"Spiral waves in colonies of the mold Dictyostelium discoideum. These patterns are created when the mold forms aggregates in response to some external 'stress', such as a lack of moisture or nutrients." (BALL, 1994)

Particles colliding in a particle accelerator

A Wada Basin is a naturally occurring fractal that can be constructed using 3 mirrored spheres as above.

Soap bubbles close up.

Discover's "Most Psychedelic Images in Science"

Each of these little critters was drawn using a very simple rule repeated over and over again (recursively). Recursion seems to pop up all over nature- whether it's coastlines that look like fractals; sea shells; or broccoli minaret. Richard Dawkins, well known for his criticism of creationism, wrote the code that generated these images. This image is printed in his book "The Blind Watchmaker" to show that as intricate and beautiful as all things in nature are, all that is required is repetition of very simple rules, weakening the intelligent design argument.