This invention deals with an integrated morphological system, herein called a morphological genome (morph genome), for design applications. This is the genome that encodes all form and is similar in intent to the biological genome that encodes all living things by its genetic code. The morph genome comprises a finite set of morphological genes, each gene specifies a distinct group of morphological transformations, each group of transformations is defined by a group of independent topological, geometric or other parameters. The morph genes and their parameters are mapped within an integrated higher-dimensional framework, with each parameter being represented along a vector in higher-dimensional Euclidean space. Each distinct number associated with a parameter or a group of parameters is represented by a distinct point in this space and is referenced by the higher-dimensional Cartesian co-ordinates of that point. This space uses a combination of discrete and continuous values for these parameters. The specific co-ordinates of any point in the space represent a genetic code for the specific form being mapped at that point. The entire space is a map of the morph genome and encodes all possible morphologies. The morph genome can be used as a design tool to generate known and new forms for applications in all fields of design including architecture, product design, environments and spaces, building or engineering structures, graphics, art, sculpture, technological devices, etc. The underlying method for the model for the morph genome applies to other fields of knowledge for systematically organizing and creating new concepts, structures, designs, information and taxonomies. The morph genome can also provide a basis for an integrated, interactive modeling environment for computers. It is a pedagogical tool for discovery and invention as well. Other applications include a graphic code for encryption as an alternative to numeric codes, and a system for representing numbers as integers, rational numbers and real numbers.