Limits and potentialities of fractals in architecture and urbanism

In the 1980's, after Mandelbrot"s publishing the fractal geometry theory and after the emergence of Complexity Theory in the 1970's, some Post-modern architects employed fractals in the design. The goal was to create complexity, deviating from Modern architecture normative and adopting a new theory in architecture. On the other hand, the recent revival and advance of complex shapes in architecture are related to the design process automation and digital fabrication possibilities. These innovations require excellent mathematical and computational knowledge from architects and urbanists, allowing them to use generative systems or iterations, for instance. Despite the intense application of fractals in architecture since then, it is possible to ascertain that these appropriations were many times unintelligent or misguided. To comprehend the application of this geometry in architecture it is necessary to explore the literature on the topic, observing the design phases which might benefit from fractals. This paper presents trends identified on a literature review (mapping study) of primary studies related to fractals aiming to produce a synthesis of evidences supporting real applications of fractals on design. We categorized the papers in to five big groups: perception analysis, urban analysis, design teaching, theoretical and conceptual critics, and architectural practice. We confirm the potential of fractals in architecture and indicate that this geometry can be applied in several design phases, from conception to detail, from ornament to urban design. However, misinformation about fractal geometry might create complications for the design process or opportunities to advance the design might be lost. We concluded that fractals offer a contribution to the design when there is theoretical and mathematical support, thus the renovation of architecture courses towards the "programming architect" profile can expand the application of fractals in architecture.