**4. Discussion**

The results summarized in the previous section are discussed in more detail in the subsections that follow.

#### *4.1. Complex Cycle Examples Arose from a Simple Model of a Cycle*

The first significant finding from formally modeling a cycle in MP was that such a simple model of a cycle (on the order of six lines of code) could produce such an impressively large and diverse number of "cycle instances" (nearly 3000 unique instances of cycle behavior when the model is run at scope 3). A very simple model of a cycle gave rise to a large number of behaviors whose complexity increased with run scope. This supports the notion that simple rules exist at the foundation of complex behaviors, and suggests that if we can distill and formalize these simple system and process behavior rules, we can (to some extent) reproduce more complex system behaviors in simulation for study and comparison with actual systems. MP also provides a capability to check for the presence or absence of model properties of interest in large sets of simulation instances. In practical terms, this means that, if we know or suspect a particular cycle instance could occur, we can query the data set to see if there are any examples of it. MP modeling therefore provides the SPT community with a means for formally testing, verifying and validating ideas that have to date only been informally discussed, debated, and refuted without automated tools to support the discourse.

#### *4.2. Cycle ISP Patterns Previously Discussed and Described Informally Were Inherently Present among the MP-Generated Examples*

Upon inspection of these automatically generated instances, it became apparent that some of the instances inherently contained similar patterns. The patterns that emerged, in fact, matched many of the identifying features for cycles that had been informally discussed and debated as part of the ongoing SPT research, including oscillation, recycling, and lifecycles. These results provide an affirmation that the earlier SPT discussions on cycling pertaining to the recognition of oscillations, recycling, and lifecycles as related ISPs was warranted and supported by results of the MP runs. There is a significant extension of this result. Just as MP generates many versions of the original ISP process in computer "space", so also does nature in real systems generate many variants on cycling in real, dimensional space (e.g., through evolution). This MP feature could lead to the examination of the potential for generation of "artificial systems" de novo in computer space.

Furthermore, MP generated both singular and compound examples of patterns, i.e., examples that contained each pattern by itself, and patterns combined with or nested within other patterns. Moreover, because MP is exhaustive in its scenario generation, we can guarantee the set of examples generated contains every possible pattern combination expressible by the model up to the scope limit [10]. As discussed earlier, scope limit is a lightweight formal methods concept that places an upper bound on the number of event iterations in the model in order to limit the simulation run time. The Small Scope Hypothesis [47] is used as a heuristic to enable us to find most of what we are interested in knowing about cycles at a small run scope (typically scopes 1, 2, or 3). Cycle patterns that present at scopes 4 and 5 are also expected to present in some shape at scope 3. Prior experiments with run scopes [48] lend some confidence to this heuristic, but these current assumptions for MP can also be tested for the Cycles ISP model as part of follow on work.

By implication, the recognition of some known patterns in the generated example set suggests that several other possible variants on cycling should also be explored. Waves, solitons, iteration/recursion, spin, and hypercycles [9] are some of the other recognized variants of the Cycle ISP that were not observed in scenarios arising from the current Cycles ISP MP model, but the as-is MP model of a cycle provides a canvas for exploring how these variants could also possibly emerge from this model or from a revised model containing refinements informed by reasoning with MP tools. The Cycles ISP MP model lays the groundwork for follow on research to determine whether the aforementioned variants should be considered as the same thing as the Cycling ISP or as completely independent ISPs. Such experiments should support the development of a repeatable methodology for using MP modeling to inform SPT research on this question and across all the 110 candidate ISPs.

#### *4.3. Positive and Negative Reinforcements Emerged in the Cycle Examples*

Although the previously discussed patterns had been recognized and debated in SPT research, we did not even discover, recognize or debate the involvement of two additional behaviors until the MP modeling exposed them: namely, "reinforcements". Among the Cycles ISP MP model examples were completely unforeseen influences and essential participation of both positive and negative reinforcements as part of the process. Reinforcements have commonly known relationships with cycles, but we did not foresee them emerging in examples from the Cycles ISP MP model. Positive and negative feedback had been argued by one SPT cohort as necessary for oscillation to occur; however, other cohorts disagreed. The presence of these patterns could provide a basis for reasoning about how positive and negative reinforcements influence cycling, as well as what "reinforcement" actually means in models of real phenomena. This discovery opens the door to a further line of questioning: How can emergen<sup>t</sup> patterns and behaviors like this inform the aforementioned debates? How were these cycling, and how likely was each instance? Should they each be explored as individual isomorphs, or be considered variations on each other? How many additional behaviors could MP discover for SPT for the other 54 or 110 ISPs?

#### *4.4. Implications for Systems Science Research*

Modeling SPTs using MP provides a promising virtual "systems laboratory" to examine billions of years of optimization or improvement or evolution of natural systems. The basic tenet of SPT is that the reason we now can see and empirically or experimentally prove the existence of common patterns (ISPs) is that all of these systems, composed of entirely different parts, originating at different times, at totally different scales, across many types of systems, solve their myriad challenges by "falling into" these common isomorphic dynamics or solutions. By definition, SPT models are prescriptive and

not just descriptive. This is their distinction from other System Dynamics (SD), or Soft Systems Methodology (SSM), or Interpretive Structural Modeling (ISM) models. They do not compete with those; they should be added to those as the possibly prescriptive component.
