Cutting across art, design and science, the importance of drawing as a system, a process or a field enabling pioneering visual and conceptual investigation, is stressed even more. With the aid of information technology, the fast growing inter-scientific investigation of complex dynamic systems and chaos, inspires the continuing expansion of art, mainly in terms of developing abstraction and visualisation research. A new understanding of phase-space enables new modes of drawing in its evolving interdisciplinary context. Particularly inspiring is the evolving relation of mathematics to abstraction and the ¿inconceivable¿, together with all those potentialities and challenges of giving complexity and chaos a geometric form. Indirect and intrinsic types of delineation are invented for the scientific ¿scanning¿ of the assumed ¿edges¿ of interacting force-fields. Even the basic geometric elements have become topologically transitive states with their own inter-dimensional ¿memory¿, statistic potentiality, generative behaviour and paradox.