I have always been fascinated by the book "Contact" by Carl Sagan. The final chapter of the book (not the film!) reports about an anomaly in the n-millionth decimal of pi, optimally visible when pi is calculated in base-11 arithmetic: A series of only ones and zeroes, composing a digital image of a circle.
My question: If there really exists such an anomaly in some base-n arithmetic for the decimals of an irrational constant, would it be detectable at all in base-m arithmetic? Would it stand out to a mathematics professional? Would it be visible to the untrained eye like mine?
In short: Assuming such an anomaly exists in base-17, and I start calculating pi in base-13 arithmetic, would I be able to detect the anomaly? How?
EDIT: The anomaly presented by Carl Sagan (I didn't reread the details) was something like this: Hidden in the representation of pi in base-11 is a section of the digits only zeroes and ones. This section has the size of a prime squared (to make it likely to try a two-dimensional approach), and if laid-out as a true square, the zeroes and ones look like a circle. I imagine something like this:
00000100000 00011011000 00110001100 00100000100 01000000010 01000000010 01000000010 00100000100 00110001100 00011011000 00000100000
My question is a little more generic, if patterns like this can be easily found, even if not the correct base is used for the analysis.