
Highest Packing Density for Sugarcane in a chunk?
Am I correct in saying this is the highest possible packing efficiency for planting as much sugarcane as possible within a single chunk?
The pattern consists of 5 block + shapes with the central block replaced with a water source. This will tile the plane with a theoretical efficiency of 80%
When limiting the pattern to a single chunk, we lose 3 plantable tiles per edge, with the exception of the bottom left corner, where one of 2 adjacent 'dead' tiles can be replaced with a water source to save the other.
I count 52 water sources and 10 'dead' tiles, making the packing efficiency (256 - 52 - 10) / 256 = 75.78125%
EDIT: It looks like I missed an 11th dead tile in the bottom right corner, which brings the efficiency down to 75.390625%
EDIT 2: This paper https://www.researchgate.net/figure/Minimum-dominating-sets-of-square-grid-graphs-for-1-n-14_fig2_220342276 (paywalled unfortunately) explores the same concept in mathematics. They were able to use 60 'water sources' in order to end up with 0 'dead tiles' for a total efficiency of 76.65625%