Loeb hosts evening of fractal festivities

Image courtesy of Mia-Dora Stein '24.

On Thursday, Feb. 15, I braved my way through a snow flurry and arrived at the Frances Lehman Loeb Art Center for a night of fractal-related activities. Over piercing winds, I heard a group of students in front of me discussing the topic with critical attention, setting high stakes for the event’s public reception. A solid showing of attendants grabbed refreshments and filed into the building. The room buzzed with excitement for the commencement of the event. Programming combined a lecture from Professor of Mathematics and Statistics Natalie Priebe Frank and the exhibition of student artwork and crafts inviting our participation, resulting in an informative yet engaging evening. 

A fractal is a mathematical concept referring to geometric shapes which contain self-similar structures at increasingly smaller scales, forming the same patterns across these degrees of size. Although I was familiar with this basic notion from various conversations—such as ones with my parents—I could never claim to truly understand the concept from a theoretical standpoint. In comparison to my past knowledge, this event provided the most illustrative and succinct explanation of fractals that I have yet to encounter, easily capturing my attention.

After the audience had gathered in the gallery, Frank was introduced by mathematics and art history double major Mia-Dora Stein ’24. Stein was a student in Frank’s “Fabricating Fractals,” a course that explored topics akin to this lecture. Frank began the talk by highlighting the generative and self-similar qualities of fractals, an artistic beauty discoverable and magnified by mathematics. In addition to her work as a professor, Frank also makes artwork that reflects these interdisciplinary pursuits. The first fractal displayed in the slideshow was the Mandelbrot set, a famous example showcasing the form of its “bulb” at increasingly smaller scales. As with any fractal, the “whole” picture resembles any of its subsequent “copies”: the smaller, self-similar parts that compose a fractal when zoomed in on. This close interrogation of shape, structure and form at miniscule levels was made increasingly possible by technological advances in the 1970s and ’80s. Frank then highlighted the occurrence of natural fractals using the example of ferns and snowflakes. These images evoked other well-known analyses of nature through mathematics, such as the appearance of Fibonacci sequences in biological contexts.

Throughout the lecture, Frank’s lightly humorous tone helped illuminate our unconscious cultural knowledge of fractals and their varied appropriations. In one instance, she compared their features to dorm room posters. For myself, background familiarity of fractals came in the form of a NOVA documentary and Tool’s album covers, although the latter may not fit stricter definitions of the term. The focus then shifted from the applications of fractals in visual arts to their mathematical properties. Frank discussed the Koch curve, a shape which is progressively built by shrinking the original line into four identical pieces and then arranging them into a pattern. By continually repeating this action, a recognizable fractal is formed; Frank eloquently broke the process down by using a succession of images visually representing this accumulation. She also noted the role of iterated function systems in mathematically constructing fractals.

Afterwards, Frank moved into a discussion of self-similar tilings, an approach to tiling utilized by notable artists like M.C. Escher. Rather than the method of observing fractals from an increasingly diminutive viewpoint, self-similar tilings move from small to large in their construction. They are framed, self-contained pieces of artwork. Motifs from two main tiling shapes or patterns can be superimposed upon one another, creating a unique result that is distinct from either of its constitutive parts. Frank included pictures of tiling she had created by hand for family members, constructed with an intricate method that vaguely resembles the mathematical precision of fractals. These two forms are ultimately different yet related, linked by the shared notion of self-similarity. The tiling specifically reminded me of ornate gardens or mazes; throughout the talk, I drew other similar associations between mathematics and artistic creation.

After questions from the audience were addressed, members of the crowd made their way out of the galleries to participate in various tiling and fractal-inspired activities. These included origami, button-making, interactive “sliders” that superimposed tilings upon one another and stamping with colored paints. Students assisted in facilitating participation, guiding others through each of the crafts. At the stamping station, I used two self-similar tiling templates with heart shapes to create a superimposed picture with pink and blue colors.

Farther down the hallway, fractal-related art made by Frank and her students was on display. Student-artist David Shively-Ertas ’24 explained the precision involved in this craft, noting that the work I was discussing with a friend had been 3D printed six times in total. Ertas’ piece resembled a modernist castle with four “towers” positioned in the corners of the square. A work by Sam Lytel ’24 reminded me of jutting cliffs and rock formations, harkening back to earlier connections made between fractals and natural geometry. On the other hand, Frank’s “Spiral Circuit” is a mobile—think baby cribs—based on self-similar tiling techniques; this particular spatial arrangement helped me rethink the possibilities of tiling beyond their use in flooring or wall designs. 

All of the featured works were distinct regarding the vision they applied self-similarity to, resulting in a plethora of original designs. Each portion of the night played a role in expanding my appreciation for fractals and the mathematics of artwork, a holistic approach to arts-event planning that functioned smoothly. Having reconsidered the interplay of art and mathematics in one’s everyday life, I left the Loeb with my stamped piece and returned to my dorm.

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