Models of consciousness are usually developed within physical monist or dualistic frameworks, in which the structure and dynamics of the mind derive from the workings of the physical world (in particular, the brain). Little attention has been given to modeling within a mental monist framework, deriving the structure and dynamics of the mental world from primitive mental constituents only. Mental monism is gaining attention as a candidate solution to Chalmers’ Hard Problem, and it is therefore timely to examine possible formal models of consciousness within it. Here, we propose a minimal set of hypotheses that any credible model of consciousness (within mental monism) should respect. From those hypotheses, it is feasible to construct many formal models that permit universal computation in the mental world, through cellular automata. We need further hypotheses to define transition rules for particular models, and we propose a transition rule with the unusual property of deep copying in the time dimension. In conclusion, we hope to dispel the notion that mental monism requires a deus ex machina, by showing that a parsimonious set of assumptions can yield a naturalistic and computationally potent mental world.