"Pink noise or 1/f noise is a signal or process with a frequency spectrum such that the power spectral density (energy or power per frequency interval) is inversely proportional to the frequency of the signal. Pink noise is one of the most common signals in biological systems."
Additional Excerpts From:
https://www.dsprelated.com/showarticle/40.php An Interesting Fourier Transform - 1/f Noise
"Power law functions are common in science and engineering. A surprising property is that
the Fourier transform of a power law is also a power law."
"Now we come to a feature that I find absolutely fascinating. In general, we have seen that a power law in one domain corresponds to a power law in the other domain. Further, there is an inverse relationship; if the time domain decays faster, then the frequency domain decays slower, and vice-versa."
"1/f noise has been observed in the strangest places- electronics, traffic density on freeways, the loudness of classical music, DNA coding, and many others."
"At least in a limited sense, 1/f noise is its own Fourier transform."
"However, no one knows what the phase of 1/f noise is, or even if it has a defined phase."
"Nevertheless, the idea that 1/f noise is its own Fourier transform is very compelling. Consider the Gaussian curve, the most important waveform associated with random events. The Central Limit Theorem tells us why the Gaussian is so commonly observed. However, it is also true that the Fourier transform of a Gaussian is a Gaussian. This seems more than coincidence– I think it is a critical clue in solving the mystery of 1/f noise."
Some interesting ideas and relationships, are they not?