Computer Explorations of Fractals, Chaos,Complex Systems, and Adaptation

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 Glossary - R

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# R

Random/Randomness     Without cause; not compressible; obeying the statistics of a fair coin toss.

Random Walk     A walk in one or more dimensions that is dictated by the outcome of a coin toss. The direction of each step of the walk is specified by the coin toss. The resulting random motion is often referred to as Brownian motion.

Rational Number     A number that can be expressed as a fraction.

Real Number     Any number that can be represented with a potentially infinite decimal expansion to the right of the decimal point. Natural, rational, irrational, and incomputable numbers are all real numbers.

Recurrent Neural Network     A network similar to a feedforward neural network except that there may be connections from an output or hidden layer to the inputs. Recurrent neural networks are capable of universal computation.

Recursive     Strictly speaking, a set or function is recursive if it is computable; however, in the usual sense of the word, a function is said to be recursive if its definition make reference to itself. For example, factorial can be defined as x! = x * (x - 1)! with the base case of 1! equal to 1. See also self-referential.

Recursively Enumerable (RE)     A potentially infinite set whose members can be enumerated by a universal computer; however, a universal computer may not be able to determine that something is not a member of a recursively enumerable set. The halting set is recursively enumerable but not recursive.

Reductionism     The idea that nature can be understood by dissection. In other words, knowing the lowest-level details of how things work (at, say, the level of subatomic physics) reveals how higher-level phenomena come about. This is a bottom-up way of looking at the universe, and is the exact opposite of holism.

Regular Expression     A definition for a class of strings that can be recognized by a finite-state automaton. An example of a class of strings that is regular would be legal mathematical expressions using only ``+'' and digits. An example that is not regular is the same legal mathematical expressions as before, but with properly nested parentheses.

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