1. What is the 1/f fluctuation? (Fluctuation Type)
As some older people may remember, a 1/f fluctuation fan was released in the 1980s. At that time, I did not know much about 1/f fluctuation and wondered what this kind of fluctuation was. When I looked into it, I was surprised to find that this 1/f fluctuation is often seen in our environment, but its mechanism was not well understood. In the process of researching the mechanism, I came up with a model and have recently reached a convincing conclusion based on this model. In my stories, I intend to write about 1/f fluctuation and the relationship between science and Buddhism based on my conclusion.
I will start by explaining what 1/f fluctuations are.
Fluctuation is sometimes called “noise”.
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There are three main types of fluctuations in nature and our environmrnt.
First, “white noise” is a fluctuation whose spectrum has approximately the same intensity at all frequencies. In the case of light, white light has the same intensity at all frequencies, so this kind of fluctuation is called white noise. Here, “spectrum” is a classification of the strength of sine waves (trigonometric functions) of different frequencies f, when a noise signal is considered as a superposition of sine waves of different frequencies f. If you imagine that light is divided into seven different colors by a prism, you can easily understand this situation. In white noise, there is no correlation between the signals, and the noise is completely irregular.
The second is “Brown noise”. When a tiny particle floats in water, the collision of many water molecules from different directions causes the particle to move randomly, and Brown noise, first discovered by Robert Brown, is like signal noise that is generated by this motion. Brownian motion is also called “drunken walking” because it resembles the motion of a drunkard. The spectrum of this noise or fluctuation is inversely proportional to the square of the frequency f, or 1/f². Thus, the spectrum has a very strong component at low frequencies and rapidly weakens as the frequency increases. The low frequency component is the “red light” in light, which is why it is also called “red noise”. Brown noise is a fluctuation in which the value of the fluctuation at a given time is strongly influenced by the value just before it, as can be understood by the fact that the next step starts from the position just before it when walking drunk. This type of fluctuation is called a Markov process.
The third type of fluctuation is “1/f noise”, which is the subject of my interest. As the name suggests, it is a fluctuation whose spectrum is inversely proportional to the frequency f. The spectrum of this fluctuation is strong in the low frequency range and weak in the high frequency range, but this tendency is not as strong as brown noise, so it is also called “pink noise” in the sense that it lies between red and white noise.
As mentioned above, the generation mechanisms of the first two of these three types of fluctuations are well known. However, the mechanism of the last one, 1/f noise (fluctuation), is not clearly understood.
In the following several stories I will focus on this 1/f fluctuation and give my idea of its generation mechanism.
