The Equation That Changed The World
(Chaos Theory)
In physics (in fact, in science) all laws are, more or less, deterministic.
That means small changes in initial conditions will result in small difference in ultimate outcomes but there is a theory, #ChaosTheory that tells us that in a complex system, small changes in initial conditions will result in vastly different outcome. These differences will increase over time.
Look the equation, this is #RobertMay's Logistic Map.
Let's take a glance :-
Definition :-
The logistic map is a one-dimensional discrete-time map that, despite its formal simplicity, exhibits an unexpected degree of complexity.
It is one of the simplest non-linear recursive equations that have chaotic behaviour. This dynamical equation is polynomial of degree 2.
Explanation with example :-
This equation defines the rules, or dynamics, of our system.
Suppose, x represents the population at any given time n, and k represents the growth rate, then the population level at any given time (n+1) is a function of the growth rate parameter and the previous time step’s population level. If the growth rate is set too low, the population will die out and go extinct. Higher growth rates might settle toward a stable value or fluctuate across a series of population booms and busts.
We see chaotic behavior - behavior sensitive to initial conditions - like this in many areas.
#Weather is a classic example - a small change in atmospheric conditions on one day can lead to completely different weather systems a few days later, most commonly captured in the idea of a #butterfly flapping its wings on one continent causing a hurricane on another continent.
Example fields influenced by Chaos theory :-
- Game theory
- Machine Learning
- Predictive analytics
- Business Intelligence
- Deep Learning
- Internet of Things
- Bigdata Analytics
