July 23, 2021 EXPO 2021 Poster

Visualizing a Fractal Representation of the British Coastline

[et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”3.22.6″][et_pb_fullwidth_post_title author=”off” comments=”off” featured_image=”off” _builder_version=”3.23.3″ title_font=”Standard||||||||” title_text_color=”#ffffff” title_font_size=”61px” title_line_height=”1.3em” meta_font=”Standard2||||||||” meta_text_color=”#ffffff” background_color=”#000000″ custom_padding=”||60px” title_font_size_tablet=”39px” title_font_size_phone=”28px” title_font_size_last_edited=”on|phone”][/et_pb_fullwidth_post_title][/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.23.3″][et_pb_row _builder_version=”3.23.3″ max_width=”1221px”][et_pb_column type=”2_5″ _builder_version=”3.23.3″][et_pb_image src=”https://thenurj.com/wp-content/uploads/2021/07/headshot-Angelina-Jaglinski.png” align_tablet=”center” align_last_edited=”on|phone” module_id=”circle-image” _builder_version=”3.23.3″ width=”40%” width_tablet=”26%” width_last_edited=”on|desktop”][/et_pb_image][et_pb_text _builder_version=”3.23.3″ text_font=”Standard2||||||||” text_font_size=”27px” min_height=”40px” custom_padding=”18px||”]Angelina Jaglinski[/et_pb_text][et_pb_text _builder_version=”3.23.3″ inline_fonts=”Times New Roman”]

Adviser: Professor Eric Chang
Subject: Physical Sciences
DOI: 10.21985/n2-hgpk-jp11

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Angelina Jaglinski is a rising junior studying mathematics and computer science in the Weinberg College of Arts and Sciences. After participating in the Northwestern Emerging Scholars Program the fall of her freshman year, she was motivated to learn more about mathematical research by joining Northwestern’s Undergraduate Research Assistant Program the following summer. Under the mentorship of Professor Eric Chang, she completed her first research project, in which she set out to create a visual representation of what a fractal coastline might look like. This experience has inspired her to seek out a career in mathematics or data science after graduation.

[/et_pb_text][/et_pb_column][et_pb_column type=”3_5″ _builder_version=”3.23.3″][et_pb_text _builder_version=”3.23.3″ text_font=”Standard2|600|||||||” text_font_size=”25px”]Abstract[/et_pb_text][et_pb_text _builder_version=”3.23.3″ text_font=”Times New Roman||||||||” text_font_size=”19px” text_line_height=”1.5em”]A famous topic in mathematics involves the theoretically infinite nature of geographic coastlines. If one were to measure the perimeter of Great Britain, for example, the smaller the measuring tool, the larger and more accurate the measured perimeter would be. This phenomenon contains similar properties to the mathematical objects known as fractals: shapes with infinitely many self-similar segments. In our research project, we set out to visualize what a fractal coastline would look like and how it would compare to its real-life counterpart. To do this, we first obtained the coordinates of the British coastline. We then wrote code to insert a fractal segment between each coordinate, thereby creating a new set of fractal coordinates. This code worked on any number of coordinates and allowed us to use several different types of fractals with any number of iterations. Once we had our desired fractal coordinates, we uploaded them to the mapping software ArcGIS to see our results. From far away, the natural coastline and the fractal coastline looked smooth and identical, but zooming in revealed more detail. It was much easier to see the places where the fractal coastline differed slightly from the natural coastline, just like how a larger measuring tool overlooks the smaller crevices of geographic coastlines. Not only did we achieve our goal of visualizing a fractal coastline, but this research provided us with several jumping-off points for future investigation, such as comparing the coastlines’ numerical perimeters, areas, and fractal dimensions.[/et_pb_text][/et_pb_column][/et_pb_row][/et_pb_section][et_pb_section fb_built=”1″ _builder_version=”3.23.3″][et_pb_row _builder_version=”3.23.3″][et_pb_column type=”4_4″ _builder_version=”3.23.3″][et_pb_code _builder_version=”3.23.3″][/et_pb_code][/et_pb_column][/et_pb_row][et_pb_row _builder_version=”3.23.3″][et_pb_column type=”4_4″ _builder_version=”3.23.3″][et_pb_code _builder_version=”3.23.3″][/et_pb_code][/et_pb_column][/et_pb_row][/et_pb_section]