How can the concept of fractals be applied to optimize urban planning and sustainable growth?

Urban planning often deals with complex systems that require an efficient use of space and resources to promote sustainable growth. Fractals, known for their intricate patterns repeating at every scale, offer a unique perspective in optimizing such systems. These naturally occurring patterns can be seen in various aspects ranging from the branching of trees to the formation of river networks. By incorporating fractal mathematics into urban design, planners can potentially enhance infrastructure efficiency, reduce environmental impact, and create resilient urban spaces that mimic natural processes. How might these principles revolutionize traditional urban planning approaches and what challenges could they present?