# Analysis, Generation, and Validation of New Boards for the Game Micro Robots
## 7 Conclusions and Future Work  
Although a variety of boards were generated using the random generator, there was a significant difference in the time taken to generate 4 \(\times\) 4 boards compared to 6 \(\times\) 6 boards, suggesting that the cost of producing 6 \(\times\) 6 boards is higher. This is due to the larger set of square combinations to combine, the larger total set of square combinations, and the greater effort required to explore all configurations when rotating and rearranging quadrants. Regarding systematic generation, the applied methodology allowed for the generation of a large number of valid 4 \(\times\) 4 boards, although this number was limited compared to the total set of possible theoretical combinations. However, this system proved to fulfill its purpose.  
Regarding the analysis, it is concluded that the generated boards show some similarity to the original boards in terms of complexity, presenting small variations. This suggests that the shape and layout of the board are closely related to the design and functionality of the board game. This consistency is due to its layout directly responding to the needs imposed by the design of the game itself. Specific and well-defined design patterns are observed, ensuring a balanced gaming experience. Therefore, the difficulty of the game is not determined by the distribution of the squares but by the game mechanics and the starting and ending points.  
Future work should focus on:  
* Finding a way to speed up the permutation of squares to explore the set of combinations faster.
* Extending our analysis by incorporating additional measures such as the average degree of vertices, and the average shortest path length, among others, to obtain deeper insights of the generated boards.
* Using heuristic algorithms to explore the search space more efficiently.
* Generating all possible game boards.
* Searching for new patterns and configurations of more complex boards.  
Finally, this work represents a significant advance in the development of a comprehensive tool that allows for the expansion of content for this type of game in a precise, fast, and efficient manner.  
Conceptualization, F.B. and N.A.B.; methodology, F.B. and N.A.B.; software, K.S.; validation, F.B., K.S. and N.A.B.; formal analysis, F.B.; investigation, F.B., K.S. and N.A.B.; data curation, K.S.; writing--original draft preparation, K.S.; writing--review and editing, F.B. and N.A.B.; supervision, F.B.; funding acquisition, N.A.B. All authors have read and agreed to the published version of the manuscript.  
This research was partially funded by the National Agency for Research and Development (Agencia Nacional de Investigacion y Desarrollo, ANID Chile), FONDECYT Iniciacion grant 11220438.  
The dataset is available from the authors upon request.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{2}{c}{**Original Board**} & \multicolumn{2}{c}{**Generated Board**} \\ \hline \multirow{2}{*}{**Type of Link**} & **Average of** & **Standard** & **Average of** & \multirow{2}{*}{**Standard Deviation**} \\  & **Links** & **Deviation** & **Links** & \\ \hline Single link & 2.06 & 1.54 & 2.62 & 1.32 \\ Double link & 7.90 & 2.82 & 8.78 & 2.99 \\ Triple link & 12.78 & 2.59 & 10.18 & 2.42 \\ Quadruple link & 8.74 & 2.48 & 9.44 & 2.83 \\ Quintuple link & 2.68 & 1.24 & 3.74 & 1.86 \\ Sextuple link & 1.58 & 1.22 & 1.14 & 1.00 \\ Septuple link & 0.24 & 0.47 & 0.10 & 0.30 \\ Octuple link & 0.02 & 0.14 & 0.00 & 0.00 \\ \hline Total links & 36 & & 36 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of links based on 50 board configurations: original board vs. generated board.