MYSTERIOUS PATTERNS

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!

For visual learners, this is a particularly accessible demonstration of an intriguing concept.