Fractal Applications in Electrical and Electronics Engineeering

Fractal, which means broken or irregular fragments, was originally coined by Dr B. Mandelbrot in the year the 1970. Fractals describe a family of complex shapes that possess an inherent self-similarity in their geometrical structure usually in nature, since the pioneering work of Mandelbrot and others, a wide variety of applications for fractals has been found in many branches of science and engineering. A fractal is a recursively generated object having a fractional dimension. Fractals are defined as the “set whose Hausdorff dimension exceeds topological dimension”. Fractal has various properties like recursive, infinite, selfsymmetry and fractional dimension (FD). Self Symmetry, Space filling and FD are most important properties which has practical applications. This paper discuss various applications of fractal in electrical and electronics engineering field few are fractal antenna, fractal capacitor, fractal image compression, fractal encoding, fractal analysis in power systems fault analysis like (High Impedance fault, Load forecast). Hurst parameter is used for real dynamic curve analysis. Lightning modeling is essential for design and testing of an aircraft in laboratory. Full scale aircraft testing of lightning stroke inside lab fractal lightning modeling is used to generate High Volt lighting discharge testing of full model aircraft on ground. Impedance matching by impedance transformer by fractals is new concept for matching loads in electronics. L-System is extensively used for biological modeling and growth modeling. L-System is also used for artificial life creation by computers. L-System fractals can be used for digital camouflaged, concealed super structures, computer generated tree and artificial life. Scale free networks are fractal networks, they are more robust. Hurst parameter (H), of traffic for scale free networks if change abruptly, it signifies attack on network. It is also proposed to monitor H for scale free network. Routing protocol and optimization techniques in networks should also choose nodes so that the network grows and forms like fractal network which are robust.