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Currently, ways to approach the design of Cyber Physical Systems in Industry 4.0 are under development. Emerging concepts of Smart Factories require the development of specialized knowledge; new working methods are also needed to manage the transition from conventional industry to industry 4.0. To achieve this objective, fractal theory could provide the appropriate knowledge and tools. Fractal systems applied to manufacturing have been widely used over the last decades to design complex adaptive systems: it allows the introduction of resilience requirements (capacity to react to changes in a turbulent environment) and to reduce the complexity of its structure, operation and management. In order to know the potential and the possibility of applying fractal theory to the design of systems in Industry 4.0, this article reviews the publications that develop fractal systems for manufacturing engineering. The review …