Their "compressed encoding" does take some advantage of sparsity, but there is enough structure in ash that their "K(X|C)" (compression scheme) can still win out over "Complexity" (compressed encoding).

Take an ash field, blank out all the honey farms (saving about 122 bits per honey farm in the "compressed encoding" for random ash density = 0.0287), stuff a honey farm in a variable Y=[Honey farm], and then add the honey farms back:

X=[ash without honey farms in compressed encoding]∪Y↓(repeat)[hf y coordinate]→(repeat)[hf x coordinate]∪Y↓...

That's 6 symbols = 30 bits per honey farm + 48 bits if you stick to 16 bit coordinates, for a net saving of 44 bits per honey farm.

Initializing the variable with a honey farm takes 207 bits (with an uncompressed pattern).

So after 5 honey farms you're already in positive observed algorithmic specified complexity. A screenful of ash ought to be enough.

Supposedly this means a screenful of ash has functional meaning. Really what it means is that ash is more compressible than a random density 0.0287 pattern.