The digital-physical workflow is tested through enabling users to physically setup the rules of a Cellular Automata algorithm. The experiments included in this work are prototype-based, which link a digital environment with an artifact-the physical representation of a digital model that is integrated with a Physical Computing System. The method aims to address the challenges of designers implementing algorithms for computational modeling. The research proposes a workflow that allows designers to create complex geometric patterns through their physical interaction with design objects. The work presented in this paper investigates the potential of tangible interaction to setup algorithmic rules for creating computational models. Despite functioning in a different way from traditional, Turing machine- like devices, CA with suitable rules can emulate a universal Turing machine (see entry), and therefore compute, given Turing’s thesis (see entry on Church-Turing thesis), anything computable. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Secondly, CA are abstract: they can be specified in purely mathematical terms and physical structures can implement them. They evolve in parallel at discrete time steps, following state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). At each time unit, the cells instantiate one of a finite set of states. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogenous, simple units, the atoms or cells. In fact, a computer that calculates prime numbers has been designed within the Wireworld system.Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Components are relatively easy to combine and the capabilities of the automaton make it Turing-complete. Using these four simple rules, it is possible to design structures such as diodes (shown below), logic gates, and clock generators. Conductors (yellow) become electron heads if exactly one or two neighboring cells are electron heads. Electron heads (blue) become electron tails in the succeeding generation. Empty cells (black) always remain empty. Wireworld uses four possible cell states and has the following rules: Wireworld is a cellular automaton that simulates electronic devices and logic gates by having cells represent electrons traveling across conductors. "Demon" artifacts, as shown below, create these spirals and are constructed from adjacent groups of cells which constantly devour each other and create a rotating pattern. Two dimensional cyclic cellular automata typically result in spiraling patterns that eventually consume the entire grid. Cycles involving more than 4 colors tend to produce patterns that stabilize more quickly when compared to 3 or 4-color cycles. One dimensional cyclic cellular automata can be used to model particles that undergo ballistic annihilation. Whenever a cell is neighbored by a cell whose color is next in the cycle, it copies that neighbor's color-otherwise, it remains unchanged. In cyclic cellular automata, an ordering of multiple colors is established. ![]() ![]() The Immigration Game and the Rainbow Game of Life can both be viewed and played here. Some investigations on the propagation of colors in the Rainbow Game of Life can be seen here. ![]() The Rainbow Game of Life is notable for being somewhat analogous to genetic properties spreading through a population of creatures. Thus, a cell which is born from two black cells and one white cell will have a dark gray appearance. The Rainbow Game of Life is similar to the Immigration Game, only newborn cells instead are colored based on the average color values of their parent cells.
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