On the Use of the Game of Life to Improve the Performance of Event-Driven Wireless Sensor Networks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 

The manuscript presents an interesting and original approach to energy-efficient scheduling in Wireless Sensor Networks (WSNs) by using Cellular Automata (CA), particularly Conway’s Game of Life (GoL), to determine when sensor nodes should be turned on or off. The core idea is to take advantage of emergent spatial-temporal patterns to coordinate node activation without relying on probabilistic scheduling or complex computation. Overall, the paper is well organized and contributes to a niche but valuable area of research. However, several key points need to be addressed to improve the manuscript and clarify its practical implications:


Concern 1:

The proposed model relies heavily on the assumption that sensor nodes can be placed precisely on a grid that corresponds to the evolution of the GoL pattern. In real-world deployments—especially in outdoor or uneven environments—this level of precision is often impractical. The authors should address how sensitive their approach is to deviations in node placement. Also, whether the system still performs well if sensors are misaligned from the intended lattice.


Concern 2:

The approach appears best suited to scenarios where the monitored phenomenon (e.g., an intruder, fire, or leak) follows a predictable path that matches a known GoL pattern. While this is clearly stated in the paper, it significantly limits the generalizability of the method. The authors are encouraged to clarify what types of applications would realistically meet these assumptions and whether the system could adapt to partially known or dynamically changing patterns.


Concern 3:

Although the paper focuses on detection probability and energy consumption, it would be helpful to include additional performance metrics such as detection delay, false negative rate, or even estimated network lifetime. These metrics would give a better-rounded picture of system performance and could help demonstrate the benefits or trade-offs of using CA-based scheduling more clearly.


Concern 4:

The authors have implemented a detailed simulation and provide extensive results, but there is no mention of real-world validation or even emulated hardware testing. Even a small-scale real deployment or inclusion of realistic noise, interference, or sensor faults in the simulation could improve the credibility and relevance of the findings. The authors should acknowledge this limitation and discuss it as part of their future work.


Concern 5:

The use of toroidal boundary conditions in the simulation is understandable from a modeling perspective, but such boundaries are unrealistic for most physical deployments. This choice may affect detection behavior near edges in a way that doesn’t reflect real conditions. The authors should either justify this modeling choice more explicitly or suggest how their method could be adapted to finite or irregular boundaries.


Concern 6:

While the figures and surface plots provide useful visual insights, their integration with the text is limited. In several places, figures are referenced but not discussed in detail example Figure 1 is not discussed in system model. Enhancing the captions and including more interpretation of what the figures show—especially in the Results section—would improve clarity and readability.

Comments on the Quality of English Language

Ok

Author Response

Concern 1:

The proposed model relies heavily on the assumption that sensor nodes can be placed precisely on a grid that corresponds to the evolution of the GoL pattern. In real-world deployments—especially in outdoor or uneven environments—this level of precision is often impractical. The authors should address how sensitive their approach is to deviations in node placement. Also, whether the system still performs well if sensors are misaligned from the intended lattice.

A.R.1.1 Indeed, this is a major point of our proposal. Our proposal is very sensitive to sensor placement in the grid in the sense that each node installed in the region of interest reacts to the neighbor activity according to the GoL rules. In this regard, if a node is not placed in the specific pattern pathway, it may never turn ON, becoming completely useless to the monitoring tasks, or worse, it can interfere with the pattern and produce a different pattern that propagates to other regions or lose the periodicity. As such, a misplaced node may produce activity in areas not intended by the system administrator, or turn OFF all nodes after some time. Hence, our proposal is only intended for very specific cases where: a) nodes cannot be moved; b) nodes are placed in very specific locations. We are well aware that this is not the common use of WSNs, but in cases where it is possible, the use of Cellular Automata renders important energy savings. When this is not possible, the use of common ON/OFF patterns is advisable.    

 

We have added a paragraph in Section I regarding this issue.

Concern 2:

The approach appears best suited to scenarios where the monitored phenomenon (e.g., an intruder, fire, or leak) follows a predictable path that matches a known GoL pattern. While this is clearly stated in the paper, it significantly limits the generalizability of the method. The authors are encouraged to clarify what types of applications would realistically meet these assumptions and whether the system could adapt to partially known or dynamically changing patterns.

 

A.R.1.2 We agree and thank the reviewer for the observation. First, the monitored phenomena must be restricted physically to the GoL pathway. For example, restricted by walls, riverbanks, vehicles on roads (but more in the sense of driveways and not in highways due to the extension of the region of interest, considering that nodes have to be placed in specific locations). Second, they are restricted by time, in the sense that the GoL pattern evolves in time. The idea would be to evolve at the same time as the phenomena, but not necessarily since the GoL would repeat again. Hence, the monitored event can be evolving slower than the GoL pattern and still be accurately observed, but not faster since it would leave the monitored path faster than nodes turning ON. 

 

In this sense, the use of our proposal in flooding, where water is physically restricted to roads in cities, and knowing the fluid dynamics, may prove to be an ideal case of study. Also, human or animal intruders in hallways, alleys, and bridges may also be a good example where our proposal works adequately. In this case, the intruder may walk at a random speed, but due to the periodicity of the GoL it can still be detected. Another potential application is in domotic scenarios, where pets (dogs, rabbits, turtles, for instance) are set loose or escape and follow well-known trajectories; in this case, there may not be a physical barrier, but we all know that these home companions are very predictable in certain cases. Hence, GoL-based WSNs would be very helpful to timely alert these events.

We have added a paragraph in Section I regarding this issue.

Concern 3:

Although the paper focuses on detection probability and energy consumption, it would be helpful to include additional performance metrics such as detection delay, false negative rate, or even estimated network lifetime. These metrics would give a better-rounded picture of system performance and could help demonstrate the benefits or trade-offs of using CA-based scheduling more clearly.

A.R.1.3 We agree. We have included the system lifetime as a performance metric. Although detection delay and false negatives would also be important performance metrics, we believe that it would require much more time since new mathematical analyses have to be developed. We have included this in the future work of our proposal.

 

We have added a paragraph and Figure 26 in Conclusion section addressing this.

Concern 4:

The authors have implemented a detailed simulation and provide extensive results, but there is no mention of real-world validation or even emulated hardware testing. Even a small-scale real deployment or inclusion of realistic noise, interference, or sensor faults in the simulation could improve the credibility and relevance of the findings. The authors should acknowledge this limitation and discuss it as part of their future work.

A.R.1.4 Absolutely, it is relevant to mention this point. This is a theoretical proposal where no physical or practical implementation of nodes is considered. This is mainly for budget and time restrictions since it would require a restricted area in the campus to implement nodes for a relatively large period using commercial nodes. We believe that if we consider in our mathematical model other parameters like noise, sensor faults, and interference, it would render closer results to practical scenarios. In this regard, it is important to mention that, in this work, we intend to show the potential benefits of using different GoL patterns in the WSN context, which we believe we have done. Future research work can be focused on the physical implementation of such dynamics, which would give more insight into the use of CA in WSNs. 

We added a paragraph in Conclusion section addressing this.

Concern 5:

The use of toroidal boundary conditions in the simulation is understandable from a modeling perspective, but such boundaries are unrealistic for most physical deployments. This choice may affect detection behavior near edges in a way that doesn’t reflect real conditions. The authors should either justify this modeling choice more explicitly or suggest how their method could be adapted to finite or irregular boundaries.

 

A.R.1.5

We understand the concern about the physical mapping of the model with reality. In the context of our approach the boundary conditions are merely for the model inner working (i.e., the Game of Life Cellular Automata). The evolution of this CA runs independent of the actual WSN. The only physical connection between the two is in the sensors positioning that turns ON/OFF the sensors. Hence, the toroidal shape is only used so that the GoL continues its evolution in time but it is not related to the physical boundaries of the WSN.

 

A paragraph regarding this issue has been added in Section

Concern 6:

While the figures and surface plots provide useful visual insights, their integration with the text is limited. In several places, figures are referenced but not discussed in detail example Figure 1 is not discussed in system model. Enhancing the captions and including more interpretation of what the figures show—especially in the Results section—would improve clarity and readability.

 

A.R.1.6 We have updated the section to reflect these changes, so the figures are incorporated into the main text and also the caption provides clearer information

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript proposes using Conway’s Game of Life (GoL) cellular automaton to govern the ON/OFF scheduling of nodes in an event‐driven wireless sensor network (WSN). By mapping alive/dead cells to active/idle sensors, the authors derive closed‐form expressions for detection probability and energy consumption, and validate their model via large‐scale Monte Carlo simulations over four canonical GoL patterns (Glider, Gosper Gun, period‑60 Gun, Simkin Gun) versus classical random ON/OFF with fixed activation probability. They report cases where GoL‐based schemes outperform uniform probabilistic scheduling in terms of detection probability per energy unit.

1. Novelty of Contribution

1. • The use of cellular automata (CA) to modulate WSN duty cycles has precedent (e.g. Banerjee 2011; Fu 2020; Reyes 2022) . The manuscript must more clearly articulate what new theoretical or practical insight arises from employing Game of Life specifically, rather than any CA. In particular:

     • Why are GoL patterns superior to simpler CA rules (e.g. cyclic CA) previously studied?

     • What unique mathematical properties of GoL (e.g. periodicity, glider propagation) yield provably better energy–detection trade‑offs?

2. Mathematical Rigor and Model Assumptions

   • Table 1 reports PON “localized” versus “unlocalized” values for each pattern, but the method of estimation (analytical limit vs. empirical average) is unclear. A brief proof or derivation of the closed‐form PON for a given periodic GoL pattern should be provided.

   • Equations (3)–(6) assume independent event occurrence and sensor placement. However, under a GoL schedule, node activity is spatially and temporally correlated. The authors should discuss how these correlations affect the validity of the simple product form Pdetection=Pevent Psensor PON.

   • The choice of Etr=1,Eon=0.9, Eidle=0.01 (Eq. 7) is arbitrary. While normalization is acceptable, include a sensitivity analysis (even in an appendix) showing how results vary when EonE_{\text{on}} and EidleE_{\text{idle}} differ by ±20 %.

3. Simulation Design and Statistical Significance

   • The authors perform 1 000 000 Monte Carlo iterations but report only mean detection probability and energy consumption surfaces. It is essential to include confidence intervals (e.g. 95 % bounds) or standard deviations on key curves to demonstrate statistical robustness.

   • The sensors are “placed randomly in the cells” for unlocalized events but “placed only where the GoL pattern acts” for localized experiments. This conflates deployment and scheduling. Suggest separating the two: keep sensor deployment fixed and vary only the ON/OFF rule to isolate scheduling gains.

4. Relevance to Mathematical Audience

   • The readers expect novel theoretical development. As currently written, the manuscript reads more like an applied‐simulation study. To strengthen its mathematical appeal, consider:

     • Formalizing the convergence properties of event coverage under periodic GoL rules.

     • Proving bounds on detection probability versus energy consumption in the limit of large lattice size.

     • Characterizing the optimal initial GoL configuration (pattern) that maximizes a weighted combination of detection and energy metrics.

 

Notation and Definitions

• • Introduce the sensor detection neighborhood nn formally when first mentioned (Section 3) and use consistent notation (e.g. rr vs. nn).

  • In Eq. (1), clarify that Nc is the total number of lattice cells and NN the expected number of sensors; add “Psensor=N/Nc” to the nomenclature table.

Literature Coverage

• • Add recent works (2023–2025) on Turing‐complete CA patterns in control systems to the Related Work, and mention why GoL is chosen over other CA such as Rule 110.

Figure and Table Presentation

• • Figures 13–24 should include axis labels and units on all axes (e.g. “Detection Probability” vs. “Energy Units”).

  • In Table 1, label columns explicitly (“Unlocalized PON” and “Localized PON”) and include the pattern period for reference.

English and Style

• • Correct minor typos: e.g. “inac­tivate” → “inactivate” (p. 1, L42), “it is given by” → “it is given” (Eq. 7 description).

  • Replace colloquial “we just use a few patterns” (p. 16) with “we evaluate representative GoL patterns”.

Comments on the Quality of English Language

English and Style

• • Correct minor typos: e.g. “inac­tivate” → “inactivate” (p. 1, L42), “it is given by” → “it is given” (Eq. 7 description).

  • Replace colloquial “we just use a few patterns” (p. 16) with “we evaluate representative GoL patterns”.

Author Response

1. The use of cellular automata (CA) to modulate WSN duty cycles has precedent (e.g. Banerjee 2011; Fu 2020; Reyes 2022) . The manuscript must more clearly articulate what new theoretical or practical insight arises from employing Game of Life specifically, rather than any CA. In particular:

• Why are GoL patterns superior to simpler CA rules (e.g. cyclic CA) previously studied?
• What unique mathematical properties of GoL (e.g. periodicity, glider propagation) yield provably better energy–detection trade‐offs?

2. R.2.1. We thank the reviewer for this observation. The choice of GoL over simpler linear CA is because the natural mapping of WSN as two-dimensional limited spaces. GoL has been studied for decades, and a vast amount of patterns have been discovered and continue to be discovered that can be adapted for physical phenomena, presenting a smarter alternative to the standard WSN approach of turning sensors ON/OFF based on a timed probability.

 

We have added this on section 4 

 

2. Table 1 reports PON “localized” versus “unlocalized” values for each pattern, but the method of estimation (analytical limit vs. empirical average) is unclear. A brief proof or derivation of the closed‐form PON for a given periodic GoL pattern should be provided.

 

2. R.2.2. Table 1 is a sample of experimental P_ON values of the selected patterns with localized and unlocalized events. These values are found by means of repetitions of the experiments with a randomized number of sensors, sensor detection radio, and localization following GoL evolution. Because the lattice can be of variable size and the focus on the practical aspects of GoL, for the time being we are not calculating an analytical P_ON value.

 

We have clarified this before Table 1.   

 

3. Equations (3)–(6) assume independent event occurrence and sensor placement. However, under a GoL schedule, node activity is spatially and temporally correlated. The authors should discuss how these correlations affect the validity of the simple product form Pdetection=Pevent Psensor PON.

 

2. R.2.3. We thank the reviewer for pointing this out. We were not sufficiently clear regarding this issue. Indeed, we assume independence of the following events: Pevent is determined only by the activity of the monitored phenomena; it is not related in any way to the sensor placement or the GoL dynamics. Psensor is the probability that there is a sensor in the square where the event is occurring. This placement is done at the setup phase of the WSN. As mentioned, sensors are placed uniformly in the squares where the GoL pattern occurs. As such, there is no relation between the ongoing event and the sensor location. Finally, the probability that a node is ON is clearly dependent on the GoL pattern, but not on the ongoing event. Recall that nodes are turning on and off not as a consequence of the event, but as a preprogrammed schedule given by the GoL dynamics. As such, the dependence on nodes turning on and off is only reflected in the value of PON (i.e., the probability that a node is on directly depends on the state of its neighbors), which we find computationally, but the events, the placement of the nodes, and the duty-cycle are independent events.

 

We have included this explanation in the revised manuscript in Section 5.

 

4, The choice of Etr=1,Eon=0.9, Eidle=0.01 (Eq. 7) is arbitrary. While normalization is

acceptable, include a sensitivity analysis (even in an appendix) showing how results vary when EonE_{\text{on}} and EidleE_{\text{idle}} differ by ±20 %.

 

A.R.2.4. We are very thankful for this suggestion. The values of these variables are set similar to proportional hardware values for these operations. We agree that a sensitivity analysis will help but for time constraints we are not able to include this analysis in this moment but we will prioritize it for future work.

 

 

5. The authors perform 1 000 000 Monte Carlo iterations but report only mean detection probability and energy consumption surfaces. It is essential to include confidence intervals (e.g. 95 % bounds) or standard deviations on key curves to demonstrate statistical robustness.

 

A.R.2.5. We thank the reviewer for this advice. We have added a confidence interval for one representative pattern in the Results section.

 

6. The sensors are “placed randomly in the cells” for unlocalized events but “placed only where the GoL pattern acts” for localized experiments. This conflates deployment and scheduling. Suggest separating the two: keep sensor deployment fixed and vary only the ON/OFF rule to isolate scheduling gains.

 

A.R.2.6. This is an important point that we also discussed in the development of this work. The reason for considering both placement and scheduling according to the GoL pattern is that if only the scheduling is varied, nodes outside the GoL dynamics are useless since they would never turn on, given that the conditions in their surroundings would never meet for them to become active. As such, we considered only placing nodes where the GoL occurs. Also, the effects of only the scheduling, leaving nodes that are never turned on, are not clear since there is energy wastage from “useless” nodes, and we considered that, for practical issues, there is no gain in installing nodes that would never sense data since events can only occur in a restricted area.  

 

We have clarified this issue in Section 3.

 

7. The readers expect novel theoretical development. As currently written, the manuscript reads more like an applied‐simulation study. To strengthen its mathematical appeal, consider:

• Formalizing the convergence properties of event coverage under periodic GoL rules.
• Proving bounds on detection probability versus energy consumption in the limit of large lattice size.
• Characterizing the optimal initial GoL configuration (pattern) that maximizes a weighted combination of detection and energy metrics.

 

A.R.2.7. We are thankful to the reviewer for this advice. And address each point

 

• Formalizing the convergence properties of event coverage under periodic GoL rules.

 

In order to have some mathematical insights we have added lines (543—557) in order to emphasize the convergence properties of event coverage under periodic GoL rules

 

• Proving bounds on detection probability versus energy consumption in the limit of large lattice size.

 

To strength some mathematical ideas we have added lines (558—565) in order to emphasize the relationship between energy consumption as the size of the lattice increases.

 

• Characterizing the optimal initial GoL configuration (pattern) that maximizes a weighted combination of detection and energy metrics.

 

Trying to characterize the optimal initial configuration that maximizes the energy

metrics we have incorporate the lines (566-567) to provoke a certain development of mathematical ideas.

 

 

8. Introduce the sensor detection neighborhood nn formally when first mentioned (Section 3) and use consistent notation (e.g. rr vs. nn).

 

A.R.2.8. We have added a definition for the sensor detection neighborhood in Section 3.

 

9. In Eq. (1), clarify that Nc is the total number of lattice cells and NN the expected number of sensors; add “Psensor=N/Nc” to the nomenclature table.

 

A.R.2.9. We have clarified in Section 5 that Nc is the total of cells with sensors of the N total cells of the entire lattice.

 

10. Add recent works (2023–2025) on Turing‐complete CA patterns in control systems to the Related Work, and mention why GoL is chosen over other CA such as Rule 110.

 

A.R.2.10. Although this is a very interesting point, we have not found relevant works on Turing-complete CA in control systems in the context of WSNs. However, derived from your comment, we have elaborated on the CA choice on response A.R.2.1.

 

11. Figures 13–24 should include axis labels and units on all axes (e.g. “Detection

Probability” vs. “Energy Units”). In Table 1, label columns explicitly (“Unlocalized PON” and “Localized PON”) and include the pattern period for reference.

 

A.R.2.10. We have updated the figures and table with the suggestions.

 

12. Correct minor typos: e.g. “inactivate”→“inactivate” (p. 1, L42), “it is given by”

“it is given” (Eq. 7 description). Replace colloquial “we just use a few patterns” (p. 16) with “we evaluate representative GoL patterns”

.

A.R.2.6. We thank the observation, and we have corrected the typos. 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a Game of Life (GoL)-inspired cellular automaton approach for adaptive node scheduling in wireless sensor networks (WSNs). The proposed method addresses key limitations of conventional on-off protocols—energy inefficiency and static event response—by introducing a local rule-based activation strategy, where nodes dynamically adjust states via neighborhood interactions. This enables spatiotemporal-aware energy conservation without compromising monitoring coverage. Experimental results confirm superior performance over fixed-probability schemes in event detection rate and energy balance, especially in scenarios with periodic event patterns.

There are some issues in this paper that require supplementation and improvement, as described below.

1. References should be numbered in the order they are cited in the text.
2. The abbreviation 'GoL' in line 15 should be noted as 'Game of Life (GoL)' upon its first occurrence in the text.
3. The detailed descriptions of figures should be provided in the main text, not in the figure captions (e.g., Figure 1, Figure 2).
4. The relationships between subfigures in Figure 1 should be clearly described.
5. The 'For...Endfor' statements are mismatched in Algorithms 3, 4, and 5.
6. The operation 'Add to sensormap' in Algorithm 1 should be explicitly defined.
7. In Algorithm 1, the statement 'For j = i + 1, i + 2, ..., n' will skip operations involving elements where j ≤ i. The authors should verify whether this is intended.
8. In line 73, 'Sensors have a detection radio that depends on their technical specifications.' The term 'detection radio' should be clearly defined.
9. For reproducibility purposes, all simulation parameters must be explicitly listed in tabular form.
10. In line 282: 'For the energy consumption units, we assume that Etr, Eon, and Eidle are equal to 1, 0.9, and 0.01, respectively.' What is the justification for selecting these specific values for Eon and Eidle? How significantly would different values affect the simulation results?
11. Discussions in Section 7 (Results) should primarily focus on quantifiable performance metrics.

Author Response

1. References should be numbered in the order they are cited in the text.

 

A.R.3.1 Done

 

2. The abbreviation 'GoL' in line 15 should be noted as 'Game of Life (GoL)' upon its first occurrence in the text.

 

A.R.3.2 Done

 

3. The detailed descriptions of figures should be provided in the main text, not in the figure captions (e.g., Figure 1, Figure 2).

 

A.R.3.3 Done

 

4. The relationships between subfigures in Figure 1 should be clearly described.

 

A.R.3.4 Done

 

5. The 'For...Endfor' statements are mismatched in Algorithms 3, 4, and 5.

 

A.R.3.5 Done

 

6. The operation 'Add to sensormap' in Algorithm 1 should be explicitly defined.

 

A.R.3.6 Done

 

 

7. In Algorithm 1, the statement 'For j = i + 1, i + 2, ..., n' will skip operations involving elements where j ≤ i. The authors should verify whether this is intended.

 

A.R.3.7 We thank you for the observation and we have updated the algorithms to reflect this point.

 

 

8. In line 73, 'Sensors have a detection radio that depends on their technical specifications.' The term 'detection radio' should be clearly defined.

 

A.R.3.8 Done

 

9. For reproducibility purposes, all simulation parameters must be explicitly listed in tabular form.

 

A.R.3.9 Done

 

10. In line 282: 'For the energy consumption units, we assume that Etr, Eon, and Eidle are equal to 1, 0.9, and 0.01, respectively.' What is the justification for selecting these specific values for Eon and Eidle? How significantly would different values affect the simulation results?

 

A.R.3.10 Thank you for pointing this out, we were not very clear in this regard in the original manuscript. The reason for this is that in many commercial nodes, such as Raspberry and Microchip nodes, the energy consumed for transmitting is similar and slightly higher than nodes processing data but not transmitting. Hence, Etr and Eon are selected in this way to reflect this case. However, nodes in low energy consumption mode, consume much lower energy levels, in this case, two orders of magnitude lower. However, we have now included new results to show different cases to show the sensibility of these assumptions.

 

 

11. Discussions in Section 7 (Results) should primarily focus on quantifiable performance metrics.

 

A.R.3.11 We agree, we have modified this section accordingly.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have adequately addressed my comments, and the paper is now ready for publication.

Reviewer 3 Report

Comments and Suggestions for Authors

No comments.