Ten years ago I was spending the days studying geologic information and the late evenings analyzing stock charts. One day it occurred to me that well logs and sea level curves had similar patterns. It later became obvious to me that the patterns on the geologic information resembled the patterns on stock charts. What did these things have in common? Nothing that I've ever determined except "sameness in form". This made me curious.
In 1987, James Gleick published a book called Chaos. This book brought knowledge of a new science to the masses. An excerpt.....
"Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the turbulent sea, in the fluctuations of wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side---these have been puzzles to science, or worse, monstrosities. But in the 1970s a few scientists in the United States and Europe began to find a way through disorder. They were mathematicians, physicists, biologists, chemists, all seeking connections between different kinds of irregularity."
Chaos theory and complexity are being studied in every imaginable field integrating science and mathematics.
In 1988, I attended a seminar on chaos theory. From that point on, I was forever curious about the relationship between "things" and mathematical algorithms. The most interesting to me has been the "s-curve" or logistic equation. We've all seen S-curves representing many things. Its first breakthrough was in studying population growth in various species.
This pattern seemed to appear constantly in stock charts.... especially on "moving averages".
Fractals are similar patterns that repeat in a variety of scales. Fractals appear naturally
in living and non-living things. Heartbeats create fractal patterns...snowflakes, clouds,
and the stock market.
This self-study of chaos and complexity has led me through over thirty books on the subject. I can't say I understand more than 10% of it, but it continues to be fascinating.