For something that can be charted, like a market, there are two dimensions. The fractal dimension at any point is a mathematical summation of something's behavior as either something that can be described with one dimension (a strong, straight-line trend) or by two dimensions (a meandering, chaotic range). Thus the dimension is calculated as being between 1.0 and 2.0 (between one and two dimensions). We typically just take the decimal portion and refer to it like basis points. So a fractal dimension of 1.35 is just called "35". This "line vs chaos" thing in theory happens at all different time scales, minutes, years, what have you, and you have to divide all this rightly for it to mean anything in the scale that's significant to you. The guiding mantra of all fractals is always "same thing, different scale".

This also applies to the geometrical rescaling and repeating that markets tend to do. Back in early February, I wrote an article, "Gold's Bull/Bear Status" on gold's apparent "new" bull market, which is likely just a repetition of a rescaled, typical, and oft repeated bull market fractal that is really all one bull market

Anyway, enough math. After looking at gold, and seeing that it currently has a very unusual fractal condition, I looked at several other key markets and found that there is a similar fractal abnormality in them as well. First, let's look again at gold: (click on image to view)

As the graph shows, gold is currently at 55, highest in 10 plus years, presaging a very strong trend coming, either up or down.

Gold is linked to many other markets, so let's take a look at the US dollar with this measure:

"Historically unstable" would be a good description of the dollar's fractal behavior since the 2014 power move up and subsequent chaotic range. The peg-to-peg gyration from 30 to 60 is very unusual for a major index, especially a supposedly stable currency, even on the weekly scale as this fractal dimensioning is calculated.

Of course gold is also supposed to be an inverse play to the stock market, although I beg to differ with that take as there have been extended periods with both rising gold and stocks, with 2002 to 2007 being a prime example. But historically, and especially lately, gold is inversely related. So let's look at stocks via the Russell 2000, because it is a broad stock market and it is a leading group. Let's calculate some fractal dimensions:

Amazingly, we find that the stock market is also jam packed with the highest fractal energy level in over 10 years. But just from this, we don't really know which way it wants to go, up or down, from looking at these graphs as they just show its fractal condition. Is there something that we could check that could be more suggestive of the direction ?

Consider copper. "Every bull market has a copper top" is ancient wisdom, noting that copper puts in a top somewhere in the late stages of a bull. And it is referred to as Dr. Copper because it has a PhD in economics. It did indeed peak clear back in 2011 before the transports, European banks or any other leader. Copper has put in attempts at bottoming ranges amidst a pronounced decline, and recently it has attracted attention to the $2.00 level as a major line in the sand.

There is the technical read where $2.00 is a Fibonacci level. But then there is the basic fact that the world's biggest trafficker in dangerous derivatives, Deutsche Bank, is highly levered to Glencore, and Glencore is very highly levered to copper staying above $2.00 a pound. An article, from

*recently explained "Barclays: Glencore Is In Big Trouble If Copper Gets $0.30 Cheaper". Copper was $2.34 at the time. The article states at the top:*

**Business Insider**Glencore is a strange hybrid company, both a commodities trader and a mining company, and it has a complicated balance sheet loaded up with different kinds of debt. There are a lot of different ways to analyze the company but perhaps the best way to think of it is like a bank that's hitting a crisis, like Lehman Brothers ... if the price of copper falls below $2/lb, you begin to get some seriously sweaty palms in Glencore's finance departmentIf this level gives way, it will be a serious debt problem with the banking system. And because $2.00 is also a psychological level, breached only in the March, 2009 and January, 2016 market debacles, it would also involve a confidence shock to all the other markets. In fractal terms, this is how copper looks now:

Each of the ranges in the decline where the fractal dimension went to over 50 resulted in a sharp collapse downward. The $2.00 per pound line in the sand is right at the red arrow I've drawn illustrating the current range. And currently we have copper at a fractal dimension of 55, the highest of the entire decline, strongly suggesting another sharp drop, this time through the $2.00 barrier. Of course, the direction could be up from here, but there is a very strong primary trend at work with copper, so the more likely outcome of the fractal situation is a continuation of this primary trend. It's showing no signs of reversal.

Oil is in a similar but much less profound state of weakness. It went to an extreme fractal dimension of 60 (monthly) in mid 2014 with oil seemingly stable at around $105. The massive move to $45 in just 6 months that followed sent the fractal dimension to below 40 in a flash. On the weekly scale, the fractal dimension went to 52 in mid 2015 with oil steady at $60, went back down to 30 as oil plummeted to $28, and is swiftly going back up as oil struggles in the $40s. It is a similar plateau and plummet progression as copper, but not nearly as fractally strong, and with the primary down trend in question as oil is trading well above its 200 day moving average.

But there is yet another market index with a once-in-10 year fractal event going on where the direction is probably more clear. Let's take a look at the VIX:

The fractal dimension reacted strongly to the 2008 event with a big build to 53, then a big dissipation clear down to 34. It didn't seem to react as strongly to the 2011 Greece scare, as if it knew it was just a passing cry of "wolf". But it has again gone to an extreme level, being violently pegged at 60 for some time now. So there would seem to be an extremely large move coming. But if it were

*down*, it would be to an absurd VIX level of around 10 or less.

Not that this hasn't happened before. We were cruising into 2007 up until March with the VIX at 10-12 before hardly anyone was worried about housing, or anything. But in our day, this would imply that stock markets will sudden go to a PE of 30, or an unprecedented burst of earnings will suddenly materialize from a weak economy seemingly beyond the resuscitation of monetary policy, the rising debt defaults will suddenly stop from the mountain of shaky loans, interest rates will "normalize", the lion shall lie down with the lamb, and pigs will fly.

It may not be just your imagination that the global economy, markets, and interest rates are going into some kind of twilight zone. The cold science of fractal analysis backs you up on that.

The collective fractal wisdom is saying buckle your seat belts, and the VIX is saying a big move will either be another big decline in stocks or a sudden trip to nirvana. I guess we could be going to nirvana, but until the evidence is convincing, it may be wise to make some preparation the other way.

If you would like more information on the fractal dimension in markets, you can read the works of Benoit Mandelbrot, who discovered and wrote about this phenomena in all areas of science. He coined the label "fractal" and founded the Chaos Theory approach to analyzing markets. His book

*has been called "the deepest and most realistic finance book ever published". There are a few product offerings that give you an FDI (fractal dimension index or indicator) along with the RSI and other technical indicators. One is from QUANTSHARE Trading*

**The (Mis)Behavior of Markets**Software. If you are a programmer, there is code written for this calculation by AmiBroker and others. You can also use someone's code at MetaStock with their Indicator Builder feature.

A word of caution about the FDI - there is no one formula for calculating it from Mandelbrot or anyone. It is a math concept and, for use with the markets, it is only as good as the talent of the writer of the program. And I have found that, when using one of these, it takes a lot of practice to use effectively. You have to learn to think like the algorithm, learn the different scales it calculates in, and make it play nice with the other good indicators. Fractal thinking is a little warped relative to conventional chart reading.