Fractal compression is a dimension altering, visual distortion technique used in digital image processing, digital video, and digital audio. This technique compresses objects so that the inter-fractal dimension approaches the dimension of the original shape. In fractal compression, an algorithm alters the dimensions of the fractal object, resulting in a new form of the object with a smaller dimension. In other words, it can convert a straight line with fractal-dimension. One example of fractal compression is the digital fractal compression algorithm being used in the movie Avatar, which alters the dimension of a planet in relation to the human life used in the spectacle of the film.
Fractals have been described by the Italian mathematician Benoît Mandelbrot in his 1974 book The Fractal Geometry of Nature, which aimed to find a scientific basis for the phenomenon of self-similarity in nature, and by Martin H. G. H. Publisser in 1974 Fractals and Chaos.[notes 2] In David A. Wallace's book Fractals, Form, Chance and Dimension (Wadsworth, Singapore, 1990; 2nd ed. 1993) Mandelbrot's ideas on self-similarity are developed in more detail; specifically, the work on quantiles without a denominator. Mandelbrot presented some of these ideas in seminars in 1969, and published the most considered account of them in his 1971 book The Fractal Geometry of Nature and the 1982 book Fractals Everywhere. d2c66b5586