For what it is worth, you don’t even need a pattern to have information. The wind blowing one rock into another leaving a scratch is information (you don’t even need the scratch, but a scratch is nice because you can see it with the naked eye).
So the result of the first die roll is already some information.
ETA: I can hear myself asking: how much information is contained in the roll of a die (with 6 equal likely “sides”)? It is log base 2 of 6, or about 2.6 bits of information.