> In some ways we can consider this to be a fractal.

Except, of course, we can't.

The term fractal is a well-defined mathematical object. There might be "self-similarity" there, but (just a fun fact) fractals are typically not self-similar, so it's not a very good litmus test.

I would like a word that means 'exhibits self-similar structure at different scales '. This is a useful definition because people outside of math can notice this pattern in our world.

If not fractal, then what word?

> If not fractal, then what word?

self-similar?

Sorry to polute your pure and precise word but outside of mathematics people will continue using fractal to mean self similar. As with many mathematical words the colloquial meaning is different.

> The term fractal is a well-defined mathematical object. There might be "self-similarity" there, but (just a fun fact) fractals are typically not self-similar, so it's not a very good litmus test.

Per the Wikipedia article, they are not well defined. Also, self-similarity of some kind is one of the requirements. Is it completely wrong, or is this a debated topic in mathematics?

How do you define a fractal? Unless you give me your definition I can make a definition match what I need.

Let's look at one paragraph from Wikipedia.

> Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.

Let's consider the context of behavior again.

A person is an object of elaborate and infinitely complicated boundary. You may look at one instance of behavior at one time and you may see a certain value, like you see at a fractal at a particular zoom and configuration. In a sense, particular details at this magnification. A family of several people has an elaborate and infinitely complicated boundary and has details of it's own, in addition to the people within it. A village... A city... A country... A planet... An organ...

Let's look at Merriam-Webster: > any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size.

Do you see how it fits?

If we consider shape more literally, it may be something like, a person has an arm to grasp things. Let's take one function, picking an object up and bringing it nearer to you. A community has an appointed person to deliver things. A country has a company to do so. A world has a certain country which is the most efficient for transport. A cell has a protein or a function of its membrane to interact with some molecules to bring them closer.

Your analogy doesn't work, because on one wall there is graffiti while on another there is nothing. One family is cold and the next is loving. What you're discussing is the systematic results of averaging out the individual actions of people. Not the same thing as a mathematical fractal, which has a fairly rigorous definition as defined by Mandelbrot, the guy who coined the term.

In a Mandelbrot fractal on one pixel you may see one value, on another you see another.

Let's say on the second wall, instead of graffiti of violence, you see a message of love. You look around the wall and you see there is a person in love, a family sharing love, a town with flowers, a peaceful city.

For a wall with nothing, it could be a value in the set that corresponds to a particular color that represents it did not meet the threshold.

Fractals don't have pixels.

Whatever you may consider to be an evaluation of it - for "looking at a fractal image" the pixel value is computed based on properties of the fractal at that particular magnification at that particular location.

Your analogy still doesn't make sense because people get murdered in front of beautiful murals all the time, and people walk past disheveled tenements without getting murdered all the time. This "fractal" nature you describe doesn't exist. You are confusing emergent properties of society with something entirely different.

I concede this argument, from your latter sentence, I am considering emergent properties at different scales to be fractal like indeed.

For the first sentence, my point was not to imply that a presence of one kind of behaviour leads to similar behaviour in related structures, but that at different scales, components of each structure may exhibit similar kinds of behaviour. E.g. a person can be considered to be violent or peaceful and so can a community. This could be from our nature of finding patterns in everything, though. Which I guess also leads to emergent properties anyway in some way, so I cannot add much more there.

Actually I am unsure if it fits the definition of emergence - "emergence occurs when an entity is observed to have properties its parts do not have on their own" - but it would be hypocritical for me to argue on that note :D