The purpose of this study is to propose a topological design principles and to analyze the space of digital architecture applying topological invariant expressive characteristics. As this study is based on topology as a science of true world's pattern, we intented to explain the concepts and provide some methods of low-level and hyperspace topological invariant Properties. Four major aspects are discussed. Those are connection theory, boundary concept, homotopy group, knot Pattern theory as topological invariant properties. Then we intented to make understand topological characteristics of the Algorithms, luring machine, cellular automata, string theory, membrane, DNA and supramolecular chemistry. In fine, the topological invariant properties of the digital architecture as genetic algorithms based on self-organization and heterogeneous networks of interacting actors can be analyzed and used as a critical tool. Therefore topology can be provided endless possibilities for architecture, designers and scientists intended in expressing the more complex and organic patterns of nature as life.
