It is well known that two dimensional subshift is much more involved than dimensional one, e.g., it is already difficult to compute the entropy of 2-dim subshift of finite type. In this research in pairs, we discuss possible applications of tree shifts and quasi self-similar tilings, both of which have intermediate complexity.

We expect their possible applications in a wide range of problems, such as semi-group action via two different algorithms, space filling curve property of fractal tiles, and construction of quasi-self similar polygonal tilings.

• Shigeki Akiyama (University of Tsubuka & Aix-Marseille Université)
• Hui Rao (China Normal University)
  
• Jung-Chao Ban (National Dong Hwa University)
  
• Chih Hung Chang (National Chiao Tung University)