We did an extensive amount of work on Chaos Theory a few years ago and duirng that period became familiar with Professor Didier Sornette, a lowly French trained associate professor at UCLA, in the image fellow mathematician Benoit Madelbrot (the father of Chaos Theory).
What attracted me to his work was his mathematical use of power series to isolate patterns and predictions from what are perceived to be highly complex and non predictable events.
These events at the time included such events as earthquakes but the financial market were quickly becoming a center of his interest, again similar to Benoit Mandelbrot who postulated from the cotton markets that there was a random generator for the markets that would allow predictability.
Both were studying Complex Systems and could see repeatable "fractals" within the apparent Chaos that when taken as a whole defined surpizingly precisely the situation. A lot of this mathematics has been applied today in graphic animation to generate complex images for entertainment.
I raise this discussion because Professor Sornette (now a full Professor at the prestigious Zurich Federal Institute of Technology) has published the following chart which I find both fascinating and highly correlated with our research.
I present it below without comment for your consideration and study.
After having introduced the subject in last month's TRIGGER$ (also see below) I cite further evidence in this month's upcoming MATA release as part of the Studies section on the evolving "Crack-up Boom".
I recommend the following video for further insights.
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