First off, an overview of the farm.
The mitochondria is the powerhouse of the cell; similarly, the humble chicken is the powerhouse of the farm.
The chicken is suspended here on a couple blocks of water. Because the chicken is programmed to float in water, it won't fall down and escape the little pillar-cage I've built around it. However, it will still(to the best of my knowledge) continue to lay eggs. The eggs will not
float, and will therefore flow down the little cage and into the water stream below, as depicted here.
The egg then flows downstream and into the hopper, depositing itself neatly in the chest below.
When this happens, it triggers the tripwire strung over the chest, which causes the pistons to extend and knock the tops off the sugar cane, as seen here(I'm standing on the wire). Since only the top blocks are knocked off, the sugar canes do not have to be replanted!
The farm can be found to the west of the spawn house(orientation calculated by a player standing in front of and facing the door), over the stone bridge I built. It's next to the beetroot/carrot/wheat triple square farm.