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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Proceedings of the World Congress on Engineering I frattali sono stati anche usati nel contesto degli algoritmi evolutivi del progetto Electric Sheep.

A fractal in three-dimensional space is similar; such a fractal may have an infinite surface area, but never exceed a certain volume.

Arte frattale

In Bunde, Armin; Havlin, Shlomo. Droste effect Mathematical beauty Patterns in nature Sacred geometry. Earth and Planetary Science Letters. Also, these may include calculation or display artifacts which are not characteristics of true fractals. By using this site, you agree to the Terms of Use and Privacy Policy.

Pattern Formation in Biology, Vision and Dynamics, pp. Physics and fractal structures. The fractal geometry of nature. The Attempt to Anticipate Everything”. MacTutor History of Mathematics.

The outputs of the modelling process may be highly artistic renderings, outputs for investigation, or benchmarks for fractal analysis. In a concrete sense, this means fractals cannot be measured in traditional ways.


However, if a fractal’s one-dimensional lengths are geometriq doubled, the spatial content of the fractal scales by a power that is not necessarily an integer. The consensus is that theoretical fractals are infinitely self-similar, iteratedand detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth.

Geometria Frattale by Nicola Saitto on Prezi

In other projects Wikimedia Commons. Different researchers have postulated that without the aid of modern computer graphics, early investigators were limited to what they could depict in manual drawings, so lacked the means to visualize the beauty and appreciate some of the implications of many of the patterns they had discovered the Julia set, for instance, could only be visualized through a few iterations as very simple drawings.

A fractal is formed when pulling apart two glue-covered acrylic sheets. Chaos and order in the capital markets: Retrieved October 18, Statistical Frathale and Fractional Dimension.

Cyberneticist Ron Eglash has suggested that fractal geometry and mathematics are prevalent in African artgames, divinationtrade, and architecture. Fractals in the physical sciences.

Similarity to Natural Scenes”. Likewise, if the radius of a sphere is doubled, geometia volume scales by eight, which is two the ratio of the new to the old radius to the power of three the dimension that the sphere resides in. 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 crattale of the concept to the study of continuous but not differentiable geomerria in the 19th century by the seminal work of Bernard BolzanoBernhard Riemannand Karl Weierstrass[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.


Self-similarity illustrated by image enlargements.

Arte frattale – Wikipedia

In questo modo, il server riduce i tratti indesiderabili e aumenta quelli desiderabili, producendo infine un’opera artistica. Doubling the edge lengths of a polygon multiplies its area by four, which is two the ratio of the new to the frattlae side length raised to the power of two the dimension of the space the geomertia resides in.

The feature of “self-similarity”, for fraftale, 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. Because of the butterfly effecta small change in a single variable can have an unpredictable outcome.

The fact that the Koch curve has a non-integer fractal dimension is what makes it a fractal. I partecipanti ad esso utilizzano come salvaschermo i frattali ottenuti col calcolo distribuitovotando quelli che preferiscono.