Pluripotency is a cellular state of multiple options. Here, we highlight the potential for self-organization to contribute to stem cell fate computation. A new way of considering regulatory circuitry is presented that describes the expression of each transcription factor (TF) as a branching process that propagates through time, interacting and competing with others. In a single cell, the interactions between multiple branching processes generate a collective process called 'critical-like self-organization'. We explain how this phenomenon provides a valid description of whole genome regulatory circuit dynamics. The hypothesis of exploratory stem cell decision-making proposes that critical-like self-organization (also called rapid self-organized criticality) provides the backbone for cell fate computation in regulative embryos and pluripotent stem cells. Unspecific amplification of TF expression is predicted to initiate this self-organizing circuitry, where cascades of gene expression propagate and may interact either synergistically or antagonistically. The emergent and highly dynamic circuitry is affected by various sources of selection pressure, such as the expression of TFs with disproportionate influence over other genes, and extrinsic biological and physical stimuli that differentially modulate particular gene expression cascades. Extrinsic conditions continuously trigger waves of transcription that ripple throughout regulatory networks on multiple spatiotemporal scales, providing the context within which circuitry self-organizes. In this framework, a distinction between instructive and selective mechanisms of fate determination is misleading because it is the 'interference pattern', rather than any single instructing or selecting factor, that is ultimately responsible for computing and directing cell fate. Using this framework, we consider whether the idea of a naïve ground state of pluripotency and that of a fluctuating transcriptome are compatible, and whether a ground state like that captured in vitro could exist in vivo.