Thread: Complexity

I'm going to ask a pretty vague (or so I think) question, and I'll explain myself if needed after I get some responses.

By what criteria and on what scale would you rate the complexity of a structure as compared to other structures?

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.

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.