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In effect, the computing-element reality model explains personally experienced reality as a computer-generated virtual reality. Similarly, modern computers are often used to generate a virtual reality for game players. However, there is an important difference between a virtual reality generated by a modern computer and the ongoing virtual reality generated by the computing elements. From a personal perspective, the virtual reality generated by the computing elements is reality itself; the two are identical. Put another way, one inhabits that virtual reality; it is one’s reality.
For the last few centuries scientists have often remarked and puzzled about the fact that so much of the world can be described with mathematics. Physics textbooks are typically littered with equations that wrap up physical relationships in nice neat formulas. Why is there such a close relationship between mathematics and the workings of the world? This question is frequently asked.
Mathematics is, in effect, the product of computation. At its base, mathematics is counting (numbers are counts); a simple algorithm. For a reality that flows directly from an underlying computation layer—the essence of the computing-element reality model—mathematics is a natural part of that reality. A finite reality that results from finite computations is going to have relationships and patterns within it that can be quantified by equations.
Note that the high degree of order and structure in our reality is a direct reflection of the high degree of order and structure in the computing-element program. To help make this clear, imagine a simple reality-generating program that generates, in effect, nothing but noise: a sequence of random numbers. For that kind of reality, even though it is finite, the only relationship or pattern within that reality that applies over a wide area is the trivial one regarding its randomness. Thus, for example, in that reality you will not find the relationships and patterns described by the equations of our physics, such as, for example, Newton’s laws.
Regarding what the computing-element reality model allows as possible within the universe: Because all the equations of physics describing particle interactions can be computed, either exactly or approximately, everything allowed by the mathematics-only reality model is also allowed by the computing-element reality model.
The mathematics-only reality model disallows particles whose interactions cannot be expressed or explained with equations. By moving to the computing-element reality model, this limitation of the mathematics-only reality model is avoided.
 For a formal treatment of the relationship between a program and its output when given the order and structure of that output, see, for example:
Chaitin, Gregory. “Information-Theoretic Computational Complexity.” In New Directions in the Philosophy of Mathematics, Thomas Tymoczko, ed. Princeton University Press, Princeton, 1998.
 Equations that cannot be computed are useless to physics, because they cannot be validated. For physics, validation requires computed numbers that can be compared with measurements made by experiment.