A fractal dimension is just one single metric out of many that characterize such systems. It is amazing how much store we put into single metrics such as these. For example, the Dow Jones Industrial Average is almost religiously perceived as the indicator of the overall state of the U.S. economy, just as body temperature is typically used as an indicator of our overall health. Better is to have a suite of such metrics such as you get from an annual physical examination, or what economists generate in order to get a broader picture of the state of the economy.
