[yor_on (OP)]

Read this.
http://focus.aps.org/story/v16/st2

Are they?
Does this mean that we have a tool for foretelling them.

[Ophiolite]

Does this mean that we have a tool for foretelling them.

From the link you posted. Second paragraph.

The paper concerns the statistical properties of earthquakes, so it does not provide a magic formula to predict where and when a quake will occur.

[blakestyger]

They are probably stochastic - only analyzable statistically.

[LeeE]

I think that the term 'Fractal' has been used inappropriately in that article.

Fractals have unlimited resolution but with a cluster of earthquakes the finest resolution is at the individual quake level; either a quake is occurring or a quake is not occurring, and although you can have clusters of clusters, and so on, each individual quake can't be endlessly sub-divided in to clusters of sub-events that resemble the parent quake.  For earthquakes to be truly fractal, each individual quake should look like a cluster of individual quakes, and then within each of those sub-divisions of each individual quake we should see similar sub-clusters, and so on.  Also, with fractals, there is something happening at every point in the set, whereas with earthquakes, if one isn't occurring, there's nothing to sub-divide.

Earthquakes are better described by Chaos theory, where seemingly small changes can have disproportionate influences on the outcome.

[Ophiolite]

Fractals have unlimited resolution but with a cluster of earthquakes the finest resolution is at the individual quake level;

Hmm. I agree that a true fractal might well have the property of infinite resolution, but there are plenty of natural phenomena which we describe as being fractal that do not have this property. Branching trees, snowflakes and coastlines come to mind. If we can apply the term fractal to these I think we can apply it to earthquakes. What do you think?

Secondly, individual quakes are not the limit. A quake is a composite events with multiple slippages at more than one point, so the 'depth' of the fractal is certainly an order or two greater than you are suggesting.

[LeeE]

I agree that the things in nature that are often described as being fractal i.e. trees, coastlines etc. are finite.  I also agree that we could identify sub-events within each individual quake, so you're right to say that we could add another couple of level of 'depth'.  Even so though, I just don't think that there's enough levels of depth for earthquakes to really qualify as fractal phenomena.

Perhaps the issue is that whereas a true fractal has infinite resolution be definition, I'm not aware of a standard definition of resolution limited fractals.  Would a phenomenon where there were just two layers of depth that were similar qualify?  I can't help thinking that there are better ways to describe such systems.

[chris]

They're more fractURE than fractAL I think!

Chris

[yor_on (OP)]

If I remember right there is a well known technique to make a 'fractal leaf' by just laying layers upon layers? I think it was mentioned in James Gleick - 'Chaos, Making a New Science'?

Don't remember the exact technique though?

"Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature.

Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples—a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. The connection between fractals and leaves are currently being used to determine how much carbon is contained in trees."

So, yes LeeE, according to Fractals, and Gleick too, I believe that they can be called fractals even when finite. In nature most everything you see are of a finite nature. It's in the mathematic modeling of those properties and in our mathematical treatment of QM we will see it differently, as I understands it?