Yaşamımızı Çevreleyen İlginç Geometrik Şekiller: Fraktallar

Abstract

The aim of this paper is to form a new fractal by using Mandebrot's Fractal and to prove that the new formed figure is also a fractal itself. This project is done by Grade 11 students of Ozel Eyuboglu High School, Ayşegül BAYAR, Valya HUBEŞ, Merve AKIN and Ece DEMiRCi with the guide of Mathematics teachers. In the first part of the project, students used Ultrafractal 4 programme, and got the formula of the new fractal. Iterations are showed algebraically by the students. The perimeter and the area of the figure are calculated. The first figure had two dimensions. The last figure's dimension was also calculated and found as a rational number nearly equal to 2. Finally, it was proved that the figure had a bounded area but an infinite perimeter, and the dimension of the figure was a rational number. The students realised that the new figure gotten by is simi lar to the figure of the castle in Italy, called "Del Monde". However, it can not be declared an endless iteration for the construction of the castle.