Wolfram’s (not entirely original) central idea in A New Kind of Science is that a science around algorithms (or more likely mappings) is fundamentally different from a science governed by equations.
This is fair enough, you can create something very big and complex, like the universe by iterating an equation more simply than by creating an instruction to make it in one go.
There are ‘equations’ which are very simple, which when mapped onto themselves will create infinite complexity. This infinite complexity implies that all other equations can be created (a universal turing machine), nested within the original.
Cellular automata demonstrating these mappings can be unbelievably simple, i.e. a two state one dimensional systems with a handful of possible rules.
My hunch - adding the parameters of natural selection (variable inheritance within finite constraints), to any information carrying system will create a UTM (information carrying implies ‘bits’ i.e. two states and at least one dimension). Variable inheritance within finite constraints implies a finite universe (at any point in time) and rules which apply in chunks (i.e. like ‘turns’ in a game or metabolic cycles). This implies a universe with ‘information exchange’, even if the universe is made of continuous quantities, information can only be exchanged between systems in discrete quanta, bits.
Defining a system is tricky with being tautological or obvious. But its clear that all systems have boundaries or membranes which allow information to be transferred and filtered. i.e. a system is a partially enclosed macroscopic ‘feature’ in a sea of elements. The membrane acts to channel information flow and possibly process it. These ‘features’ require corresponding partner ‘features’ (which can be nested within the parent or external to it) made up of components of the same type (possibly in turn made up of sub components, determining their absolute granularity) for information to flow using compatible ‘bits’ of the same flavor.
So that’s all you need:
1. Systems comprised of a finite number of bits (the cells in a cellular automaton, perhaps the surrounding ‘environment’ can even be infinite) 2. cycles of interaction between systems (flow of bits), 3. Inherited rules of interaction (any rule, the rules will morph to ‘useful’ ones, under natural selection and perhaps information exchange via the same flavor of bit implies rules, the inheritance is defined by the physics of the systems), 5. Inaccuracy in the rules (so that natural selection can apply).
The inaccuracy in the rules could be as a result of noise in the system (i.e. the environment, consisting of a sum total of other systems than the ones in question). In other words only a truly isolated system would have no variation, and there is no such thing as a truly isolated system.
Since a simple two state system can create a UTM, the ‘meta rules’ which define what the universe of possible rules are might be fixed and simple.
This leaves the only variable, being the level of noise. This might even imply some sort of self organized criticality, where the universe of what existed over time was tuned and lay on a boundary between too much noise and too little.
So all you need for a recipe for the universe is:
Interaction between macroscopic features and time.
Emergent features as a result of acting under natural selection are implicit in the information exchange itself and require no other variables.