What is chaos theory?

Chaos theory can be described as "science of surprises".

It revolves around non-linear and unpredictable systems, and teaches us to expect unexpected things. Most areas of science focus on solving predictable models, such as gravity, chemical reactions, and electricity. Chaos theory focuses on completely unpredictable or controlled models, such as disturbance, weather, and stock markets. These phenomena are often described by classification mathematics, which revolves around the infinite complexity of nature. Many objects in nature have identifiable attributes, including landscapes, clouds, trees, internal organs, rivers .; Many systems that we live in include complex, chaotic behavior. Before speaking more deeply about the principles of chaos theory, take a brief look at chaos theory.

History

Edward Lorenz.

In 1961, a meteorologist named Edward Lorenz made a remarkable discovery. Lorenz took advantage of the latest computer of the time to forecast the weather. He was extremely excited with the idea of ​​creating a mathematical model to solve unpredictable models. In this mathematical model, he loaded in a set of accurate representations of the current weather; This set of numbers will predict future weather a few minutes from the current time. After successful implementation of the program, Lorenz focused on improving long-term predictability. This can be done by returning the forecasted feedback of the previous forecast data to the computer. As a result, Lorenz's model can be accurately predicted every month, even year by year, not just by minute as before.

One day Lorenz decided to run the weather forecast again. Because he wanted to save time, he did not choose to start over, instead taking a value that had run half in the computer program and used it as a starting point to restart the program. After drinking coffee, he turned around and discovered something completely unexpected. Although the new predictions of the original computer were the same as before, there are two sets of forecasts that differ significantly. Is there any error in calculation?

Lorenz quickly realized that the computer produced predictive results in the form of 3 decimal places, but the numbers put into the initial processing had 6 decimal places. That is, while Lorenz started the second run of the program with 0.506, the first run actually used the 0.506127 number. A different part in thousands of other parts has resulted in a remarkable result. It is like a blow of a butterfly's wing can create a gust of wind blowing into your face. The initial weather conditions were almost the same, but the latter two were not the same. Lorenz found the seeds of chaos.

The principles of chaos theory

There are many other theories in chaos theory. The most famous and important theory is "Butterfly Effect" - a butterfly flapping its wings in New Mexico can cause a storm in China. From flapping wings to the formation of a big storm can take a very long time, but there is a relationship between them. If the butterfly does not flap its wings at a specific point in space / time, the storm will not occur. A more understandable and philosophical example to describe this effect is that, the smallest actions we take will lead to a significant impact in our lives for a long time. long.

Butterfly effect

The next branch of chaos theory is "Unpredictable" (Unpredictability) . It is a fact that we can never know all the initial conditions / conditions of a complex system, meaning that we cannot hope to predict the final result. that a complex system will create. Even the slightest errors in monitoring the status of a system will be greatly amplified, making every forecast incorrect. Because it is impossible to assess the effects of all butterflies and disturbing actions similar to a butterfly's wings in the world, accurate forecasting of weather over a long period of time will always be the thing. impossible.

The third theory is "Mixing" (Mixing) and "Feedback" (Feedback) . "Mixing" or "Disturbance" implies that the two adjacent points in a complex system will eventually be in very different positions after a certain period of time. An example of this theory is that two water molecules lie close to each other, but then "one person at a time", wandering somewhere in different parts of the ocean, or even in different oceans. . A group of balloons dropped into the sky together will also fall in very different locations. Regarding "Feedback", systems often become chaotic when there is the presence of feedback. An example of this behavior is the behavior of the stock market. When the value of a stock rises or falls, people tend to buy or sell that stock. This in turn contributes to the price impact of stocks, causing its value to continue to increase or decrease further chaos.

Mandelbrot Fractal.

One of the last things to talk about when discussing chaos theory is "Fractional" (Fractal) . A distinction is a geometric pattern with no end points. They are infinitely complicated motifs that when you zoom in or zoom out at a certain rate, the result still gives an original similar pattern. They are created by repeating a simple process over and over again in an ongoing feedback loop. With the core being recursive, the classification is an image of dynamic systems - a picture of chaos. Geometrically, they exist in our familiar dimensions. The patterns are extremely familiar, because in nature there are many such patterns, including the composition of trees, rivers, coastlines, mountains, clouds, shells, storms . Very many other subjects are related to chaos theory, but the above mentioned subjects are the most interesting and important things.