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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Circular houses appear in circles of circles, rectangular houses in rectangles of rectangles, and so on. But in measuring an infinitely “wiggly” fractal curve such as the Koch snowflake, one would never geomettria a small enough straight segment to conform to the curve, because the jagged pattern would always re-appear, at arbitrarily small scales, essentially pulling a little more of the tape measure into the total length measured each time one attempted to fit it tighter and tighter to the curve.

Evidence for seismically-induced fluid pulsing”. Visite Ftattale Modifica Modifica wikitesto Cronologia. Encyclopedia of Complexity and Systems Science.

Arte frattale

Retrieved October 18, Fractals Mathematical structures Topology Computational fields of study. The same fractal as above, magnified 6-fold.

Models may simulate theoretical fractals or natural phenomena with fractal features. One way that fractals are different from finite geometric figures is the way in which they scale. Crystal growth, biological cell growth and geometry. Ancient Polykleitos Canon Vitruvius De architectura. Same patterns reappear, making the exact scale being examined difficult to determine. The connection between fractals and leaves, for instance, is currently being used to determine how much carbon is contained in trees.

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Fractal patterns have been reconstructed in physical 3-dimensional space [29]: Wikimedia Commons has media related to Fractal. The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, with several notable people contributing canonical fractal forms along the way. In Bunde, Armin; Havlin, Shlomo.

In a interview with Michael SilverblattDavid Foster Wallace admitted that the structure of the first draft of Infinite Jest he gave to his editor Michael Pietsch was inspired by fractals, specifically the Sierpinski triangle a. Doubling the edge lengths of a polygon multiplies its area by four, which is two the ratio of the new to the old side length raised to the power of two the dimension of the space the polygon resides in. From DNA to the Heartbeat”. Fractal Brains Fractal Thoughts”.

Fractal art and Mathematics and art. Journal of Archaeological Method and Theory. Springer Series in Computational Neuroscience. A fractal is formed when pulling apart two glue-covered acrylic sheets.

Geometria Frattale by Nicola Saitto on Prezi

Images of fractals can be created by fractal generating programs. Actin cytoskeleton [52] Algae Animal coloration patterns Blood vessels and pulmonary vessels [47] Coastlines Craters Crystals [53] DNA Earthquakes [30] [54] Fault lines Geometrical optics [55] Heart rates [22] Heart sounds [23] Lightning bolts Mountain goat horns Mountain ranges Ocean waves [56] Pineapple Psychological subjective perception [57] Proteins [58] Rings of Saturn [59] [60] River networks Romanesco broccoli Snowflakes [61] Soil pores [62] Surfaces in turbulent flows [63] [64] Trees Brownian motion generated by a one-dimensional Wiener Process.


Tutti e quattro i tipi di frattali sono stati utilizzati come base per arte e animazione digitali. In questo modo, il server riduce i tratti indesiderabili e aumenta quelli desiderabili, producendo infine un’opera artistica.

Because of the butterfly effecta small change in a single variable can have an unpredictable outcome. Retrieved February 4, 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.

The fractal geometry of nature. Mandelbrot himself summarized it as “beautiful, damn hard, increasingly useful. Buddhabrot Orbit trap Pickover stalk. Altri progetti Wikimedia Commons.

As mathematical equations, fractals are usually nowhere differentiable. 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 fraftale finer, previously invisible, new structure.

Now, consider the Koch curve.