**3. Results**

A simple formal model of the Cycles ISP starting with just two lines of MP code (version 1) exposed patterns of oscillation, positive reinforcement, negative reinforcement, and combinations thereof. Revisions to this model (version 2) contained six lines of code and exposed these same patterns plus additional patterns of lifecycle, recycling, and all combinations thereof. Table 2 provides the run statistics for the number of cycle examples produced at each scope and the scenario generation times on MP-Firebird.



1 Macbook Air, macOS version 10.13.3, 2.2 GHz Intel Core i7, 8 GB 1600 MHz DDR3.

The number of possible combinations of unique cycle patterns is visible in the exponential growth in the number of scenarios as scope increases. From a small model of six lines of code, we see that thousands of cycle scenarios are possible. These numbers represent the exhaustive set of cycle model scenarios, providing full coverage of possible outcomes up to the indicated scope [10].

An objective of this research was to see if any MP behavior scenarios presented mini-models of previously discussed variants for the Cycle ISP. We indeed found patterns for oscillation, recycling, and lifecycles in the MP model of the Cycle ISP. We did not isolate patterns for waves, solitons, iteration/recursion, spin, and hypercycles during this initial effort, but these may become evident after further inspection or refinement of the model and consideration of different discinyms for event names. The act of modeling may raise significant new questions about these currently considered variants on cycling that challenge the SPT community's initial hypotheses of their being the same pattern as cycling. Constraining the list of variants on cycling would be an important advance in SPT and to applications of cycling to SE.

One surprising result from this research was the presence of both positive and negative reinforcements in the cycle examples. These were not anticipated or identified as directly associated with the Cycles ISP in previous SPT research. Cycles and Feedbacks are actually separate systems processes in the current consensus on SPT, if we consider positive and negative reinforcements as positive and negative feedbacks. SPT has linkage propositions that connect + and − feedback with oscillations, but this has been challenged by SE members of INCOSE in past International Workshop discussions. It appears models of real biological systems incorporate feedback to ge<sup>t</sup> oscillating behavior but that this is less known in the physical sciences. To have independently found them in MP event traces of cycling brings new information to the SE debate.

There is precedent for this development, from an MP modeling perspective. MP has delivered surprising scenarios before by containing unanticipated behavior examples in models by different users, of different systems, in different domains [33,37,39,41,44]. This research adds to the body of work showing MP's ability to illuminate unexpected emergen<sup>t</sup> behaviors, and potential to be put to use for the SPT research.
