"The maximum density still life problem (MDSLP) is a hard constraint optimization problem based on Conway's game of life. It is a prime example of weighted constrained optimization problem that has been recently tackled in the constraint-programming community. Bucket elimination (BE) is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory required to apply BE is too high, a heuristic method based on it (denominated mini-buckets) can be used to calculate bounds for the optimal solution. Nevertheless, the curse of dimensionality makes these techniques unpractical for large size problems. In response to this situation, we present a memetic algorithm for the MDSLP in which BE is used as a mechanism for recombining solutions, providing the best possible child from the parental set. Subsequently, a multi-level model in which this exact/metaheuristic hybrid is further hybridized with branch-and-bound techniques and mini-buckets is studied. Extensive experimental results analyze the performance of these models and multi-parent recombination. The resulting algorithm consistently finds optimal patterns for up to date solved instances in less time than current approaches. Moreover, it is shown that this proposal provides new best known solutions for very large instances."

An HTML5 audio sequencer based on Conway's Game of Life

"The B36/S125 (or "2x2") cellular automaton is one that takes place on a 2D square lattice much like Conway's Game of Life. Although it exhibits high-level behaviour that is similar to Life, such as chaotic but eventually stable evolution and the existence of a natural diagonal glider, the individual objects that the rule contains generally look very different from their Life counterparts. In this article, a history of notable discoveries in the 2x2 rule is provided, and the fundamental patterns of the automaton are described. Some theoretical results are derived along the way, including a proof that the speed limits for diagonal and orthogonal spaceships in this rule are c/3 and c/2, respectively. A Margolus block cellular automaton that 2x2 emulates is investigated, and in particular a family of oscillators made up entirely of 2 x 2 blocks are analyzed and used to show that there exist oscillators with period 2^m(2^k - 1) for any integers m,k geq 1."

Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's dynamics well, and which express its dynamics badly. We apply the tools to investigate a range of examples in Conway's Game of Life and Hopfield networks and demonstrate that they capture some basic intuitions about emergent processes. Finally, we formalize the notion that a process is emergent if it is better expressed at a coarser granularity.

Attention conservation notice: Once, I was one of the authors of a paper on cellular automata. Lawyers for Wolfram Research Inc. threatened to sue me, my co-authors and our employer, because one of our citations referred to a certain mathematical proof, and they claimed the existence of this proof was a trade secret of Wolfram Research. I am sorry to say that our employer knuckled under, and so did we, and we replaced that version of the paper with another, without the offending citation. I think my judgments on Wolfram and his works are accurate, but they're not disinterested.

With that out of the way: it is my considered, professional opinion that A New Kind of Science shows that Wolfram has become a crank in the classic mold, which is a shame, since he's a really bright man, and once upon a time did some good math, even if he has always been arrogant.

"We have developed a Nagel-Schreckenberg cellular automata model for describing of vehicular traffic flow at a single intersection. A set of traffic lights operating in fixed-time scheme controls the traffic flow. Open boundary condition is applied to the streets each of which conduct a uni-directional flow. Streets are single-lane and cars can turn upon reaching to the intersection with prescribed probabilities. Extensive Monte Carlo simulations are carried out to find the model flow characteristics. In particular, we investigate the flows dependence on the signalisation parameters, turning probabilities and input rates. It is shown that for each set of parameters, there exist a plateau region inside which the total outflow from the intersection remains almost constant. We also compute total waiting time of vehicles per cycle behind red lights for various control parameters."

This feature takes a look at cellular automation, an algorithmic simulation useful in games, and discusses its use in titles like Minecraft and Dwarf Fortress, as well as other examples, and explains how it can be useful in the context of a game in development.

First few notes hit the spot.

Cool little music toy based on cellular automata. Would love to get MIDI output. Could/should be implemented as VST plugin?

"WolframTones works by taking simple programs from Wolfram's computational universe, and using music theory and Mathematica algorithms to render them as music. Each program in effect defines a virtual world, with its own special story--and WolframTones captures it as a musical composition."

Via qwghlm, a CA music generator. Beautiful.