![]() ![]() Literature includes many examples of CA that can produce visually appealing animations as artifacts. The smooth search space is evident because small changes to many of the components in the Bugs rule produce a CA that appears visually similar to the original Bugs CA. This encoding and generalization of GOL provides a smooth enough search space to be optimized by a GA. An extended Moore neighborhood for radius 1 are the 8 cells around the center cell a radius of 2 include the 24 cells that form two rectangles around the center cell. This string specifies a neighbor radius (R) of 5, 0 history states (C), the middle cell (M) is included in the neighbor count, the neighbor count for survival (S) is between 34 and 58, the neighbor count for birth (B) is between 7 and 11, the neighborhood is an extended Moore (NM) neighborhood. For example, the CA Bugs, is written in the Larger than Life form of R5,C0,M1, S34.58, B34.45,NM. Larger Than Life has even been scaled to neighborhood sizes of radius 25 and beyond. Larger than Life is a GOL-like family of CA that allow the size and type of neighborhood to be varied. ![]() The update rule for GOL can be written as B3/S23, which means a cell is born with a neighbor count of 3, survives with a neighbor count of 2 or 3, and dies in all other cases. Researchers have generalized GOL to a family of update rules that specify the neighbor counts at which a cell should be born or survive. Other examples of a smooth search space for CA exist. The fact that many of these rules are no more than one or two binary digits away from each other is indicative of a smooth search space that increases the chances of a GA finding its way to locally optimal solutions. For example, an ECA is usually encoded as a decimal number that represents an 8-bit pattern that specifies a new cell value based on the 8 possible combinations of the three cells immediately above the target cell. The number of alive cells present in a CA neighborhood is referred to as its neighbor count.įamilies of update rules are typically expressed in some sort of encoding. This arrangement of 8 neighbor cells is referred to as a Moore Neighborhood, named in honor of Edward F. These cells are arranged on a 2D rectangular grid of cells where each interior cell has 8 neighbors that influence how that cell is updated. MergeLife is a continuous CA where each cell is a 24-bit RGB encoded color. One notable generalization of GOL is SmoothLife, where GOL is adapted to a continuous domain however, the resulting animation is still monochrome. GOL has previously been adapted from discrete to continuous. ![]() Ĭontinuous CA are a generalization of the more common discrete CA where the states are expressed as continuous numbers. Likewise, Elementary Cellular Automaton (ECA) rule 110, which was studied extensively by Stephen Wolfram, was proven to be Turing complete. GOL was shown to be Turing complete-capable of computing anything that can be computed with a Turing machine. In artificial chemistry, scientists have implemented self-replicating cells through a CA. In 1996 a team performed computations with a genetic algorithm (GA) for global coordination. Though many CA, such as GOL, were introduced as recreational mathematics or generative art, there are practical applications. The quintessential example of a CA is Conway’s Game of Life (GOL). Because the true animated behavior of these CA cannot be observed from static images, we also present an on-line JavaScript viewer that is capable of animating any MergeLife 16-byte update rule.Ĭellular automata (CA) are a class of computer model that are made up of a grid (or other organization) of cells that move between discrete states as dictated by an update rule. Several update rules produced from this paper exhibit complex emergent behavior through patterns, such as spaceships, guns, oscillators, and Universal Turing Machines. The results of this research are several complex and long running update rules and the objective function parameters that produced them. Also introduced are several novel fitness measures that when given human selected aesthetic guidelines encourage the evolution of complex animations that often include spaceships, oscillators, still life, and other complex emergent behavior. This update rule provides a fixed-length genome that can be successfully optimized by a GA. A simple 16-byte update rule is introduced that is evolved through an objective function that requires only initial human aesthetic guidelines. We present MergeLife, a genetic algorithm (GA) capable of evolving continuous cellular automata (CA) that generate full color dynamic animations according to aesthetic user specifications.
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