The quadtree encoding allows us to describe a 2N×2N black and white image as a sequence of bits (0 and 1). Those sequences are to be read from left to right like this:
"11" indicates that the current region contains only white pixels.Consider the following 4×4 image (colored marks denote places where a split can occur):
This image can be described by several sequences, for example : "001010101001011111011010101010", of length 30, or "0100101111101110", of length 16, which is the minimal sequence for this image.
For a positive integer N, define DN as the 2N×2N image with the following coloring scheme: the pixel with coordinates x = 0, y = 0 corresponds to the bottom left pixel, if (x - 2N-1)2 + (y - 2N-1)2 ≤ 22N-2 then the pixel is black, otherwise the pixel is white.What is the length of the minimal sequence describing D24 ?