“Emergence of Self-Replicating Structures in a Cellular Automata Space”, 1997-12-15 ():
Past cellular automata models of self-replication have always been initialized with an original copy of the structure that will replicate, and have been based on a transition function that only works for a single, specific structure [such as von Neumann’s construction or Langton’s ant].
This article demonstrates for the first time that it is possible to create cellular automata models in which a self-replicating structure emerges from an initial state having a random density and distribution of individual components.
These emergent self-replicating structures employ a fairly general rule set that can support the replication of structures of different sizes and their growth from smaller to larger ones. This rule set also allows “random” interactions of self-replicating structures with each other and with other structures within the cellular automata space.
Systematic simulations show that emergence and growth of replicants occurs often and is essentially independent of the cellular space size, initial random pattern of components, and initial density of components, over a broad range of these parameters. The number of replicants and the total number of components they incorporate generally approach quasi-stable values with time.
…This simulation is characterized by the initial emergence of very small, self-replicating loops and their progressive evolution to increasingly large and varied replicants. During this process a replicant may collide with other loops or with free-floating components, and either recover or self-destruct. Thus, by epoch 500 (upper right of Figure 1), very small self-replicating loops of size 2 × 2 and 3 × 3 are present. By epoch 1500 a 4 x 4 loop is about to generate a 5 x 5 loop in the middle left region. At epoch 3,000 the biggest loop is 8 × 8 and it is about to generate a 9 × 9 loop. By epoch 5,000 many very large loops have annihilated each other and only one intact 10 × 10 loop is left. By epoch 7,500 all large loops have died, but there are new 3 × 3 loops in the space. These loops will replicate and it is not clear when (if ever) this example will cease its activity. In this example, the size of the replicating structures became too big to fit comfortably in such a small world (40 × 40 only), and the large loops started to annihilate each other.
…The results reported here show for the first time that non-trivial self-replicating structures can emerge in a cellular automata space initialized with a randomly distributed set of components. Unlike past cellular automata models, the initial states in our simulations did not contain any replicating structures, and were different in each simulation. The emergence of replicating loops was quite robust, occurring in 80⁄81 simulations having different space sizes, densities of components, and initial configurations of these components.
Once small self-replicating loops appeared, they gradually increased in size, eventually reaching an average size that was characteristic of the size of the cellular space. However, the number and size of self-replicating loops never reached an equilibrium. Instead, these values oscillated around an average value. The oscillations were of varying amplitude and non-periodic, suggesting that the behavior of the model has a chaotic dynamics.