  We are concerned with how the implementation of growth determines the
expected number of state-changes in a growing self-organizing process. With
this problem in mind, we examine two versions of the voter model on a
one-dimensional growing lattice. Our main result asserts that the expected
number of state-changes before an absorbing state is found can be controlled by
balancing the conservative and disruptive forces of growth. This is because
conservative growth preserves the self-organization of the voter model as it
searches for an absorbing state, whereas disruptive growth undermines this
self-organization. In particular, we focus on controlling the expected number
of state-changes as the rate of growth tends to zero or infinity in the limit.
These results illustrate how growth can affect the costs of self-organization
and so are pertinent to the physics of growing active matter.
