The Fibonacci sequence is fixed, but the digit patterns are not.
The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...) is the same in every base, but palindromes, digit patterns, and terminal digit cycles all change.
The Pisano period π(b) is the period of the Fibonacci sequence mod b — equivalently, the cycle length of the last digit. In base 10 the last digit repeats every 60 terms; in base 7, every 16.
Numbers in red are palindromic Fibonacci numbers.
Numbers in blue mark Pisano period boundaries (where the last-digit cycle restarts).