Mathematics Extended Essay (Grade: A)

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본 문서는 2019년도 IB에서 A를 받은 Mathematics Extended Essay 입니다. Math EE는 특히나 창의력과 옳은 방향을 요하여 혼자 작성하기 힘들다는 것을 잘 알고 있습니다. 이때 알맞은 자료를 참고하여 구성과 방향을 벤치마킹하는 것이 매우 중요합니다. 본 EE는 작성하는 데 수십, 수백 시간이 소요되어 많은 정성이 들어갔으니 Math EE를 작성하실 때 참고하시면 정도 (正道) 로 가는 데에 큰 도움이 될 것입니다. 뿐만 아니라 본 EE의 고득점을 얻는 포인트를 참고하셔서 벤치마킹하시면 Math EE에서 좋은 점수를 얻으실 수 있을 것입니다.

Title: Modeling time series and analyzing its fractal dimension using fractal interpolation function
Research Question: How can fractal interpolation functions be used to model time series and calculate their fractal dimension?





I. Introduction

A fractal is an object that exhibits self-similarity (Falconer 22). Self-similarity is a property that a similar shape can be identified at different scales looking at the object (Falconer 22). The more self-similar an object is, the more complex it looks (Chaos, Fractals and Dynamics). A lot of time series data, such as which are data ordered by time, display this feature and this feature commonly correlates with real-life phenomena (Kantelhardt 4). For example, in electroencephalogram (EEG) signals, if the patient is has an epileptic seizure, his EEG signal looks more complex than a non-epileptic patient’s EEG signal (Neurocomputing). To incorporate this feature of self-similarity when modeling EEG signals, functions called fractal interpolation functions can be used. These fractal interpolation functions can convert the raw data into an analyzable function that displays self-similarity (Manousopoulos 1). Not only they can model these signals, they can also measure fractal dimension, which is a measure to quantify the level of self-similarity (Barnsley 223).

By doing this, fractal interpolation functions can take data points that are not even part of the raw data points into consideration. There have been many algorithms devised in academics to measure a fractal’s fractal dimension using the raw data only, but there has not been much development in measuring the fractal dimension using fractal interpolation functions (Navascués 2)…


  • 총 페이지수: 56  pages
  • 과목명: Extended Essay (Mathematics)
  • 주제: Modeling time series and analyzing its fractal dimension using fractal interpolation function
  • The file is in PDF format. 
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Mathematics Extended Essay (Grade: A)

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