Many of the emblematic buildings constructed at present shows many formal and technological innovations that have not been satisfactorily resolved by the existing CAAD software. Frank 0. Gehry's Guggenheim Museum in Bilbao is a good example of architecture whose shapes and design are very advanced from the concepts and tools used by CAAD. The search for new creative resources, from the educational and professional point of view, must be a priority. This will be the only way to get that CAAD contributes essentially in the process of architectural innovation, instead of merely being a reproduction tool. From this viewpoint the computer exploration of the three dimensional form is presented in here. The concept of abstract art, that has been successfully applied to painting and sculpture in this century is used as a way to experiment, design and create architecture. This paper juxtaposes three approaches, three different ways of understanding the abstract character, with the purpose to create new objects and environments, which are exclusively characteristic for computer space. This juxtaposition shows how creative and innovative activities in the field of CAAD can be developed using different intellectual bases: intuition, mathematical formulas and genetic algorithms.