I thought of this example of a complex system that you can understand but not know. You can understand the system and all its elements but not know what it's next state will be.
From Alice’s Adventures in Wonderland by Lewis Carroll
"Get to your places!" shouted the Queen in a voice of thunder, and people began running about in all directions, tumbling up against each other: however, they got settled down in a minute or two, and the game began.
Alice thought she had never seen such a curious croquet ground in her life: it was all ridges and furrows: the croquet balls were live hedgehogs, and the mallets live flamingos, and the soldiers had to double themselves up and stand on their hands and feet, to make the arches.
The chief difficulty Alice found at first was in managing her flamingo: she succeeded in getting its body tucked away, comfortably enough, under her arm, with its legs hanging down, but generally, just as she had got its neck nicely straightened out, and was going to give the hedgehog a blow with its head, it would twist itself round and look up in her face, with such a puzzled expression that she could not help bursting out laughing; and, when she had got its head down, and was going to begin again, it was very provoking to find that the hedgehog had unrolled itself, and was in the act of crawling away: besides all this, there was generally a ridge or a furrow in the way wherever she wanted to send the hedgehog to, and, as the doubled-up soldiers were always getting up and walking off to other parts of the ground, Alice soon came to the conclusion that it was a very difficult game indeed.
The players all played at once, without waiting for turns, quarreling all the while, and fighting for the hedgehogs; and in a very short time the Queen was in a furious passion, and went stamping about, and shouting "Off with his head!" or "Off with her head!" about once in a minute. Alice began to feel very uneasy: to be sure, she had not as yet had any dispute with the Queen, but she knew that it might happen any minute, "and then," thought she, "what would become of me? They're dreadfully fond of beheading people here: the great wonder is, that there's any one left alive!"