Simple Simon

copy n paste special!!!!!!!!!!

March 17, 2007

copy n paste special!!!!!!!!!!

Oh no!

Fooled again!

I really believed that you wrote this yourself Pencil Neck! I was astounded by the simplified and eloquant manner that you managed to convey such a complex theme. I was proud to be a Bedlingtonian once more! Until, Monsta pointed out the above. I like a good fractal mind, it's good you're all checking them out!

barry_jones · March 17, 2007

i find the universe very complex....take mars....years ago it seemed huge...same as the milkyway....but now you can get then mini size and in packs of 12!! mindblowing!

Chris40 · March 17, 2007

i find the universe very complex....take mars....years ago it seemed huge...same as the milkyway....but now you can get then mini size and in packs of 12!! mindblowing!

Now THAT i understand!

Dave · March 17, 2007

who had a spirograph when they were kids they were good werent they... pretty shapes and stuff ..

Monsta® · March 17, 2007

i remember etchasketch? that thing were you moved the dials and it drew a picture! marvelous

Joe Rooney · March 17, 2007

I believe the retired officer has some charm & character. You must have minions in life who know their
place......
For Joe:
Fractals - Beautiful Mathematics
Fractals are mathematically generated shapes which have some special properties. The most common types of fractal, which you may have encountered before on snazzy postcards or on the Internet, are the Julia sets and the Mandelbrot set. These are both named after the mathematicians who discovered them, Gaston Julia (1893 -1978) and Benoit Mandelbrot (1924- ).
The word fractal stands for 'fractional dimensions' because a fractal does not have an integer (whole number, eg 1, 2, 56, 12 but not 1.63 or 1/2) number of dimensions. To try and clarify this a bit, recall that a line is one-dimensional (1-D), a plane is 2-D and a cube is 3-D. A fractal line, however, can be 1.675-D or 1.0032-D. If this sounds a bit odd, that's because it is. Basically it's a mathematician's way of describing how crinkly a line is.
The origins of fractals lie in the work of Lewis Fry Richardson (1881 - 1953), who asked the seemingly simple question, 'How long is the coastline of Britain?'. If you measure this quantity from a globe of the Earth, with a poorly printed outline of Britain, you might get the answer of a few thousand kilometres. If you measure it from an accurate map with a higher resolution, you would get a greater answer because of all the extra crinkles that show up with a more precise line. However, if you took a metre rule and walked around Britain measuring the coast, the answer arrived at would be bigger again, because a metre stick at that scale would fit into a lot more of the crinkly bits than showed up on the map. If you used a 10cm ruler, again your answer would be bigger, and so on ad infinitum. This leads us to conclude that the coastline of Britain has an infinite length - it is a fractal. The edge of any fractal is in fact infinite, and no matter how small a piece of the line you examine is, it will also be infinite. In effect, since you can make a crinkle as tiny as you like, you can fit an infinite number of crinkles into a tiny space.
The Extremely Complex Bit
Fractals are generated by iterations (repetitions) of a simple formula - for a Mandelbrot fractal z = z2 + c, where z and c are complex numbers. A complex number is a number made by adding a real number (any normal number you can think of is a real number, eg 1, 2.342, pi, -34.232323) to an imaginary number (a real number multiplied by the square root of minus one, this equals i). z begins at 0 + 0i (basically zero) and c is given by the complex plane mapped1 to the screen, so to generate the pixel in the very middle of the screen, c = 0 + 0i. The initial z is squared, and c is added, and again, and again, until the magnitude of z goes above a certain number - generally about four gives good results. The number of iterations required for this to happen is taken as the colour of the pixel. If z never goes above the value, the pixel is given the value 0.
Fractals were originally regarded as nothing but a mathematical curiosity, but now they are being used in computer generated imagery and in image compression technology. Fractals are at the heart of chaos theory, which tries to describe how a tiny initial change in conditions can produce entirely different end results. It is interesting to note how pixels close to each other on a fractal image can have completely different colours. Chaos theory can be used to describe the motions of planets or analyse population changes, so fractals are at the heart of a lot of modern science.
And I have still have a Simple Simon

Thanks for the explanation Pencil Neck. It explains an extremely complex subject in terms which I find both relatively clear, and simple. Even without the benefits of a mathematical education, I found myself able to follow the logic of it all.

It also confirms my earlier wisdom in taking History and Economics. That, I had, and still have, an affinity for!

It bothers me not that it is not original to you. Thank you for bringing it to my attention.

Several people like yourself, and especially my good friend Swalnalla, have steered me to many subjects and sources of enlightenment that I would probably never have experienced on my own. None of us can excel in every field, but with educated help we can broaden our understanding of many things normally beyond our ken.

Thanks again, Joe

Hamburger Pimp · March 17, 2007

I get the impression he's pissed and hasn't a clue.

I fear you have that whole mote/beam/eye thing going on again.

A recent article in New Scientist tells of a small number of cosmologists who believe in the theory that the universe is a fractal (i.e it's made of a number of number of bits which is each a smaller copy of the whole - like a fern leaf or a broccoli).

The second "Fractal" thread posted the exact same text but in a smaller font. A rather amusing juxtaposition of form and content, I thought.

Perhaps a bit too subtle for this forum, where animated mooning smilies carrying offensive banners and badly spelled nonsense in very large type are the comedic devices of choice.

Monsta® · March 17, 2007

this is boring me out my brain god help! i dont want to watch open uni on the telly! please stop!

Sw@lnalla · March 17, 2007

Fractals were originally regarded as nothing but a mathematical curiosity, but now they are being used in computer generated imagery and in image compression technology. Fractals are at the heart of chaos theory, which tries to describe how a tiny initial change in conditions can produce entirely different end results. It is interesting to note how pixels close to each other on a fractal image can have completely different colours. Chaos theory can be used to describe the motions of planets or analyse population changes, so fractals are at the heart of a lot of modern science.
And I have still have a Simple Simon

In imagery fractals work well but the discussion surely is time, Luciano Pietronero doesn't offer any explanation for this on any freely available page. Maybe he doesn't have Papal approval?

Mars bars and Etchasketch.......LOL Go 4 it CK

Perhaps a bit too subtle for this forum, where animated mooning smilies carrying offensive banners and badly spelled nonsense in very large type are the comedic devices of choice.

Not quite up to your favoured Viz magazine standards. ? :blink:

Joe Rooney · March 18, 2007

this is boring me out my brain god help! i dont want to watch open uni on the telly! please stop!

Monsta dear Monsta,

I need a little clarification here!

Are you really asking God, the same god to whom you vociferously object in other posts, for "help".

Just thought I would ask!

Joe

Monsta® · March 18, 2007

Monsta dear Monsta,
I need a little clarification here!
Are you really asking God, the same god to whom you vociferously object in other posts, for "help".
Just thought I would ask!
Joe

like that will ever happen, we must obey, we must obey get bent! the only one i obey is santa clause cause he's a bit more believable!

he's got flying reindeer now thats something!

Pete · March 18, 2007

like that will ever happen, we must obey, we must obey get bent! the only one i obey is santa clause cause he's a bit more believable!
he's got flying reindeer now thats something!

Now theres a fairy story.

Monsta® · March 18, 2007

Now theres a fairy story.

yeah like jesus walking on water!!!!! and moses parting the red sea! ho ho ho its magic! :blink: :lol:

Blank · March 19, 2007

yeah like jesus walking on water!!!!! and moses parting the red sea! ho ho ho its magic!

I agree.

Pencil_Neck · March 19, 2007

copy n paste special!!!!!!!!!!

Whatever.......read "To Kill a Mocking Bird".......

Monsta® · March 19, 2007

Whatever.......read "To Kill a Mocking Bird".......

no rather not! rather read "misery" reminds me of you!!! :lol:

Pencil_Neck · March 20, 2007

no rather not! rather read "misery" reminds me of you!!!

Tiresome :blink:

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