Understanding Fractals by Watching The Bachelor
- Posted by Greg Harmon
- on March 30th, 2012
Nature is full of fractals and the fractal model has been used to explain everything including markets. What does that mean? Wikipedia puts forth this definition – A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are “the same from near as from far”. Fractals may be exactly the same at every scale, or they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself.
There is some disagreement amongst authorities about how the concept of a fractal should be formally defined. The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth. Fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature
That is a mouthful. And who knows what it means. I prefer to use an analogy from The Bachelor to help explain it. If you watch reality television this may work for you as well. Like the Bachelor, the series of charts above, look similar on different time frames. Lining up each season of the Bachelor in a time line, he will always be amazed at the beginning by all the gorgeous girls, whittle it down to a few, one which is the worst of the bunch, the “Bitch”, then pick that girl, propose to her and break up on the after show that same night. This pattern happens over and over again. But digging a little closer, within each season patterns exist. There is always the girls being supportive of each other and ganging up on the “Bitch”, dates with the Bachelor where they are all in love after 5 minutes and then jealousy as they realize he is just a ‘Playa’ moving on to the next girl. Week after week this goes on. At the next level down, within each show, there are also patterns. Scantily clad ladies prance around as the date cards arrive, reading out the name or names of his next conquest. The winners are obsessed with kissing him and just as some action might be getting good you hear Chris, the host, say “Coming up…” signalling a commercial you need to fast forward through. So no matter if you look at the long term multi-season level or cut it down to the season or episode level the result is the same. Patterns an structure exists like the 4 timeframe chart of price action above.
For another explanation, if you have not seen the father of Fractal math, Mandelbrot discuss the topic it is worth a look. Sorry no video form the Bachelor, but this is better.
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Gregory W. Harmon CMT, CFA, has traded in the Securities markets since 1986. He has held senior positions including Head of Global Trading, Head of Product Development, Head of Strategy and Director of Equity. (More)
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