A note on fractal interpolation vs fractal regression - Serpa, Cristina (2021)
Fractals fascinates both academics and art lovers. They are a form of chaos. A key feature that distinguishes a fractal from other chaotic phenomena is the self-similarity. This is a property that consists of replicating a shape to smaller pieces of the whole. In other words, making zoom in or zoom out gives similar perspectives of the same fractal thing. We may find these shapes everywhere and nature presents many examples of fractal creations. An amazing case is the romanesque cabbage. Mandelbrot is the father of the term fractal and studied various examples (see [3]). Constructing a fractal is a simple task to do, just consider an initial configuration and a replication rule for smaller scales. This is how one gets, for example, the Sierpinski triangle, the dragon curve, or the Koch Snowflake. A simple rule creates complicated shapes with non-classical geometries. Analytically, it is also possible to define fractals as solutions of a system of iterative func tional equations. Barnsley defined such a system in [1]. This non-classical geometric concept has attracted many researchers when they are faced with the need to analyse real data with irregular characteristics.