Mysterious Patterns: Finding Fractals in Nature

Through examples of what fractals are and what they aren’t, this photo essay introduces a complex mathematical idea in a simple, inviting way.

Using a straightforward text and eye-catching photographs, the Campbells start with the familiar: spheres, cones, cylinders—shapes readers can find and readily name in their environments. But then they move on to the more elaborate forms: a head of broccoli, the flower of a Queen Anne’s lace, a tree. In 1975, Benoit Mandelbrot gave a name to natural shapes with smaller parts that look like the whole shape. He called them fractals. Photographs of whole and divided flower and broccoli heads, set on plain backgrounds, demonstrate how smaller parts repeat the shape of the whole. A double-page spread of forked lightning shows another example. Even mountain ranges are made of smaller mountains. Further, smaller images remind readers that the shapes can be called fractals only if the repeating parts diminish in size. In conclusion, the author of Growing Patterns (2010) provides instructions for drawing the interesting fractal pattern that surrounds each page number. An afterword by mathematician Michael Frame offers more information about Mandelbrot and introduces the possibility of a real-world application of this abstract idea: invisibility cloaks!

The husband-and-wife team behind Growing Patterns: Fibonacci Numbers in Nature (2010) demystify the concept of fractals, which mathematician Benoit Mandelbrot used to help understand complicated shapes in nature. "Every fractal shape has smaller parts that look like the whole shape," explains Campbell, with an illustration of a tree's dividing branches making the idea instantly clear. Elsewhere, an image of the airways, veins, and arteries in a pair of human lungs beautifully illustrates the notion of repetition in fractal patterns, echoed through figurative language: "Lungs continue to develop inside our bodies throughout childhood, growing like a tree to fill the space inside our chests." This fascinating exploration should awaken readers' powers of observation and appreciation for the intricacies of nature. Ages 5-7. (Apr.)

Gr 3-6--The team who explored the Fibonacci sequence in Growing Patterns (Boyds Mills, 2010) returns with a similar book about fractals. Until 1975, there was no name for shapes in nature in which smaller parts looked like the whole shape. Then mathematician Benoit Mandelbrot, who had been thinking about and studying these patterns, named them fractals. Using clear text and outstanding color photographs, Campbell explores the concept of these unusual shapes. Beginning with circles, cones, and cylinders, she leads readers carefully and concisely through examples of fractals such as trees, rivers, mountains, broccoli, lightning, and lungs. The photographs, sometimes highlighting the ever-smaller pieces of a vegetable fractal against a black background, sometimes drawing back to give a aerial view of a geological feature, are crisp and precise and underscore the clear text. The book invites readers to construct a geometric fractal as a hands-on exemplar of the concept. An afterword reveals more of Mandelbrot's background and work, which will be an inspiration to budding scientists/mathematicians.--Marge Loch-Wouters, La Crosse Public Library, WI