Fractals- complex but having minimal entropy?

[bcrelling]

Fractals are just many iterations of a very basic formula, so they can be described with little information, and yet they are extremely complex given enough iterations.

Can they be described as low entropy despite their complexity?

 

[mathman]

Fractals are mathematical constructions. Entropy is a physical concept. What do you have in mind when connecting them?

 

[bcrelling]

Fractals are mathematical constructions. Entropy is a physical concept. What do you have in mind when connecting them?

Ok I should clarify, I'm referring to entropy in the information theory sense of the word, not the thermodymamic sense.

To illustrate the concept, a chess board where the squares on the top half are all black and the bottom half are all white can be described with little information and hence is a low entropy configuration. A chess board where the colour of each square was decided by the toss of a coin would likely be high entropy and take more information to accurately describe.

I ask the question on fractals as fractals are produced by iterations of a simple process and so should be low entropy, and yet they might be viewed as highly complex.

 

[meBigGuy]

You are right that a seemingly complex diagram or sequence can be described by a simple iteration and so therefore contains little information. But there are many seemingly complex sequences or expressions that have a simple basis (for example an lfsr based random number generator). Given to an unknowing stranger, the numbers will seem random, but the person who designed the generator thinks otherwise.

If course, the trick is to be able to do the opposite. Take a complex sequence and then discover a simple way to express it. That would be the goal of fractal compression. http://en.wikipedia.org/wiki/Fractal_compression

 

[bcrelling]

You are right that a seemingly complex diagram or sequence can be described by a simple iteration and so therefore contains little information. But there are many seemingly complex sequences or expressions that have a simple basis (for example an lfsr based random number generator). Given to an unknowing stranger, the numbers will seem random, but the person who designed the generator thinks otherwise.

If course, the trick is to be able to do the opposite. Take a complex sequence and then discover a simple way to express it. That would be the goal of fractal compression. http://en.wikipedia.org/wiki/Fractal_compression

That's interesting, I wonder macro economic data could be compressed via this method and then somehow used to predict price changes?

 

[mathman]

Side comment: Why did you post it in classical physics, when it turns out to be more of a mathematics question?

 

[bcrelling]

Side comment: Why did you post it in classical physics, when it turns out to be more of a mathematics question?

I only saw the options under the physics heading- this forum is bigger than I thought!

 

[meBigGuy]

Non-linear dynamic (chaos) analysis is a trading buzzword I think, and there are all sorts of publications relating stock market data and fractals.