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In this paper we have defined one function that has been used to constructdifferent fractals having fractal dimensions between 1.58 and 2. Also, we triedto calculate the amount of increment of fractal dimension in accordance withthe base of the number systems. Further, interestingly enough, these veryfractals could be a frame of lyrics for the musicians, as we know that thefractal dimension of music is around 1.65 and varies between a high of 1.68 anda low of 1.60. Further, at the end we conjecture that the switching from onemusic fractal to another is nothing but enhancing a constant amount fractaldimension which might be equivalent to a kind of different sets of musicalnotes in various orientations.

On the Interesting World of Fractals and Their Applications to Music