3D visualization of complex 2-dimensional dynamics

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610020
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: Ishii Yutaka 九州大学, 数理(科)学研究科(研究院), 准教授 (20304727)
• Co-Investigator(Kenkyū-buntansha): ARAI Zin 北海道大学, 理学研究科, 准教授 (80362432)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 複素ヘノン写像 / ジュリア集合 / 可視化 / ヴァーチャル・リアリティ

Outline of Final Research Achievements

The purpose of this project is to visualize some mathematical objects generated by complex dynamics in dimension two by employing 3D virtual reality system, deduce mathematical conjectures through the visualized images, and create an archive to put several data of the images. The results we obtained consist of the following three points: (1) Non-commutativity of the projection from 4D to 3D and rendering, (2) Dynamical interpolation of the Julia sets as point cloud data, (3) Creation of an archive to preserve image data of the Julia sets.

Free Research Field

力学系理論