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A theorem, also called the iteration theorem, that makes use of the lambda notation introduced by Church. Let phi_x^((k)) denote the recursive function of k variables with ...

A fractal derived from the Koch snowflake. The base curve and motif for the fractal are illustrated below. The area enclosed by pieces of the curve after the nth iteration is ...

An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the ...

A fractal curve created from the base curve and motif illustrated above (Lauwerier 1991, p. 37). As illustrated above, the number of segments after the nth iteration is ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...

A number of fractal curves are associated with Peano. The Peano curve is the fractal curve illustrated above which can be written as a Lindenmayer system. The nth iteration ...

An operator which describes the time evolution of densities in phase space. The operator can be defined by rho_(n+1)=L^~rho_n, where rho_n are the natural invariants after ...

Consider the sequence {x_n}_(n=0)^infty defined by x_0=1 and x_(n+1)=[3/2x_n], where [z] is the ceiling function. For n=0, 1, ..., the first few terms are 1, 2, 3, 5, 8, 12, ...

The Pythagoras tree is a fractal constructed iteratively from a right triangle with squares erected on each of the sides. Subsequent iterations add additional similar right ...