we approximated their Hausdorff dimensionD. For non-fractal shapes,Dtakes on integer values (a square has 2, a cube has 3, and so on), whereas for fractals, it can be non-integer, with different fractals having
Further, the homogeneous relation between the fractal dimension of the dyadic Sierpinski triangle and its randomness is investigated. Finally, the fractal interpolation function with variable scaling is implemented on the Sierpinski triangle by defining its Laplacian.Gowrisankar, A....
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The fractal dimension of the Sierpinski Triangle is larger than the Koch Curve, its value is 1.58. We also see fractals in algebra. They are seen in the beginning of modern Mathematics with the middle third Cantor Sets. These sets display properties of self-similarity and have fine structures...
broccoli to blood vessels, fractals can be noticed everywhere in nature. The application of fractals can be seen in fractal antennas, digital imaging, computer graphics, computational geometry, geology and many other fields. Man made fractals include the Cantor set, Sierpinski triangle, and the Mand...
The complexity of a given object can be illustrated as a FD by considering the well-known Sierpinski triangle2 as an example: It has the basic fractal properties described before as being self-similar and recursive. Assuming the initial triangle is equilateral with sides one-unit long. The typi...
He was known for contributions to set theory (research on the axiom of choice and the generalised continuum hypothesis), number theory, theory of functions and topology. Well-known fractals are named after him (the Sierpinski triangle, the Sierpinski carpet and the Sierpinski curve), as are ...
A fractal is a curve or a geometrical structure with a characteristic recurring pattern that can be symmetric or asymmetric. Examples are Koch’s snowflake, Sierpinski’s triangle, and the Mandelbrot set fractal. The pattern keeps repeating itself when zoomed in to the geometrical structure incremen...
Sierpinski Triangle. Although its topological dimension is 2, its Hausdorff-Besicovitch dimension is log(3)/log(2)~1.58, a fractional value (that's why it is called a fractal). By the way, the Hausdorff-Besicovitch dimension of the Norwegian coast is approximately 1.52, its topological ...
Fractals are fascinating, not only for their aesthetic appeal but also for allowing the investigation of physical properties in non-integer dimensions. In these unconventional systems, many intrinsic features might come into play, including the fractal dimension and the fractal geometry. Despite abundant...