Explain and explore the mathematics behind fractals and how they appear in natural phenomena.

I need to write a research paper according to the following information. Research Paper: Students will pick a topic with the instructor’s approval. The paper will require learning about a topic you have not already learned, or diving much deeper into a topic already learned. You should research the topic throughout the whole semester and write a paper that gives enough information to write a thorough paper. These are usually at least 15 pages. You should use reputable sources. You will be required to meet with me or another faculty member individually at least 5 times throughout the semester to go over the progress you have made. You will also need to keep a journal with a time log on how much time you have spent and what you accomplished within that time. You will submit a copy of your journal entry at least 24 hours before your weekly meeting. You will also hand in rough drafts throughout the semester. For your weekly meetings, it is expected that you come prepared with the work you have done. If you show up empty-handed, this will not count as one of your meeting times and you will need to reschedule a time. Based on the above information, this paper would require me to work with the essaypro tutor so that we can have the journals and rough drafts along the way before the final paper. If you are able to complete it before the given time, that’s still okay, as I would use the said journal notes as I meet with my instructor for the weekly meetings. Below I had a few suggestions with a brief description: Mathematical Modeling of Epidemics: Explore the mathematical models like the SIR model that describe the spread of diseases. Given recent events, understanding the mathematics behind pandemics is very relevant. Applications of Game Theory in Economics: Dive into how mathematical strategies can predict the decision-making processes in economic scenarios. Mathematical Analysis of Neural Networks: Explore the mathematical underpinnings of neural networks and deep learning. Look at activation functions, backpropagation, and the optimization techniques involved. Chaos Theory and its Applications: Investigate how deterministic yet unpredictable systems operate. This could be especially interesting if you explore its implications in weather forecasting, engineering, etc. Optimization in Supply Chain Management: Look at how mathematical optimization techniques (like linear programming) are applied to make supply chains efficient. The Math Behind Cryptography: Dive into the world of codes and ciphers, exploring how mathematics ensures data security in the digital age. Fractal Geometry in Nature: Explore the mathematics behind fractals and how they appear in natural phenomena. Mathematical Techniques in Image and Signal Processing: Explore how math is used to process images (like in CT scans or MRIs) or signals (in radio communication, for example). Mathematics of Financial Derivatives: Dive into the complex world of financial math, understanding options, futures, and other derivatives. Network Theory and its Applications: Explore how math is used to study networks, be it social networks, internet structure, or even transportation grids. For the initial project proposal: Title: Choose one of the above or any other topic you’re interested in. Objective: A brief statement of what you aim to achieve with this research. Methodology: Describe how you plan to approach the topic. Will you focus on theory, or will you run simulations? Maybe a combination of both? Preliminary Bibliography: List a few primary sources you plan to start with. For applied math, sources like arXiv, Google Scholar, JSTOR, or your university’s library database can be good places to start. Expected Outcomes: While it’s early, try to outline what you hope to present in your final paper. Will you be demonstrating the utility of a particular math technique in a specific field? Will you be comparing methods?