From Harvard Natural Sciences Lecture Demonstrations this experiment caught my eye as it illustrates emergent properties really well. Patterns that are not found in the single entity but arise from the variance in it’s mutlitude. The effects of an emerging property correlates rather then being in direct causal realation to its parts.
In philosophy, systems theory, science, and art, emergence occurs when "the whole is greater than the sum of the parts," meaning the whole has properties its parts do not have.
Definition from Wikipedia – Emergence