IFSAM: A New Mathematical Technique for Additive Manufacturing based on Iterated Functions System

Optimization of geometric structures and shapes is currently an important part of applied research. the aim of this work is to use some mathematical methods to give tools for mounting geometric structures characterized by a self-similarity (fractals for example). The natural continuation of this montage is the transition to an automation of the 3D printing of objects. The mathematical approach used is based on iterated functions system (IFS). Indeed, based on an appropriate IFS, we define an operator W, as a superposition of all functions of the system, starting with a contraction of the geometric form representing the basic structure. The model we are trying to develop aims to create the equation of cellular structure and to apply the developed technique to a certain multiplicity number to obtain the desired structure.