Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper innovatively combines the classical mathematical structure of Pascal’s triangle with the formal technique of Petri nets, constructing a Petri net model capable of uniformly generating Pascal’s triangle, the Sierpiński triangle, and the Gaussian distribution. Meanwhile, it integrates Kandinsky’s artistic style to achieve visual representation, successfully building a cross-disciplinary bridge among mathematics, computer science, and art.

Suggestions for Improvement and Refinement：

1. The paper does not explicitly mention key performance indicators of the constructed Petri net, such as the number of places/transitions at different depths (e.g., depths 12 and 512), the time complexity of token operations, and the operation efficiency of the Python implementation (e.g., rasterization time consumption at depth 512). It is suggested to supplement these quantitative data and compare them with traditional calculation methods (e.g., directly generating Pascal’s triangle through recursion) to further highlight the efficiency advantages or applicable scenario boundaries of the Petri net model.

2. It is suggested to unify the reference format (e.g., in accordance with GB/T 7714 or journal requirements) and supplement the summary of core viewpoints of key literature to enhance the pertinence and readability of citations.

Conclusion: This paper has made valuable explorations in the Petri net modeling and interdisciplinary presentation of Pascal’s triangle, with strong innovation and academic nature, and reliable core conclusions. If the above suggestions can be adopted to supplement model performance data, refine theoretical derivation, deepen visualization interpretation, and standardize citation format, the quality of the paper will be further improved. Based on a comprehensive evaluation, it is recommended to publish the paper after revision and improvement.

It is truly touching that someone persists in researching Petri nets in today’s AI era.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please find attached a PDF file with the review report.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

See the attached report and revise.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This paper studies Pascal’s triangle and discusses how to model it with Petri nets under simple arithmetic rule. The paper shows that this single Petri net unifies three mathematical objects: Pascal’s Triangle, the Sierpinski’s Triangle, and the Gaussian distribution by routing tokens randomly at each branching. The paper is interesting and novel. As a minor comment, it is suggested to discuss some engineering and real-world applications of this technique.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

The authors use Petri Nets to model the patterns observed in three well known mathematical objects: Pascal's triangle, Sierpinski's triangle, and the Gaussian distribution. As their title suggests, their proposal lays in the middle of mathematics and art.

The topic is very appealing and the writting is didactic. My only two concerns are:

In line 158, it says "choaos" instead of "chaos".

The title suggests that mathematics are used to find artistic and mathematical objects. Naturally, that is the case. However, going "from math to math" sounds redundant. So, the title might me improved. A naive suggestion is: "Petri Nets as a bridge between mathematics and art: the case of Pascal's triangle".

Author Response

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Author Response File: Author Response.pdf