ABSTRACT
Fractal geometry begins by dealing with linear fractal’, i.e., the fractal with self-similarity, but the concept of fractals is not dependent on being self-similarity. Some invariant sets under transformation group with respect to the geometric inversion also behave the character of fractal, and are called self-inverse fractals. In this chapter, the concept of fractal geometry derived from geometric inversion and a celebrated self-inverse fractal are introduced. It discusses two examples of self-inverse fractals (soap and eggs). Since liquid crystals are relatively unknown, the people describe them by paraphrasing Bragg in 1934. Since liquid crystals are relatively unknown, the people describe them by paraphrasing Bragg in 1934. Some liquid crystal phases constitute a model of a soap-like organic system. For the application of self-inverse fractals, the people have confidence in fractal simulations of macromolecule chains and the ductile damage evolution of material.
