This is nothing more than numerology... just parodeilia in another form.

Illuminating, in that it shows just how powerful the human brain is at pattern matching and finding false order in even random noise, particularly if we help it out by working the data a bit to produce a pleasing result.

Random? Why yes. See, the current conjecture is that Pi is a Normal Number:

https://en.wikipedia.org/wiki/Normal_number

"[This] means that no digit, or combination of digits, occurs more frequently than any other, and this is true whether the number is written in base 10, binary, or any other base."

Put another way, "A normal number can be thought of as an infinite sequence of coin flips (binary) or rolls of a die (base 6)."