These patterns were first noted by the mathematician Benoit Mandelbrot, after whom the 'Mandelbrot set' is named. His 1983 book, The Fractal Geometry of Nature, shows the prevalence of such forms in all manner of realms, ranging in scale from microscopic particles of dust to entire galaxies in space. His ideas were at first received with considerable skepticism, but have since been widely accepted and better understood; their combination of widespread applicability and mathematical elegance sets them as a remarkable leap in the understanding of the world around us.
In passing, I'd like to note that this is the 100th post on this blog since I began it in February of 2009 -- I'm still finding new things to write about, and I look forward to many more posts and responses to come. Since the start, we've had 34,833 pageviews, from all around the world -- over 4,000 from Canada, 3,000 from Australia, 1,800 from Poland, 1,500 from Germany, more than 1,000 from Ireland, the Netherlands, Itay, and Hungary, and even 409 from India!
My thanks to everyone who has read and posted on the site.