Review Reports
by
- Bernat Espigule *,
- David Juher and
- Joan Saldaña
Reviewer 1: Samer H. Al-Ghour Reviewer 2: Rasul Kochkarov
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsPlease open the attachment file
Comments for author File: 
Comments.pdf
Moderate English language modifications are needed
Author Response
In this revised version of the paper, we have addressed nearly all the remarks and suggestions provided by the referee. We sincerely appreciate your thorough review of the manuscript and your constructive feedback. Below, we present a detailed response to the referee's comments.
1. The paper’s specialized language and numerical documentation may constrain its accessibility to readers without a strong foundation in fractal geometry and complex analysis.
3. The paper accepts a certain level of earlier information around fractal geometry, iterated work frameworks, and complex examination, which may make it challenging for perusers without this foundation to completely appreciate the authors commitments.
Response (to points 1, 3):
Although a certain level of specialization in the language is unavoidable, we have been careful to provide all necessary definitions, previous results and references in order to achieve a completely self-contained manuscript. However, we have expanded Section 1 by adding two new paragraphs with more background information and explanations of fundamental concepts.
2. The paper’s focus on a particular type of fractal (collinear fractals) and a specific aspect of their behavior (connectedness locus) may make it less engaging for readers interested in broader subjects or more general applications.
Response:
The two new aforementioned paragraphs are intended to justify that the election of collinear fractals (and their associated connectedness loci) as a subject of study is not arbitrary and comes from a long-standing tradition in the area of fractal geometry. We have reinforced this idea with new bibliographical references.
4. Whereas the paper notices visualization, it does not include figures or pictures to demonstrate the fractals or their properties, which may make it harder for perusers to imagine and understand the concepts.
Response:
The manuscript contains 10 coloured figures illustrating: two examples of fractals (figures 1, 2), some connectedness loci (figures 3, 5, 10), some convexity sets (figure 4), the region Xn (figure 6), and the arguments of the proof of the covering property (figures 7, 8, 9). Such figures have very detailed captions and marks and have been referenced in the text.
5. The paper may not be specically pertinent to other fractals or more common frameworks, which may restrain their effect and pertinence to a broader gathering of people.
6. The paper's center on specialized subtle elements and numerical proofs may eclipse the broader suggestions and centrality of the inquiry, making it less locks in for perusers curious about the "huge picture" or more common applications.
Response:
The two new aforementioned paragraphs highlight the broader implications of our research. In particular, we have tried to emphasize the connections with classical problems in Algebra, Geometry and Topology.
We hope this revision address your comments and improve the manuscript’s accessibility and relevance to a broader audience.
Note: We have carefully reviewed the English language of the manuscript to enhance its clarity and accessibility. Please refer to the updated document “CollinearFractals_Revised.pdf” for detailed changes.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper is devoted to collinear fractals and the Bandt hypothesis for large values of degree n. The expansion of the degree of n in collinear fractals is an urgent problem, which the authors emphasized in the first part of the article with a large literary review. At the same time, it is worth noting that the list of references contains only 5 sources, the release date of which is less than 5 years – the rest of the works are older, but at the same time relevant to this field.
In terms of figures, I would like to note that Figure 11 is not clear enough, it is better to enter certain marks on it.
In part of the general remarks, it is necessary to note where the vector ψ came from or write a link to where the entry form from 4.3 was taken from. Also, a reference to Figure 11 is needed in the text, since in this version figure 11 is separate from the article.
Despite the presence of small comments, the article will be interesting for readers and experts in the field of fractals.
Author Response
In this revised version of the paper, we have addressed nearly all the remarks and suggestions provided by the referee. We sincerely appreciate your thorough review of the manuscript and your constructive feedback. Below, we present a detailed response to the referee's comments.
It is worth noting that the list of references contains only 5 sources, the release date of which is less than 5 years – the rest of the works are older, but at the same time relevant to this field.
Response:
We have updated our reference list to include more recent publications from the last five years that are relevant to the field. Specifically, we have added two new paragraphs at the beginning of the Introduction. These additions not only update our references but also highlight recent advancements and ongoing research related to collinear fractals and their connectedness loci.
In terms of figures, I would like to note that Figure 11 is not clear enough, it is better to enter certain marks on it. Also, a reference to Figure 11 is needed in the text, since in this version figure 11 is separate from the article.
Response:
We have merged Figure 11 with Figure 10 and we have:
• Added labels and markers to highlight key features and components within the figure.
• Included a detailed caption that explains the elements presented in Figure 10.
In part of the general remarks, it is necessary to note where the vector ψ came from or write a link to where the entry form from 4.3 was taken from.
Response:
We have reordered the equations in the paragraph preceding Lemma 4.3 and we have added the following remark: "The vertex ψ(c,n) was obtained by imposing the geometric conditions prescribed in the proof of the covering property (Lemma 4.3)". This remark intends to make it clear that the expression of ψ(c,n) in terms of c and n is not borrowed from previous works but has been derived from geometric arguments.
We hope this revision address your comments and improve the manuscript in the terms expressed by the reviewer.
Note: We have carefully reviewed the English language of the manuscript to enhance its clarity and accessibility. Please refer to the updated document “CollinearFractals_Revised.pdf” for detailed changes.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have modified the paper based on my comments, so I recommend publishing the paper.
Comments on the Quality of English LanguageThe language is fine