Tuesday, December 15, 2009

Update on fractal landscapes

I had mentioned these fractal landscapes to an old college friend, and he had this to add:

With the caveat that looking *like* a fractal isn't the same as being a fractal, a fractal has organizing rules that are in a recursive relationship. So it seems to me that the two organizing rules are gravity and the electromagnetic force that holds materials together, and the 'recursion' is moving the materials around, primarily water but also wind. But I could be wrong.

I think that's an important point. A lot of fractal geology is mere "appearance," rather than true "behavior." But I think he's got a good point about the combination of gravity and the EM force. The disjunct between scales might be bound by the ability of materials to resist gravity (displayed in such things as a mineral's hardness, etc.). On top of that, there are continental-scale behaviors of crust, which allows for things like uplift and sedimentation in the first place. The reason the Sierpinski Triangle outcrop looks like it does is due in large part to the well-partitioned sedimentary cycles within the outcrop - breaking it up into nearly perfect thirds, top to bottom.

I've been doing a lot more thinking, rather than synthesizing lately, but I think the note about the EM force and gravity is an important one. Since much of what we see on the landscape is a tug-of-war between gravity, which tends to bring things towards the center of the Earth, and the EM force, which helps resist it. There's probably a bit of influence by the Strong and Weak Nuclear forces in there too. Although, I think crustal properties such as bulk modulus are more affected by the EM force, but it might be fun to look into the combination of the EM and Weak Nuclear forces, since much of our Earth's internal heat is provided by nuclear decay.

Another way to think about it: there appears to be a minimum size to silt grains generated by impacts with larger particles. At small enough scales, gravity can't generate enough energy to knock atoms apart - so there's another scale at work when it comes to very tiny silt-type grains. And don't forget the completely different behavior of clay minerals!

Of course, this EM force and the ability of minerals to resist breaking down plays a key role in any critique of a marine origin for the Coconino Sandstone. Yes there are mica grains in the sand. Yes, mica is softer than quartz. But there are more forces at work besides Moh's fancy little scale.

1 comment:

  1. In our river models, the plastic media we use shows changes in behavior at around 0.2mm--at that point electromechanical forces take over and cohesion becomes significant, and model channels stop behaving like real world systems. Overall scaling on these is controlled by gravitational acceleration and viscosity, the two variables you can't scale down along with geometry. With model:reality scales (including particle size) of >1:150 or so, channel behavior is remarkably similar in models and the real world. A very complex topic I'm currently struggling with!