a combination. The Game of Life is undecidable, which means that given an initial pattern and a later pattern, no algorithm exists that can tell whether the later pattern is ever going to appear. This is a corollary of the halting problem: the problem of determining whether a given program will finish running or continue to run forever from an initial input. Oblique spaceships Until the 2010s, all known spaceships could only move orthogonally or diagonally, whereas the existence of moving patterns that move like knights had been predicted by Berlekamp since 1982. The spaceships which move neither orthogonally nor diagonally are commonly referred to as oblique spaceships. On May 18, 2010, Andrew J. Wade announced the first oblique spaceship, dubbed "Gemini", that creates a copy of itself on (5,1) further while destroying its parent. This pattern replicates in 34 million generations, and uses an instruction tape made of gliders oscillating between two stable configurations made of Chapman–Greene construction arms. These, in turn, create new copies of the pattern, and destroy the previous copy. In December 2015, diagonal versions of the Gemini were built. Self-replication On November 23, 2013, Dave Greene built the first replicator in the Game of Life that creates a complete copy of itself, including the instruction tape. In October 2018, Adam P. Goucher finished his construction of the 0E0P metacell, a metacell capable of self-replication. This differed from previous metacells, such as the OTCA metapixel by Brice Due, which only worked with already constructed copies near them. The 0E0P metacell works by using construction arms to create copies that simulate the programmed rule. The actual simulation of the Game of Life or other Moore neighbourhood rules is done by simulating an equivalent rule using the von Neumann neighbourhood with more states. The name 0E0P is short for "Zero Encoded by Zero Population", which indicates that instead of a metacell being in an "off" state simulating empty space, the 0E0P metacell removes itself when the cell enters that state, leaving a blank space. Iteration From most random initial patterns of living cells on the grid, observers will find the population constantly changing as the generations tick by. The patterns that emerge from the simple rules may be considered a form of mathematical beauty. Small isolated subpatterns with no initial symmetry tend to become symmetrical. Once this happens, the symmetry may increase in richness, but it cannot be