The "all-over" abstract canvases that Jackson Pollock produced between 1943 and 1951 present a pedagogical challenge in how to account for their apparently chaotic structure. One reason that they are difficult to teach about is that they have proved notoriously difficult for art historians to come to terms with. This is undoubtedly a consequence of their abstraction. In 1950, "Time" magazine referred to them as "chaos," prompting Pollock to wire a heated reply, "NO CHAOS DAMN IT." Pollock's claim of "no chaos" can, however, be unpacked. This article looks at how a scientific analysis based on Chaos Theory and fractal patterns can be used to demonstrate to students that the paintings are indeed chaotic, but that this in turn provides evidence of an internal structure, an order within the chaos. This order is mimetically similar to other chaotic patterns and systems, from coastlines to economic systems. The author's overall position in this article is one of skepticism as to what such analysis ultimately has to offer in art historical, aesthetic, or pedagogical terms. (Contains 1 figure and 46 notes.)