Mathematician Benoit Mandelbrot coined the term “fractals” in 1975 to describe complex patterns he identified in nature. Picture a head of broccoli, Queen Anne’s lace, or a tree. Each contains small parts that look like the whole. In the new children’s book “Mysterious Patterns: Finding Fractals in Nature” (Boyds Mills), Sarah C. Campbell, aided by photographs she and her husband, Richard P. Campbell took, explains what does (lightning) and doesn’t (a swallowtail caterpillar’s markings) constitute a fractal. She delivers a tidy education, gives a nod to the use of fractals in the built world, and offers the hope that readers will invent new uses.