I know it says no financial questions but I think this is more of a physics question...

I'm an artist by profession but I like to study science as a hobby. I was researching chaos theory around the time the pandemic struck and, incidentally, had just purchased a little bit of stock using a phone app.

When the lockdown was announced and the stock market crashed, I thought I noticed properties of chaos theory unfolding (really quickly) in my time series.

Specifically, I saw a fractal shape consisting of a "bump, double-bump" unfold periodically and then scale up and repeat.


The scaling upward is a periodic-doubling and the scaling forward is based on the fibonacci sequence. This is the cascade to chaos scaling of the feigenbaum diagram.

Slope Equation

Fibonacci Sequence

I've been recording the movement using screen caps and photoshop for the past 1.5 years and I'm looking for someone familiar with chaos theory to look at my notes to see if I have something significant or not.


I have a 40 page pdf I can send if anyone would like to see it.


  • 1
    $\begingroup$ A slightly broader concept is 'dynamical systems theory', chaos being just one kind of dynamics that can occur. You're seeing some kind of dynamics, probably not period doubling, but will need to take a closer look (and think about what these variables actually represent) to be sure $\endgroup$ Jul 24 at 23:19
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    $\begingroup$ Question probably belongs on money.stackexchange.com e.g. under tag technical-analysis or stock-analysis $\endgroup$ Jul 24 at 23:22
  • $\begingroup$ You can mail me the pdf (contact in my profile). I may as well see all the details:) $\endgroup$ Jul 25 at 2:28
  • $\begingroup$ Thanks, Mitchell, I sent you the pdf. $\endgroup$
    – ChaosCabal
    Jul 25 at 2:47
  • $\begingroup$ What is the question? $\endgroup$ Jul 25 at 4:43

The pattern you have noticed may well be real, but it is not period doubling in the chaos sense. You have noticed a pattern in time. You see a pattern and later you see a similar pattern.

Period doubling is different. To see it, you would have to play days of the stock market after the lockdown over and over, with different parameters each time. Perhaps with a partial lockdown once, and a more severe lockdown the next time.

If period doubling were in play, you would see a smooth and steady market with no lockdown. When you did a partial lockdown, you would see the market bounce back and forth between two values. A stronger lockdown would make it bounce repeatedly between $4$ values. Stronger still would produce a market with 8 values. And so on.

These markets are getting closer and closer to chaos, but have not reached it. Chaos begins when you have a lockdown strong enough to produce an infinite number of values. The market would repeat only after an infinite time.

Needless to say, the market does not ever behave in a nice smooth repeatable way. This might in part be because you never hold all the conditions that affect it steady. It might be something else.

But do be careful about noticing patterns and expecting them to repeat. There is some truth to the old joke - There is a guaranteed way to make a small fortune in the stock market: Start with a large fortune.

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – rob
    Jul 25 at 21:08

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