Last time we have seen that we can recover power-law distribution from a superposition of exponential distributions. This idea served a basis for our [1] paper. When presenting some of these results at a conference I was asked question if exponential distribution is necessary, can't one use normal distribution instead?

Would you like to code your own cellular automata program? Similar to our Wolfram's elementary automatons or (more than likely (partially because our app is really old)) better? Watch the following video by the Coding Train channel to learn how to do that using p5.js library.

In the previous post we have asked a simple question - what if gap duration is distributed according to a power-law distribution. Our answer was an apparently pure 1/f noise. But how could the power-law distribution arise? While in some materials some quantities indeed follow power-law distribution (such as blinking times in quantum dot experiments [1]), most materials have exponentially distributed generation and/or recombination times. So then, can we construct a power-law distribution from superposition of exponential distributions?

In the last post we have assumed that the event rate of the individual processes making up the superposition needs to be distributed according the bounded Pareto distribution. And we have seen that in \( \alpha = 0 \) case, 1/f noise will be obtained. But superposition of such processes seems to be very demanding assumption, maybe we can choose another assumption? Here we will see what happens if we assume that gap times are assumed to follow bounded Pareto distribution, while the pulse times will still follow exponential distribution.

Recently we have been looking a lot into Poisson process and other related more physical topics. But the things we have been talking about also applies to our earlier more social science related works. This video by Mathemaniac discusses how the statistical methodology behind the Poisson process can be used to understand queues. As usual, we invite you to watch this fascinating video!