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An Investigation into Analysis on Non-PCF Fractals
In order to have a better grasp on what a fractal is, we will demonstrate how to construct a fractal through Iterated Function Systems (IFS). While not the only way to construct a fractal, this method is fairly intuitive and will be referenced later on. Prior to explaining what an IFS is, we will first cover a few important definitions. The overall focus of this paper is to highlight some analysis techniques for fractals, alongside some application and extension of these techniques. In order to bring a notion of calculus to fractals we will focus on discretizations of their domains. One can think of this approach as analogous to examining the limits of difference quotients and Riemannian sums in calculus. We will refer to these discretizations as graphical approximations.
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