In probability theory, a stochastic system is one that is indeterminate. A stochastic system is a system whose behavior is non-deterministic. When Xenakis came to Le Corbusier's office, he was a trained engineer. Xenakis brought training in several mathematical forms that LC felt encouraged to apply to his architectural works. This includes Stochastic systems, which Xenakis first applied to the windows of LC's housing project in Reze, 1950 - 54.
Stochastic window pattern at the Housing Project in Reze, Le Corbusier, with Xenakis. Stochastic systems are also applied to sound, and to urban planning and design.
Ronchamp by Le Corbusier: Stochastic window patterns.
Stochastic window patterns by Sanaa // K. Sejima. Stochastic window pattern, borrowed from Le Corbusier / Xenakis.
Neumes: shown above: Neumes is the basic element of Western and Eastern systems of musical notation. From the Greek word for breath : pneuma. Neume, shown above: a Gregorian chant.
In the 9th century Neumes became shorthand mnemonic aids for the proper melodic recitation of chant. Neumatic recitation was first developed in the Eastern Roman Empire (today's sountern Turkey, Syria, Lebanon, and Isreal). Above: Gregorian Neumes. Le Corbusier and Xenakis considered the windows at Ronchamp to have been placed as a 'Neume' - or Neumatic notation of a Chant.
Sound Urbanism // Sound Ecology. Victoria Meyers architect
