Toward Error-free Manufacturing of Fractals

Fractals are self-similar-scale-invariant entities and often used for modeling complex shapes including natural (e.g., plant, leaf, flower, animal, landscape, etc.) and aesthetically valuable ones (e.g., shapes used in jewelry, buildings, etc.). The purpose of this study is to provide more insights into the error-free manufacturing of fractals. In particular, Hilbert-type space-filling fractals and Iterative Function System based fractals (leaf-like shapes) are manufactured by using both additive (stereolithography) and subtractive (milling) manufacturing processes. The manufacturing errors are identified and the plausible solutions for overcoming the errors are outlined. The findings demonstrate that novel manufacturing process, tooling, and algorithms are needed for achieving error-free manufacturing of fractals.