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Subject says it all. In Minecraft, carrots grow through 8 different stages. 4 of which can be visually seen. But, the Wiki article contains no information on how long it takes a carrot to move through each of the stages. I'm interested in the end to end growth time. Since, this is a random process, how likely per game tick is a carrot to grow? is this known? I could not find it on the Wiki.

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Growth Chart

Explanation:

Growth requires a light level of at least 9 in the block above the plant.

The farmland block the crop is planted in gives 2 "points" if dry or 4 if hydrated.

For each of the 8 blocks around the block in which the crop is planted, dry farmland gives 0.25 "points," and hydrated farmland gives 0.75.

Note that if a field is bordered with anything besides more farmland, the plants at the edge will grow more slowly.

If any plants of the same type are growing in the eight surrounding blocks, the "point" total is cut in half unless the crops are arranged in rows.

That is, having the same sort of plant either on a diagonal or in both north-south and east-west directions cuts the growth chance, but having the same type of plant only north-south or east-west does not.

The growth chance is only halved once no matter how many plants surround the central one.

The growth probability is then 1/(floor(25/points) + 1).

Source: http://minecraft.gamepedia.com/Tutorials/Crop_farming#Growth_rate

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