Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic ...

We describe new families of random fractals, referred to as " V-variable " , which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of " variability " : at each magnification level any V-variable fractals has at most V key " forms " or " shapes ". V-variable random fractals have the surprising property that they can be c...

Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multivaried spectrum of fractals usage in ...

Study on properties of general Sierpinski fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. Like other fractals, general Sierpinski fractals are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. In [22], the authors the geometric modelling of a class of general Sierpinski fractals and their geometric ...

Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers....

“Fractal” is a word invented by French mathematician B.B. Mandelbrot around 1970s. He claimed that many patterns of Nature, such as clouds, mountains and coastlines are not lines nor circles which are smooth, but are so irregular, fragmented and exhibit an altogether different level of complexity. From this viewpoint, he called the family of those shapes as fractals. Especially, he made special...

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In the 1988 textbook "Fractals Everywhere" M. Barnsley introduced an algorithm for generating fractals through a random procedure which he called "chaos game". Using ideas from classical theory of covering times Markov chains we prove asymptotic formula expected time taken by this to generate $\delta$-dense subset given self-similar fractal satisfying open set condition.