Mandelbrot: Iteration


„Such a repetition of an arbitrary operation is known as ‚iteration,‘ and in the present case suffices to transform seeming dullness into boundless excitement. The motivation for iteration and many of its most important properties come straight from physics. In iteration, physicists see a simplified view of the ’state‘ of a dynamical system and its evolution in time. By definition, a dynamical system is a transform that obtains its state today from its state yesterday, and its state tomorrow from its state today. Therefore, to obtain the state tomorrow from the state yesterday, one may apply the basic transform twice in succession. But one may also apply the iterated transform once.“ (p. 260) #Mandelbrot #iteration

Mandelbrot, Benoît B., Fractals and Chaos. The Mandelbrot Set and Beyond. New York: Springer 2004, ISBN 978-1-4419-1897-0.

Serres: La théorie des correspondances


„L’itération de descriptions semblables le désigne comme théorie des correspondances de région à région, de contenu sémantique à contenu sémantique, de multiplicité à multiplicité.“ (72sq.) #Serres #itération #semblables #correspondance #multiplicité

Serres, Michel, Le système de Leibniz et ses modèles mathématiques. Étoiles -Schémas - Points. Paris: PUF 42001. 834 S.

Serres: L’itération


„[L]’itération […] va être à la source de l’infini“. (p. 143) #Serres #itération #infini

Serres, Michel, Hermès I. La communication. Paris: Minuit 1968.