Not relevant fiction context
Paul's journey in the mathematical forest began this early morning. You know, he is a Biomathologist! He saw a lot of spectacular plants, geometrical flowers and fractal cabbages.
Now, he is taking a moment for himself. He sit on a perfect cube and deeply breath contemplating the math world that is surrounding him.
Paul's gaze is soon attracted to a binary tree.
The binary tree has two colors, red and grey and grows with a logical pattern.
After looking at it for a bit, Paul realizes that the tree is not colored symmetrically so he correctly guesses that what he is looking at is only half of the tree.
He wants to understand the color pattern to predict how the future leaves will be colored.
When the b-tree grows, it adds 1 layer in the top, spawning two leaves for each current top node per year. So, if at year 0 we have only the root, this tree is at year 6. Also the color of nodes does not change anymore once they are spawned.
Can you help him?
Paul observes that as soon as a grey node is encountered while traversing the tree, all the nodes above it are grey too. So the properties of a grey node are inherited by all the spawned node from that node.