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The Rule 110 cellular automaton (often called simply Rule 110) [a] is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life. Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. [2]
A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...
[11] [32] This is why the infinitely-many-zeros problem is decidable: just determine if the infinitely-repeating pattern is empty. Decidability results are known when the order of a sequence is restricted to be small. For example, the Skolem problem is decidable for algebraic sequences of order up to 4.
A common algorithm design tactic is to divide a problem into sub-problems of the same type as the original, solve those sub-problems, and combine the results. This is often referred to as the divide-and-conquer method; when combined with a lookup table that stores the results of previously solved sub-problems (to avoid solving them repeatedly and incurring extra computation time), it can be ...
Below is a shear mapping with infinite order. Below that are their compositions, which both have order 3. In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. The process of repeatedly applying the same function is called iteration. In this process, starting from ...
As long as the system is responsive, infinite loops can often be interrupted by sending a signal to the process (such as SIGINT in Unix), or an interrupt to the processor, causing the current process to be aborted. This can be done in a task manager, in a terminal with the Control-C command, [9] or by using the kill command or system call.
An object whose irregularity is constant over different scales ("self-similarity") is a fractal (examples include the Menger sponge, the Sierpiński gasket, and the Koch curve or snowflake, which is infinitely long yet encloses a finite space and has a fractal dimension of circa 1.2619).
This repeating pattern resembles the repeating pattern of set and unset pins on the gears of a pinwheel cipher machine, justifying the name. [1] If the fraction of time that is required by each task totals less than 5/6 of the total time, a solution always exists, but some pinwheel scheduling problems whose tasks use a total of slightly more ...