Tutorials/Potato farming

Potatoes are a food item that can be planted, consumed or cooked in a furnace to make a Baked Potato. When consumed, they restore 1 hunger point. Potatoes can be farmed and harvested on farmland, the same way as farming wheat and carrots. When farmed, they pass through 8 stages, but has 2 stages per texture, just like carrots. Fully grown potato crops drop 1 to 4 potatoes and have a 2% chance of dropping an additional Poisonous Potato. Currently, potatoes can be found as a rare drops from zombies and also in NPC Villages alongside wheat. Bone meal can be used to immediately mature the potato to its last stage of growth, but fortune tools do not have any effect on potato crops.

Growth Rate
Potatoes share the same growth mechanics as carrots and wheat. (Carrot Farming)

Potato growth is prompted by random update ticks (the same random events that, for example, create smoke particles above torches and play cave noises). For a given block a random update occurs an average of once every 82 seconds. However the delay can vary widely, and it is even possible (albeit very unlikely) for a crop to be updated multiple times in the same frame. During every update a potato crop gets a chance to grow to the next stage. Any farmland in the 9 blocks below the potato add to its chances to grow. {Further Explanation Needed} If any potatoes are growing in the eight surrounding blocks the growth probability is cut in half, unless the potato is arranged in rows. {Further Explanation Needed}

For the fastest growth, a solid layer of hydrated farmland with crops in rows is ideal. {Further Explanation Needed} Under these conditions, the probability of growth during each update is approximately 30%, and most (4/5) planted potatoes will reach maturity within 19 minutes (about 1-1.5 minecraft days)

Placing a row of non-farmland blocks next to a row of potato crops reduces the growth probability to about 24%. {Further Explanation Needed} This is best possible arrangement when using sticky pistons for automatic harvesting. Most planted potatoes in this case will reach maturity within 25 minutes (about 2.25 minecraft days)

Replacing all unplanted farmland with other blocks reduces the growth probability to about 17%. {Further Explanation Needed} This is also the approximate probability if potatoes are planted outside of rows (but on pure hydrated farmland). {Further Explanation Needed} In either case, most planted potatoes will reach maturity within 31 minutes (about 3.5 minecraft days)

The absolute worst-case conditions for growing are two potato crops placed diagonally on dry farmland. In this case the growth probability is approximately 4%, and it will take about 2 hours for most of the potatoes to reach maturity (about 6 minecraft days)

Compact design
The best way to save space is to make a vertical farm. The farm can be both over or under the ground, and there must be two blocks height between floors in order to fit the player who must replant manually the crops. One water block irrigates an area of 9 by 9 blocks, and the block under the water must be solid to keep the water. Therefore you can build a "tower" with a 9 by 9 blocks area (11 by 11 with its walls), with a central column of water and solid blocks to prevent water from spilling.

Keeping that compact design in mind, the following farm design uses two central columns instead of one to irrigate (water blocks), light (Jack O Lantern blocks) and automatically retrieve the crops (dispensers charged with water buckets). With just one central column and a 9 by 9 blocks farm the water dispenser won't be able to reach all the crops.

Two ways to trigger the water dispensers are shown in the video: with buttons and tripwires (need more space than buttons). Using redstone circuitry will take much more space.