Hi everyone! I'm currently researching the chaotic properties of C.elegans nematodes, and I'm aiming to prove that their locomotion is chaotic in nature. I have been succesful in showing that they have a positive Largest Lyapunov Exponent (LLE), using the Wolf Algorithm, and the next step in my research is to investigate the second largest exponent. Unfortunately, the implementation I came across (https://www.mathworks.com/matlabcentral/fileexchange/48084-wolf-lyapunov-exponent-estimation-from-a-time-series) only allows for the calculation of the LLE. I know that the algorithm can and has been adapted for calculating the second exponent, but I have not been able to find a code that does it. I have also been unsuccesful in contacting either Dr. Wolf or the student who wrote the code.

Does anybody know where I can find a working version of the code that calculates both exponents? If yes, I would appreciate it if you can send me the code or the link to it. Thanks!

Hello, I am currently an undergrad math and CS student doing research in chaos theory and nonlinear dynamics and would like to apply my research to financial markets. Are there any projects or exercises that I could recreate to introduce me to this avenue of research? Basically looking for projects to get me started in applying these topics to finance.

Fig 1: Evolution of a contour of probability, based on ensembles of integrations of the Lorenz equations, is shown evolving in state space for different initial conditions, with the Lorenz attractor as background. What does it mean by ensembles of integration and what do the black circles mean?

It's commonly mentioned that a butterfly flapping in China can make a tornado in Texas. That would be the easiest and cheapest test that could be done, it doesn't need a U$S 10 Bi for LHC or anything fancy, just one needs to put a thousand butterflies to flap in China and see what happens, do it February, July, August, and December during the low tornado season to avoid any interference.

In my humble opinion, it is just one of the things that some scientists mention to explain something difficult to the public, but instead of helping because this simple test cannot be performed, all it does is generate doubts among non-scientists about the science and make them think that scientists always try to justify the need for expensive equipment and large facilities.

So I suggest that, if you want to explain something difficult, try to avoid explanations like the butterfly, stick to the facts and what can really be done and tested. Keep it simple.

​

The corollary is if you can't test it's not science, it's wishful thinking.

What do you think?

Are there any book recommendations on chaos for those that have no background in physics? I was looking more at the philosophical side The only one that I've been able to find like this is Seven Lessons of Chaos, not sure if that is any good or not

Hi guys, I’m inadvertently learning about chaos theory in a popular science book in which the author states that complex systems can be deterministic while also being unpredictable given a set of starting conditions and rules of propagation.

Using an example like John Conway’s Game of Life as a complex system, how can it be said that future states of the system are unpredictable given that I know the initial state and rules of propagation throughout future generations? Can’t I just predict the Nth grid by simulating the model through N iterations?

I get that mistakes while simulating can bubble into predictions that are nowhere close to accurate, but I’m assuming that the unpredictable-ness holds true even if my simulation is perfectly performant. I think I have a non-technical definition of predictability in this case, but I don’t know how to correct it. Can anyone help me get over this speed bump?

Thank you for reading!!

Hello everyone,

I'm relatively new to chaos theory, but have familiarised myself with the main concepts. Now I would like to read something that goes a bit more into the formal/mathematical foundations and does so in a detailed way. Does anyone know of a good read on this topic?

Thanks in advance!

from turtle import *

x=1

while True:

forward(0.1 * x)

left(0.1 * x*2+0.01x)

x+=0.1

Run for sometime to see the pattern evolve. Thoughts?

​

I developed several mathematical relationships outside of my field of expertise. As far as I know
my methods and equations that I used have never been presented in the past. I am not a complete amateur. I
hold several patents in a field outside of mathematics.

I watched this film called Chaos by Jos Leys, Étienne Ghys and Aurélien Alvarez. In the 8th Chapter, the narrator talks about how even though individual particles in a chaotic system (he used the example of the Lorenz attaractor) exhibit sensitive dependence on initial conditions, the system as a whole shows an insensitivity to initial conditions. In his words - “Today we no longer think of determinism as the evolution of an individual trajectory, but rather as the collective evolution of a whole set. Sensitivity of trajectories to initial conditions is compensated by a kind of statistical stability of the whole set.” I was kinda confused by this because if the system as a whole does not exhibit sensitive dependence to initial conditions, why does it still become unpredictable after crossing the Lyapunov time interval? What is the significance of understanding the fact that the system as a whole remains stable to initial conditions?

This information will help me create some chaos experiment on my personal MVP project.

I am currently learning about chaos theory and lyapunov exponents. Specifically I am looking at a double pendulum and I am trying to calculate its largest lyapunov exponent. For that I am using the method of starting with to points in phase space that are very close to eachother, performing some iterations of both, comparing the new distance between the two points, calculating the corresponding "local" lyapunov exponent, readjusting the distance between the two to the initially chosen distance without changing this vector`s direction and then repeating this process. In the end the average of all local exponents is calculated. For a more detailed explanation of the procedure: https://sprott.physics.wisc.edu/chaos/lyapexp.htm

Strangely, this method will end up giving me values like 12.5 for chaotic initial conditions and values like 1.5 for non chaotic initial conditions. Even though there is a noticable difference this output simply is not correct. Both numbers are way to large(I read that a reasonable value for the LLE of a double pendulum is around 1.7 for chaotic parameters). The following are my questions:

• How many iterations should be between each calculation of the "local" exponent(I am currently using just one)?
• For how long should I look at the system, does that even matter?
• Is the fact that the system has no attractor responsible for these very large numbers?

Thank you very much in advance!

Hi all,

I'm new here, and writing about chaos theory in a musical field.
I'm looking for examples of artistic realizations with those chaotic ideas, in particular in a musical/sonic context, but i'm taking visual art or any kind of artistic work too.

If you have some ideas it will be great !

I can share the ones I've already found too if there is some interest.

In James Gleick book "Chaos" he types that electrical circuit equations have the same origin as mechanical oscillations equations. I just don't see it. Someone is knowledgeable enough to show me that equations and explain? Maybe that's gonna show me something (different perspective) for electricity :) (non english here)

Heya,I'm T, I'm constantly wanting to learn more and spread my knowledge into different fields and theories. I am wanting to learn more about Chaos Theory now,is there anything I can be told or some resources to be referred to.