>>6
The number shown by
>>5 is an example of a "non-periodic pattern", although I'm not sure if that's what it's actually called or if he made up that term (I suck at vocab). Either way, the number he has shown does have a pattern, you could write up a program to write it digit-by-digit using simple rules.
Here's a classic example quoted out of the book "The Art of the Infinite - The pleasures of Math".
"1. print 5.
2. print one more 6 in a row than were printed before the “5” of the previous step.
3. return to step 1.
Once we set the machine in motion it prints “5” after the 0. initially there, giving us
0.5
then, because there were no 6s printed before the 5, it prints one 6:
0.56
and cycling back to its first order, prints 5 again:
0.565
now it will print two 6s
0.56566
then a 5, then three 6s
0.565665666 . . .
You see the pattern of this non-repeating pattern: the strings of sixes grow ever longer, and no cycle can possibly occur. We have, with a few words, cast an infinite line with an irrational hooked on its receding end—an irrational which has a unique location, somewhere between 56/100 and 57/100."
As you can tell the pattern generated is "non-periodic" because it doesn't repeat in a set period, although that doesn't mean that it's not a pattern (even though it is still irrational).