The second important feature of power law is fractal.
The author's connection between power law and fractal makes me instinctively curious, or rather skeptical.
Later, I found the problem because when I saw the following "power law distribution function", an expression of exponential function appeared in my mind! I confused the power law distribution with the exponential distribution.
My first reaction to this question is: power law, exponent and fractal must all be derived from mathematical concepts, right? !
Go back to the source and find the corresponding mathematical definitions and expressions of these concepts.
The more valuable materials found are:
1. Definition and difference of exponential distribution and power law distribution (Poisson distribution and gamma distribution)
2. From exponential decay law to power law distribution law-weak but not too weak strong minority.
Comparing the probability density expressions of two distributions together is the name given according to the function type of their expressions.
Draw them in the same linear coordinate system, and the similarity is difficult to distinguish. But if you put it in a log-log coordinate system, it is easy to distinguish. In logarithmic coordinate system, the curve of power law distribution is a straight line.
The final conclusion seems to convince myself.
In order to verify whether this conclusion is correct, we can try to do the following some other days: deduce several conclusions according to this logic, or do several functions according to this law, and then draw graphs to see if these graphic effects really have the characteristics of "fractal".
Harvest: The understanding of power law distribution and fractal is deepened, and some basic concepts are further distinguished, such as [power function, exponential function]? With what? Power law distribution function and exponential distribution function are completely different concepts and belong to two systems. Although they are related to some extent, their connotations are quite different, so they can't be linked roughly according to the literal meaning.