This tends to happen with many a complex entity. The number of configurations something has rises exponentially with the number of its building blocks, be they neurons or snowflakes. Dump 10^12 snowflakes on the lawn and you will find a vast number of combinations, no two alike. There's no question that neurons are even more complex than snowflakes - not the least of which because the properties of snowflakes are not synergistic: they do not enhance each other. Neurons do. The brain has been described as the most complex thing in the universe. It is no wonder that it produces complex patterns unrivaled in the universe. That does require it to have any ineffable qualities beyond those we see.