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A loopship is any self-constructing spaceship that travels by repeatedly creating a signal storage loop that is large enough to hold a complete representation of the construction recipe for that same memory storage loop. Examples include the orthogonal loopship, the self-synthesizing oblique loopship, and the self-synthesizing glide-reflecting loopship. In each case, the loop receives a single copy of the recipe, stores it, and sends out two identical copies.

The first copy of the recipe is used to construct a new signal storage loop, and the second copy is directed into the new loop to repeat the cycle. The previous loop circuitry self-destructs cleanly after it has emitted two copies of its contents.

Known technology would allow for the construction of a loopship that travels diagonally, using any of several possible designs. An explicit example of a diagonal loopship has not yet been constructed. With a custom rule, a single 0E0P metacell might be considered to be a type of loopship, and could support a diagonal direction of travel. But unless custom adjustments are made to the mechanism, this will have a much more complex lifecycle than a standard loopship; among other things, it would create several extra temporary signal loops during its replication process.