Chaos theory/Butterfly Effect

Every single time you interact with other people you change the future.

Just blowing your horn in traffic could prevent a marriage, murder, accident, suicide etc...

Drving slow could do same as you displace what would happen if you were not involved. SO if you want to have a huge impact on the future get out and do stuff that gets other peoples attention or changes there direction. It is probably impossible to actually track, and see what changes you make but you certainly are doing so.

If you sit at home in front of a T.V all alone you are still changing the future by not being else were.

Just smiling at someone may cause the birth of a future President!

Really wierd if you think about it.

Good ATS topic!!



[edit on 25-9-2004 by Xeven]

I find for even integer powers of m/n the max seed value is (b+1/a)^(n/m)
This works even when a*b < p , p being the optimal chaotic produce of a & b

For odd integer powers of m/n the max seed value is essentially 1 (0.999999999)
it does drop when a*b < p , but i have not figured how this works.

I am thinking there should be some macro formula that works for both odd and even integer m/n values and hopefully for fractional values as well.

*putting goggles on* Clyde Crashcup shall return!

edit: transcription error

[edit on 30-9-2004 by slank]

< < < c R a S h ! > > >
Clyde Crashcup has returned . . .

In my totally inept mathmatical way i have thought of a possible comprehensive wrapper 'max seed value' function.
cos((m/n)*pi/2)*(b+1/a)^(n/m) + sin((m/n)*pi/2)(additional term here . . .)

this formula works when m/n is an even integer when a*b < = p
it also works when m/n is an odd integer but only when a*b = p

The acid test would be if it worked when a*b < p and an odd integer and also when m/n is not an integer

Off to try some acid.
edit: transcription error

[edit on 30-9-2004 by slank]

.
< < < c O l L i S i O n ! > > >
dilute acid solution has produced . . .
cos((m/n)*pi/2)*(b+1/a)^(n/m) + sin((m/n)*pi/2)*(b^(n/m))
thought: easier formula i believe might be (b+cos((m/n)*pi/2)/a)^(n/m)
The main question is if the sine, cosine mechanism works for non-integer values.
(note: for odd m/n a*b must be equal to or less than p for it to be essentially chaotic.)
Stay tuned for the next Riveting installment . . .
edit: formula error

[edit on 30-9-2004 by slank]

.
experimentally for the limited cases where m/n is a non-integer i have tried the max seed value is b^(n/m)
so the previously suggested sine cosine idea didn't work.
Alternatively I thought it could be an imaginary value that would work better:
max_seed = ( b - (i^(m/n))/a )^(n/m)
That would cause the 1/a value to become imaginary for any case except where m/n is an even integer.
Not sure what the implications of this might be, except perhaps x should be a complex variable.
Am out of my depth here.
.

Tried one sample of a complex 'x' variable for m/n=1 ; it went asymtotic for all values other than zero.

Have found a new chaotic function:

4*(sin(0.3*x)-cos(x))

The 4 coefficient determines chaotic qualities of function,
zero to about 1.5 it converges
from about 1.6 to 3 it goes from simple to complex rythyms
about 3.5 it begins to get somewhat chaotic
at 4 it is definitely chaotic
seems to converge around 6.8 or 6.9
at 7 it goes to a tight rythym
7.3 goes chaotic
at around 9 it gets rythmic again.
will need to explore this to see if i can come up with a predictive numerical explanation.

I believe to get a chaotic function you have to have some kind of continuous curve that rises and then falls again, like a negative parabolic that is shifted above the x axis. [read upside down 'U']
It may need to be a parbolic type curve with a single rise side and a single fall side, I'm not sure whether or not it would work with a multiple hump curve.
.

.
New Chaos function:
abs(((1-(x-1)^2)^0.5)-((1-x^2)^0.5))
Which is simply the upper right quadrant of the unit circle about the origin and about (1,0)
and taking the absolute value of the difference between the two.

I tried using a simple circle and then an ellipse but had no success creating chaos.
But when i tried this difference it worked.

I am beginning to think chaos depends on a difference between two functions, but have no
proof of that. All of the chaos functions so far I have run across are the difference between
two functions.
.

I think this is a great topic , and it is true a chain of actions of thoughts change the future for instance if hitler's mother was unable to have children no ww2, alot more people, maybe no cold war, just like today if a man stops to tie his shoe he could be killed by any number of things, what a deadly world we live in