Fractals: An Eclectic Survey, Part-I
Round 1
Reviewer 1 Report
In this paper, the authors worked on the survey of fractals, which are geometrical shapes and patterns that repeat their geometry in small, large, full, and partial scales. Fractals are basically helpful in solving problems where regular euclidian geometry is not able to. For example: modeling the clouds, projecting the surface of the unseen surface of mountains, and many more. The authors made the paper easy to read, used many references and definitions, and made the paper accessible to someone with little to no knowledge of fractal. The paper is divided into two parts: first, the authors provided glossaries of fractals, their definitions, mathematical formulations, artistic application, and many more. Second, the authors focused on complex engineering and industry problems. Although the paper is long (33 pages), the author made it smooth and easy to follow. The mathematical portions are correct and scientifically sound. Please check the typos and grammatical in the text, and cite or delete the uncited reference.
Once these corrections are made, the paper can be accepted to get published in this prestigious journal.
Author Response
Thanks to reviewer for providing fruitful comments and suggestions to improvement of this manuscript. Please see responses step by step in attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Review of Fractals: An Eclectic Survey, Part-I by Akhlaq Husain, Minikyala Navaneeth Nanda, Movva Sitaram Chowdary, and Mohammad Sajid for the journal Fractals and Fractional by Jay Friedenberg
Remove parentheses from abstract, not necessary
Fractals exist also in the auditory domain in which case they are temporal as well as spatial.
A differentiation also needs to be made between exact fractals and natural ones, i.e., those that are deliberately constructed or designed vs. those that appear as the result of emergent forces in nature. For a recent publication on the aesthetics of this former category see:
Friedenberg, J. (2021). Judged beauty of fractal symmetries. Empirical Studies of the Arts. 40(1), 1-21. DOI: 10.1177/0276237421994699.
Are the clothing and balloon examples in Sections 6 and 7 necessary? Same for coloring books. If they are the same types of fractals found in other media, then why are they described here?
Book recommendations might best fit as a section at the end, listing a small collection of the most important works. Also, recommendations of fractal generating software and analysis like FracLac should be included.
Why start with the Mandelbrot set? It seems better to have a more general mathematical introduction to fractals first, defining fractal dimensionality and other key defining features first. It seems Section 3 ought to come before Section 2.
Dimensionality is introduced by not mathematically defined until later, these two sections are separated.
The graphics are excellent. Table 1 is quite nice.
Other related topics that the authors may wish to introduce include: the Lyapunov exponent and lacunarity.
Again, discussions of coastlines occur in separate locations. Consider putting these together.
The seven friezes and 17 wallpaper patterns are not mentioned. A discussion of symmetries and symmetry properties of 2-D pattern and their relation to fractals seems missing.
What is the difference between a fractal and non-fractal tesselation? Give examples.
Rep tiles are not defined.
Is it really the case that fractal arts are "rarely generated by hand" given their ubiquity in all fields of the arts? Is this in reference to deterministic or mathematical fractals only? If so, please quality. Fractals may be created without explicit conscious awareness of what they are or what their properties are.
There is some redundancy in describing the Mandelbrot set here and earlier on.
Author Response
Thanks to reviewer for providing fruitful comments and suggestions to improvement of this manuscript. Please see responses step by step in attached file.
Author Response File: Author Response.pdf
