Introduzione alla modellazione di forme naturali tramite geometria frattale Corso di Grafica Facoltà di Informatica Magistrale. In mathematics, a fractal is a subset of a Euclidean space for which the Hausdorff dimension strictly exceeds the topological dimension. Fractals are encountered. L’arte frattale è creata calcolando funzioni matematiche frattali e trasformando i risultati dei calcoli in immagini, animazioni, musica, o altre forme di espressione.

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Progress in wavelet analysis and applications: The word “fractal” often has different connotations for laymen as opposed to mathematicians, where the layman is more likely to be familiar with fractal art than the mathematical concept. Bytwo French mathematicians, Pierre Fatou and Gaston Juliathough working independently, arrived essentially simultaneously at results describing what are now seen as fractal behaviour associated with mapping complex numbers and iterative functions and leading to further ideas about attractors and repellors i.

Arte frattale

There is some disagreement amongst mathematicians about how the concept of a fractal should be formally defined. The same fractal as above, magnified 6-fold.

The Patterns of Chaos. Ancient Polykleitos Canon Vitruvius Frattalee architectura. Earth and Planetary Science Letters. Wikibooks has a book on the topic of: By using this site, you agree to the Terms of Use and Privacy Policy.


If done correctly, the efficiency of the emission process can be maximized. A fractal is formed when pulling apart two glue-covered acrylic sheets.

Fractals in the physical sciences. According to Falconer, rather than being strictly defined, fractals should, in addition to being nowhere differentiable and able to have a fractal dimensionbe generally characterized by a gestalt of the following features; [2].

Note, however, that the topological dimension of the grattale of the Hilbert map a set in R 3 is 1. The mathematical roots of fractals have been traced throughout the years as a formal path of published works, starting in the 17th century with notions of recursionthen moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century by the seminal work of Bernard BolzanoBernhard Riemannand Karl Weierstrass frattwle, [9] and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 20th century.

Frattalr Journal of Physiology. Evidence for seismically-induced fluid pulsing”. Fractal art and Mathematics and art.


Geometria Frattale by Nicola Saitto on Prezi

However, if a fractal’s one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer. Revisiting Pollock’s Paintings Reply “. Springer Series in Computational Neuroscience. La musica frattale associa ai risultati dei calcoli dei toni musicali o altri suoni.

Fractal – Wikipedia

Romanesco broccolishowing self-similar form approximating a natural fractal. Frontiers in Human Neuroscience. Physiological and methodological implications”.

Form, Function, and Fractal Dimension.

In Di Ieva, Antonio. Critical phenomena in natural sciences: Polykleitos Canon Vitruvius De architectura.

Fractal defrosting patterns, polar Mars. Altri progetti Wikimedia Commons. When two-dimensional fractals are iterated many times, the perimeter of the fractal increases up to infinity, but the area may never exceed a certain value.

A Laboratory Observation”, Nature In other projects Wikimedia Commons. Encyclopedia of Complexity and Systems Science.