论文标题
Sierpinski四面体和其他分层分形的图像的图像
Projected images of the Sierpinski tetrahedron and other layered fractal imaginary cubes
论文作者
论文摘要
Sierpinski四面体具有非凡的特性：预计它将朝三个正交方向的正方形，此外，以众多方向的Lebesgue措施进行了积极的措施。本文提出了一种表征方向的方法，沿sierpinski四面体和其他类似的分形3D对象预计将以正度度量进行集合。我们将此方法应用于分层的虚构立方体，并为它们实现全面的特征。分层的虚构立方体被定义为具有分层结构的迭代功能系统的吸引子，预计将其用于三个正交方向的正方形。在此类中，Sierpinski四面体，T骨和H-骨架是示例性的情况。
The Sierpinski tetrahedron has a remarkable property: It is projected to squares in three orthogonal directions, and moreover, to sets with positive Lebesgue measures in numerous directions. This paper proposes a method for characterizing directions along which the Sierpinski tetrahedron and other similar fractal 3D objects are projected to sets with positive measures. We apply this methodology to layered fractal imaginary cubes and achieve a comprehensive characterization for them. Layered fractal imaginary cubes are defined as attractors of iterated function systems with layered structures, and they are projected to squares in three orthogonal directions. Within this class, the Sierpinski tetrahedron, T-fractal, and H-fractal stand out as exemplary cases.
