Clearing
The Clearing is a horocyclic area filled with a single, infinitely-large Mutant Ivy. It requires 5 Mutant Saplings from the Overgrown Woods. Unlike the Overgrown Woods, Ivy can only grow on hexagonal tiles here; heptagons are prohibited to them, thus making their incredibly fast growth somewhat more manageable.
The root of the infinitely-large Mutant Ivy is infinitely far away, so it can never be killed; however, large chunks of it can be cut off by cutting the branch points of large clusters of branches. Due to the restriction of the Ivy branches to non-heptagons, the player can make constant progress towards the root (though this never ends because the root is infinitely far away), each time cutting away larger and larger clusters of branches. The size of clusters thus cut increases exponentially as the player enters deeper into the clearing; thus after a certain depth the number of leaves cut will become so large they require scientific notation to express, such as 2.5E23 (a huge number whose first digit is 2, followed by another 23 digits). There is an achievement for cutting 1E99 Mutant Ivy parts in the Clearing.
Some distance into the clearing, Mutant Fruit will start appearing on the heptagons between branches. The fruit is only collectible when they are next to at least 1 branch; if all branches next to them have been cut, they will rot away. Once the player collects more mutant fruit, Giant Foxes will start appearing, who are angry because the player is destroying the plant that's giving them infinite food for zero effort.
Once there are too many Giant Foxes around, it will become increasingly harder to make progress on cutting the Mutant Ivy, so the player would do well to retreat. Retreat is generally not a problem because the Ivy cannot grow on heptagons, which slows it down enough that the player will be able to outrun it after some time.
Strategies
To reach the 1E99 Mutant Ivy parts achievement, it is best to avoid picking any fruit whatsoever -- this will prevent Giant Foxes from spawning. Then the only task left is to careful persistence to cut increasingly larger clusters of Ivy branches as one works one's way in the direction of the root.