The term attractor is used to mean the set of states towards which other states in a given basin of attraction asymptotically approach in the course of evolution - the trajectory will always fall onto the same attractor. Many natural systems can be characterized as being chaotic - cosmic, meteorological, heart and brain of living organisms and so on. For a chaotic system, its strange attractor represents the envelope of possibility within which its future motion will be contained. These considerations make the attractor concept very useful in evolution studies, including the brain evolution studies. Brain evolution is a complex chaotic weave of processes bound by diverse rules and principles, and the factors driving evolutionary changes in brain structures probably changed over time. Nevertheless, brain evolves not altogether randomly, but in accordance with a set of leading laws or principles and human brain shares the same basic anatomical plan which is found in all mammals and even in amphibians and reptiles. Thus, nature has provided us with a robust message that the brain could be seen as an attractor over the course of evolution. In other words, biological evolution of higher animals is directed by their brain. Hopefully, these chaotic considerations and my humble CEREBRART work will prompt readers to seek more supporting evidence for the chaotic brain evolution theory.