Dynamics of creative mental activity are examined in waking and dreaming processes which manifest beyond normative waking consciousness. Some consider such phenomena to be pathological or meaningless. Alternatively they may be viewed in new and healthier ways, in the context of adaptive mental controls, using nonlinear dynamical/chaos theory. The first example involves the innovativeness reported with mild mood elevation in bipolar mood disorders, linked to a compensatory advantage model of everyday creativity. With adequate controls, such mood elevation may open adaptive creative mental possibilities (in fact, for all of us). Tension between divergent and convergent thinking-as noted by J.P. Guilford, and common to many models of creative process-can further "edge of chaos" states and raise the odds of bifurcation to new and creative chaotic attractors. The second example involves REM sleep and dream phenomena, where the self-organizing brain coordinates the dream's component parts to generate unusual dream narratives. However fanciful, such divergent and condensed dream content may lead to creative insights and adaptive narratives (there are famous examples) in the light of day, when interpreted or further developed, by bringing convergent processing to divergent processing. In each case, one finds the abnormal is not necessarily pathological-and sometimes can be usefully exceptional. One consequence of a dynamical view and these examples is the need, in all of us, for greater openness to experience, and acceptance of a greater divergence of expression and behavior (vs. conformity) in ourselves, our culture, and our world.