Algorithm
The word "algorithm" itself derives from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized "Algoritmi". A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem (decision problem) posed by David Hilbert in 1928. Later formalizations were framed as attempts to define "effective calculability" or "effective method". Those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, and Alan Turing's Turing machines of 1936–37 and 1939.
Algorithmic art
From one point of view, for a work of art to be considered algorithmic art, its creation must include a process based on an algorithm devised by the artist. Here, an algorithm is simply a detailed recipe for the design and possibly execution of an artwork, which may include computer code, functions, expressions, or other input which ultimately determines the form the art will take. This input may be mathematical, computational, or generative in nature. Inasmuch as algorithms tend to be deterministic, meaning that their repeated execution would always result in the production of identical artworks, some external factor is usually introduced. This can either be a random number generator of some sort, or an external body of data (which can range from recorded heartbeats to frames of a movie.) Some artists also work with organically based gestural input which is then modified by an algorithm. By this definition, fractals made by a fractal program are not art, as humans are not involved. However, defined differently, algorithmic art can be seen to include fractal art, as well as other varieties such as those using genetic algorithms. The artist Kerry Mitchell stated in his 1999 "Fractal Art Manifesto":