Suppose the leaf was giant.

And suppose the algorithm would attempt to add a new cell \\(x\\) at the fringe of this giant leaf.

\\(x\\) needs the standard rate of fluid flow to support it. Call this flow amount \\(y\\).

Now \\(y\\) would have to be added to the flow through every pipe on the path from the root to \\(x\\).

Suppose there are \\(N\\) pipes along this path.

Since we said the leaf was giant, this means that \\(N\\) is large.

Were \\(\alpha\\) to be close to 1, then adding \\(x\\) to the leaf would incur a large cost, because all of the pipes along this long path would need to be widened.

But when \\(\alpha\\) is small, this hardy matters, and it is no problem to feed \\(x\\) through a long chain of pipes -- so \\(x\\) gets added, and the leaf continues to grow,

And suppose the algorithm would attempt to add a new cell \\(x\\) at the fringe of this giant leaf.

\\(x\\) needs the standard rate of fluid flow to support it. Call this flow amount \\(y\\).

Now \\(y\\) would have to be added to the flow through every pipe on the path from the root to \\(x\\).

Suppose there are \\(N\\) pipes along this path.

Since we said the leaf was giant, this means that \\(N\\) is large.

Were \\(\alpha\\) to be close to 1, then adding \\(x\\) to the leaf would incur a large cost, because all of the pipes along this long path would need to be widened.

But when \\(\alpha\\) is small, this hardy matters, and it is no problem to feed \\(x\\) through a long chain of pipes -- so \\(x\\) gets added, and the leaf continues to grow,