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Academia Letters
Article
License: CC BY
Data sources: UnpayWall
Academia Letters
Article . 2021 . Peer-reviewed
Data sources: Crossref
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A Note on Fractal Interpolation vs Fractal Regression

Authors: Serpa, Cristina;

A Note on Fractal Interpolation vs Fractal Regression

Abstract

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.

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Portugal
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Keywords

Fractal interpolation, Fractal regression

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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