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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In a concrete sense, this means fractals cannot be measured in traditional ways. Journal of Archaeological Method and Theory. For other uses, see Fractal disambiguation.

A straight line, for instance, is self-similar but not fractal because it lacks detail, is easily described in Euclidean language, has the same Hausdorff dimension as topological dimensionand is fully defined without a need for recursion.

However, if a fractal’s one-dimensional geometfia are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer. The outputs of the modelling process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal analysis. The Journal of Physiology.

A physics talk for non-physicists” PDF. Buddhabrot Orbit trap Pickover stalk.

Fractal – Wikipedia

Le immagini frattali sono grafici dei risultati dei calcoli, le animazioni frattali sono sequenze di questi grafici. In a interview with Michael SilverblattDavid Foster Wallace admitted that the structure geometgia the first draft of Infinite Jest he gave to his editor Michael Pietsch was inspired by fractals, specifically the Sierpinski triangle a. In questo modo, il server riduce i tratti indesiderabili e aumenta quelli desiderabili, producendo infine un’opera artistica.


Fractals Mathematical structures Topology Computational fields of study. Archived from the original on October 12, The Fractal Geometry of the Brain. University of New South Wales. Wikibooks has a book on the topic of: The mathematical concept is difficult to define formally, even for mathematicians, but key features can be understood with little mathematical background. This also leads to understanding a third feature, that fractals as mathematical equations are “nowhere differentiable “.

Fractal basin boundary in a geometrical optical system [55]. These images, such as of his canonical Mandelbrot setcaptured the popular imagination; many of them were based on recursion, leading to the popular meaning of the term “fractal”.

There is some disagreement amongst mathematicians about how the concept of a fractal should be formally frattalee.

Geometria Frattale by Nicola Saitto on Prezi

Retrieved October 18, Circular houses appear in circles of circles, rectangular houses in rectangles of rectangles, and so on. Retrieved February frwttale, Images of fractals can be created by fractal generating programs.

Collegamento interprogetto a Wikimedia Commons presente ma assente su Wikidata Errori del modulo citazione – pagine con errori in urlarchivio. Because of the butterfly effecta small change in a single variable can have an unpredictable outcome.

From Wikipedia, the free encyclopedia. Images and other outputs of modelling are normally referred to as being “fractals” even if they do not have strictly fractal characteristics, such as when it is possible to zoom into a region of the fractal image that does not exhibit any fractal properties.

Fractals, A Very Short Introduction. By using this site, you agree to the Terms of Use and Privacy Policy.


The same fractal as above, magnified 6-fold. 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. Mandelbrot himself summarized it as “beautiful, damn hard, increasingly useful.

In Losa, Gabriele A. The connection between fractals and leaves, for instance, is currently being used to determine how much carbon is contained in trees.

Arte frattale

Fractal canopy Space-filling curve H tree. Pattern recognition Emergence Frathale and art. Chaos and order in the capital markets: Toward geometira unified theory of development: Having a fractal dimension greater than its topological dimension, for instance, refers to how a fractal scales compared to how geometric shapes are usually perceived.

Pattern formation in biology, vision and dynamics. The feature of “self-similarity”, for instance, is easily understood by analogy to zooming in with a lens or other device that zooms in on digital images to uncover finer, previously invisible, new structure. From DNA to the Heartbeat”.

If this is done on fractals, however, no new detail appears; nothing changes and the same pattern repeats over and over, or for some fractals, nearly the same pattern reappears over and over. Statistical Self-Similarity and Fractional Dimension. Droste effect Mathematical beauty Patterns in nature Sacred geometry.