芸術科学会論文誌 投稿用カバーシート ■ 論文種類(以下のうちから一つ選択) ・原著論文 ■ 論文分野(以下のうちから一つ選択) ・科学系分野 ■ 該当特集(以下のうちから一つ選択) ・一般論文 ■ 論文題名(和文、英文) Automatic Generation of 3-D Linear Fractal Shapes with Quadratic Map Basins Animation ■ 著者名(和文、英文) Hussein Karam, Masayuki Nakajima ■ 著者所属(和文、英文) Ain Shams University, Faculty of Science, Math. & Computer Sc. Dept. Abbassia, Cairo, Egypt 東京工業大学 大学院 情報理工学研究科 Graduate School of Information Science & Engineering, Tokyo Institute of Technology ■ 著者e-mail huss20@hotmail.com, nakajima@img.cs.titech.ac.jp ■ 連絡担当者の氏名、住所、所属、電話、Fax、e-mail 中嶋 正之 〒152-8552 目黒区大岡山2-12-1 tel. 03-5734-2813 fax. 03-5734-2817 nakajima@img.cs.titech.ac.jp ■ 論文概要(和文400字程度、英文100ワード程度) Quadratic map basins is a method used to generate the images of Julia and Mandelbrot sets and has been applied to visualize the attractors of iterated function systems (IFS). Three dimensional extension of such mapping with animation is an aspiring goal and a challenging task. In this paper an extension algorithm of quadratic map basin for classifying points in the complement of a 3-D linear fractal shapes are discussed. Such extension produces fractal surfaces that exhibit self-similarity and suggest smooth evolution under animation. The proposed technique has fast computations and simple representation whereby a computer can automatically select parameters and generate a large collection of aesthetically appealing 3-D fractal patterns. The simple representation and the speed of computation of our algorithm make 3-D fractal patterns reliable for interactive machine.