**Butterfly effect** . It refers to the sensitivity of the initial conditions within a system , within the framework of *Chaos Theory* . The notion assumes that the slightest variation in the conditions of a system can cause it to evolve in entirely different ways. Therefore, a small initial disturbance, through an amplification process, can generate a very large effect.

## Summary

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- 1 Origins
- 1 Chaotic systems

- 2 Butterfly effect
- 3 Sources

## origins

The physics as known, is relatively recent. This does not mean that in antiquity, the human being did not pretend to give a more or less rational explanation to the natural phenomena of the world around him, especially when he verified certain regularities.

These regularities served him to predict future events, and not only that, to find synchronies between certain phenomena. However, both the scientific knowledge based on rigorous experiment and the equally rigorous application of mathematics to physics are recent.

### Chaotic systems

For Poincaré the chaotic systems were determined by a set of initial conditions, however these could never be known with absolute precision and consequently little by little the memory of them would be lost and the systems would become unpredictable.

Deterministic laws were followed, but the exact solution of the equations involved was impossible. Thus, for example, planetary systems, prototype of the maximum cosmic clock, seem to evolve according *to Kepler’s laws* , which can be deduced by application of Newton’s and the law of gravitation , however these laws are only rigorously valid if interactions are not considered. between the different planets.

However, these do occur and produce infinitesimal disturbances in the motion of the planets. Therefore, it cannot be assured that these disturbances will not end up over time by unbalancing the whole and that it may become “chaotic”.

Curiously, the disturbances referred to are not a product of chance, they are a consequence of Newton’s own laws .

Poincaré’s ideas were somewhat forgotten, although the progress of physics continued with two breaks:

*The Theory of Relativity*, in which space and time were no longer absolute and the mass of a mobile depended on its speed.*The quantum mechanics*, in that the measured-object binomial instrument measure – bound third wheel, the operator, and the measurement accuracy was limited intrinsically by the Heisenberg uncertainty principle.

Around 1960 , the meteorologist Edward Lorenz was studying the behavior of the atmosphere , trying to find a mathematical model or set of equations that would allow the behavior of large air masses to be predicted from simple variables, using computer simulations . In other words, such a model would allow for weather predictions.

Lorenz made different approaches until he managed to fit the model to the influence of three variables expressing how they change over the time the speed and temperature of the air. The model was made up of three fairly simple mathematical equations known today as the *Lorenz Model* .

## Butterfly effect

Lorenz was greatly surprised when she observed that small differences in the starting data (something apparently as simple as using 3 or 6 decimal places) led to large differences in the model’s predictions; in such a way that any small disturbance in the initial conditions of the system, could have a great influence on the final result. For this reason it was very difficult to make long-term weather predictions.

The empirical data provided by meteorological stations today have inevitable errors, if only because there are a limited number of observatories unable to cover all points on the planet . This causes the predictions to deviate from the real behavior of the system.

Lorenz attempted to explain this idea by a hypothetical example. He suggested imagining a meteorologist who would have been able to make a very accurate prediction of the behavior of the atmosphere , using very precise calculations, and using very accurate data.

He then suggested that such a prediction could be totally wrong because he had not taken into account the flapping of a butterfly on the other side of the planet. That simple flutter could introduce disturbances into the system, leading to the prediction of a storm .

From here came the name of ** the butterfly effect** that, since then, has given rise to many variations and recreations.

It is the amplification of errors that can appear in the behavior of a complex system.

The ** butterfly effect** is one of the behavioral characteristics of a chaotic system, in which the variables change in a complex and erratic way, making it impossible to make predictions beyond a certain point, which is called the prediction horizon.