In this paper, power chaos is proved for left model shift mapping in bilateral symbol space.

This paper provides a new model shift mapping in the bilateral symbol space, which shows that this shift mapping is chaotic.

This article summarily comments meanings of the relevant"spaces"in syntax research, while lays emphases on"Cognitive Space"as its theoretical footstone,"Symbolic Space"as its abstract expression for realistic space and"Topologic Space"as the calculation basis of syntactical model, so as to understand these.

An interesting measure in symbolic space is studied,which is defined by a very useful method of repeated subdivision.

The comparingmapδ on the symbolic space is topologically conjugate to the shift map σ.

Firstly, this paper has discussed the topological properties of the shift space, which is an important tool to study the fractal set, and itself is also a self-similar set.

In this paper, we firstly discuss the topological properties of the shift space, which is an important tool to study fractal set, and itself is also a self-similar set.

The combination of different elements in space symbols can convey aesthetic feelings such as beauty of emotions,beauty of idea,functionality and multi-dimensionality,which also offers a new experience,a new perspective and a new direction to viewers in addition to the transmission of information.