The beautiful and complicated Mandelbrot set has captivated mathematicians since the first computer images of the set were drawn in the 1970s and 1980s. In this talk we’ll take a walk around the infinite intricacies of the Mandelbrot set, exploring the spirals, finding Fibonacci, and answering the question every maths student wonders when they first meet the Mandelbrot set: why do we care about this pretty picture?