# Fractals, Chaos and Non-linear Dynamics

• aricho
In summary, the movie "The Bank" revolves around a mathematical genius who has spent years researching and utilizing Fractal geometry, chaos theory, non-linear dynamics, and the work of Mandelbrot to predict the exact movements of the stock market. He believes that by being able to predict infinity, predicting the stock market becomes an easy task. However, there is debate on whether this is truly possible given the complexities and unpredictability of the market. It is suggested that learning about neural nets, stochastics, Markov models, and operations research, as well as programming, would be helpful in understanding and potentially predicting the stock market. Some argue that predicting the market relies heavily on expert opinions and cannot be fully measured or predicted due to factors
aricho
in the movie "the bank" a mathematical genius predicts the exact movements of the sharemarket after years of research and attempts. he uses Fractal geometry, chaos theory, non-linear dynamics and of special interest to him was the work of mandelbrot and his work regarding fractals.

He says, "if we can predict $$\infty$$, then predicting the stock market is easy."

Firstly, is this possible?

Secondly, To be able to predict the exact movements of the market in a defined 30 minute space for example, before it happens, what inputs would be needed? (like previous price data?, economic probability?) how would it be applied?

I am immensley interested in this and would appreciate any help,
Thanks

Well, correct me if I am wrong, but stock markets depend on what a lot of experts think. But due to the Heisenberg's Uncertainty Principle we would not be able to fully measure such a thing.

We could probably get a lot of approximations of the stock market with varying degrees of accuracy my simplifying the whole thing, but beyond that I don’t see what can be done.

hmm

well excuse my language but this actually is a correct term for traders. a "big swinging dick" is a person who is famous for their trading, and are so closley watched, every thing they do is copied and therefore has an effect on the market. the main forces on the market are supply and demand.

Keeping this in mind, and also "if we can predict $$\infty$$" do you think it's possible?

any school with classes in Neural nets(optional)/ stochastics / markov models and operations reserach shouhld give you the materials you need. Be sure to learn programming as well since this will be your application

...as for inputs like weather and disease you input the prior few years depending on the range of research your doing. mmm i think it was the measles was done at a period of 60 years input

aricho said:

I am immensley interested in this and would appreciate any help,
Thanks

Start simple: the quintessential reference, "Chaos and Fractals" by Peitgen.

neurocomp2003 said:
...as for inputs like weather and disease you input the prior few years depending on the range of research your doing. mmm i think it was the measles was done at a period of 60 years input

ok, so i imput the past into the magical black box formulae to predict the future?
would anything else be needed? like probability ect...?

aricho said:
well excuse my language but this actually is a correct term for traders. a "big swinging dick" is a person who is famous for their trading, and are so closley watched, every thing they do is copied and therefore has an effect on the market. the main forces on the market are supply and demand.

Keeping this in mind, and also "if we can predict $$\infty$$" do you think it's possible?
I don't even know what you mean by the phrase "if we can predict infinity", it seems nonsensical to me, I deal with infinity day in and day out in maths classes, I don't quite get what that means.

But yes, these people are very good at "approximating the market", if they knew things exactly then they'd probably be a lot richer...

it sounds lke nonsense (predicitng infinity) and is just film making dressing thigns up. dynamical systems and stochastic processes are used to study the markets (what do you think quant analysts do?). there is a limit to any model's accuracy since the mathematics is only an approximation (you realize that the boom of the 80s when people got disgustingly rich was a mathematical one - a bunch of mathematically trianed people figured that they could do a better job of predicting the markets than traders operating on hunches). Heck, you can even do degrees with financial mathematics in them. but to absolutely and completely predict anything with 100% accuracy that is that complicated we know to be impossible, and that isn't even allowing for "human factors" such as a terrorist attack.

You know what, how fitting for such a thread: We got, I don't know, 5 or 6 different models to predict the path of hurricane Dennis and they're all different! Way to go guys . . . I'm watching two butterflies outside of my window right now fluttering aroung the azelaes . . . a storm is brewing . .

Zurtex said:
Well, correct me if I am wrong, but stock markets depend on what a lot of experts think. But due to the Heisenberg's Uncertainty Principle we would not be able to fully measure such a thing.

We could probably get a lot of approximations of the stock market with varying degrees of accuracy my simplifying the whole thing, but beyond that I don’t see what can be done.

Heisenberg's Uncertainty has little to do with stock market fluctuations, or any other deterministic classical chaotic system. It pertains only to quantum indeterminacy.

Curious3141 said:
Heisenberg's Uncertainty has little to do with stock market fluctuations, or any other deterministic classical chaotic system. It pertains only to quantum indeterminacy.
What I meant is that you could not measure what somebody was actually thinking because that would alter it. Surely stock market predictions of 100% accuracy would require to actually know what everyone is thinking who would affect the market?

Or am I in fact over thinking the situation?

he says stuff like, "with this mathematics, things that we never though possible to predict now can be. e.g. cloud formations" also, he is trying to predict "sentiment" in a way.

"all the current methods of prediction do the same thing, try to predict what one person is going to do, but trying to predict what 100 people will do is much much eaiser"

He uses fuzzy logic, Mandelbrot fractals, chaos theory, fuzzy logic and nonlinear dynamics.

Is it possible to use these things to predict the markets?

aricho said:
he says stuff like, "with this mathematics, things that we never though possible to predict now can be. e.g. cloud formations" also, he is trying to predict "sentiment" in a way.

"all the current methods of prediction do the same thing, try to predict what one person is going to do, but trying to predict what 100 people will do is much much eaiser"

He uses fuzzy logic, Mandelbrot fractals, chaos theory, fuzzy logic and nonlinear dynamics.

Is it possible to use these things to predict the markets?
He uses fuzzy logic twice then?

That is nonsense, what you are able to do is 'approximate' what things are going to do. When you have more data (e.g more people) it means that you take an average that will generally follow a trend, however it means you have to take out the possibility of extreme circumstances.

Zurtex said:
What I meant is that you could not measure what somebody was actually thinking because that would alter it.

But what does even a single person's thought have to do with Heisenberg's UP ? Quantum effects are important in the state of individual electrons, less important in the behaviour of a single neurone, and surely completely annulled by averaging out in the behaviour of an entire forebrain. At least that's what I would assume, but it doesn't seem unreasonable.

Surely stock market predictions of 100% accuracy would require to actually know what everyone is thinking who would affect the market?

The individual may be a difficult quantity to predict, but the herd is predictable, for the most part.

Or am I in fact over thinking the situation?

Maybe just a little.

can we please just dismiss thi sfilm as being a complete load of &$^£*&$&&£ (use your preferred expletive).

## 1. What are fractals?

Fractals are geometric shapes or patterns that have a self-similar structure, meaning they look similar at any scale. They are created through the repetition of a simple pattern or process.

## 2. How do fractals relate to chaos and non-linear dynamics?

Fractals are closely related to chaos and non-linear dynamics because they exhibit chaotic behavior, meaning that they are highly sensitive to initial conditions and can produce complex, unpredictable outcomes. Fractals can also be generated through non-linear equations, demonstrating the connection between fractals and non-linear dynamics.

## 3. What is the significance of fractals in science?

Fractals have many applications in science, including in the study of natural phenomena such as coastlines, clouds, and blood vessels. They are also used in computer graphics, data compression, and modeling complex systems in physics, biology, and economics.

## 4. Can fractals be found in nature?

Yes, fractals can be found in many natural systems, such as trees, snowflakes, and mountains. These systems exhibit self-similar patterns and are often generated through non-linear processes.

## 5. How are fractals used in technology?

Fractals have been utilized in various technologies, such as in computer-generated images and animations. They are also used in data compression algorithms to reduce file sizes and in antenna designs for better signal reception. In addition, fractal geometry is used in the development of efficient and sustainable urban designs.

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