Randomness in pi and other irrational numbers

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This is a post I read about pi while looking for stuff about tau -which is two times as much as pi.

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This makes me wonder, why does only pi contain such randomness? Don't other non-repeating and non-terminating numbers (like $sqrt(2)$) also have the same quality? Is this just a silly post that is only being biased towards pi, or is this random behavior only inherent to pi?

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The simplest example of a "universe" number is the Champernowne constant,

$$0.12345678910111213141516\dots$$

Among others, it contains the $n$ first decimals of $\pi$, for any $n$.