Thread: Complexity

A start would be 1 over the entropy.

...good question.

'How many edges has it got?'.

Well...

I would probably say based on the number of nonredundant, working systems in the structure.

Originally Posted by A Roxxor

Well...

I would probably say based on the number of nonredundant, working systems in the structure.

Agreed

An extension of my previous idea; the length of the description required to fully describe it.

So a cube of any size is not very complex, because you only need to say it's a cube and what one of the lengths is.

A cube divided into 1,000,000 alternately coloured slices is also not complex because you can describe it very quickly as I just have, as there is an obvious pattern.

The brain is a very complex object as there are around 100,000,000,000 neurons with no pattern you can use to generalise them.

Question; in this definition, is the Mandelbrot set infinitely complex or very simple?

Simple. There is a pattern to it.

111000111000111000111000 may look confusing, but it's simple. It has a pattern. The next numbers are predictable.

1230984029384029352763923095720384 is complex. There is no pattern. The next numbers are not predictable.

In structures, a cube cut into 1000 smaller cubes of equal size is simple.

A cube cut into 2389 smaller figures, random in all 3 dimensions is complex.

Simple. There is a pattern to it.

There's not, each bit is different.

sort of. Whenever you zoom in, you see a copy of what the original was. There is a pattern to it.

It isn't a copy. It's slightly different.

Originally Posted by A Roxxor

Well...

I would probably say based on the number of nonredundant, working systems in the structure.

This works fairly well. If we're talking about mathematical objects, this would be the number of independent objects in a space.

Originally Posted by Xei

It isn't a copy. It's slightly different.

The Mandelbrot set has some sort of "induced" complexity. Personally, I wouldn't call it complex because to generate it in any arbitrary fidelity requires a computer program about 10 lines long. And to increase the resolution does not require a lengthening of the computer program. That would suggest that the embedded fractals are, in fact, self-similar enough to call them computationally identical to the whole.

Originally Posted by Xei

An extension of my previous idea; the length of the description required to fully describe it.

So a cube of any size is not very complex, because you only need to say it's a cube and what one of the lengths is.

A cube divided into 1,000,000 alternately coloured slices is also not complex because you can describe it very quickly as I just have, as there is an obvious pattern.

The brain is a very complex object as there are around 100,000,000,000 neurons with no pattern you can use to generalise them.

Question; in this definition, is the Mandelbrot set infinitely complex or very simple?

Probably infinitely complex. Because it is a fractal and it has no pattern.

What about the Sierpinski Triangle? That would be simple, right? Because it has a pattern.

I don't know much about fractals though, or even how they are generated.

Originally Posted by A Roxxor

Probably infinitely complex. Because it is a fractal and it has no pattern.

What about the Sierpinski Triangle? That would be simple, right? Because it has a pattern.

Sierpinski's Triangle is a fractal that follows a pattern.

But you can represent the Mandelbrot set by Zn+1 = Zn^2 + c.

Wait, it doesn't have a pattern because it has to connect to the previous limb...okay. Your right.

Is a non equilateral triangle more complex than a square?

Yes.

Originally Posted by Omnius Deus

Is a non equilateral triangle more complex than a square?

No. It has three verticies, and three edges. A square has four verticies, and four edges.

If I understand this correctly...

But it has less sides to it.

But a square follows a defined pattern.

Which makes it less complex

Let's say you have three sides but the angles don't add up so two sides aren't touching.

You can complete with the shape with one more line, or potentially with infinite different lines and points. However, as an incomplete shape, it's just 3 sides.

Or take a math equation, such as 2+3=5. If you add 2n+3n=5n, is it more complex now? The n is irrelevant, the equation is still technically just 2+3=5, or even just n=n. You add arbitrary stuff to give it complexity, but the equation requires absolutely no addatives to reach equivolence.

Originally Posted by A Roxxor

Probably infinitely complex. Because it is a fractal and it has no pattern.

What about the Sierpinski Triangle? That would be simple, right? Because it has a pattern.

I don't know much about fractals though, or even how they are generated.

The Mandelbrot set is generated by a very simple iteration. Like I said, you can draw a Mandelbrot with any given resolution in about 10 lines of code. That makes it finitely complex, and not very complex at all.

Originally Posted by A Roxxor

Which makes it less complex

An equilateral triangle and a square are about the same because they have the same amount of structure. It's not the number of sides that counts, it's the number of definite things you can say about it. For example, a square has 4 90 degree angles. An equil. triangle has 3 60 deg. angles, etc.

Now, an isosceles triangle has less structure and hence less complexity because the angles can vary.

Deus:

...Which means that 2+3=5 is the same as 2n+3n=5n.

Remember, redundant systems are ruled out

The Mandelbrot set is generated by a very simple iteration. Like I said, you can draw a Mandelbrot with any given resolution in about 10 lines of code. That makes it finitely complex, and not very complex at all.

I see...

Well, what is more complex, then? A mandebrot fractal or an amino acid?

How does being able to change the angles make something less complex?

And roxxor, is 3+4+3+4 more complex than 7+7?

Originally Posted by A Roxxor

Well, what is more complex, then? A mandebrot fractal or an amino acid?

That's a close one. Depends on the exact amino acid. We're comparing unique computer instructions used in drawing a mandelbrot to the number of element positions in the acid, basically. For small amino acids it's roughly the same.

Originally Posted by Omnius Deus

How does being able to change the angles make something less complex?

Would you call the static on a tv screen that isn't hooked up "complex"? Hopefully not, otherwise we're not anywhere near the same page.

When you loosen the restriction on the angles, you take away some of the structure, or relationships, between the elements that make up an object. Less structure means less complexity.