I am a student who wants to major in architecture but holds a dear love for math. Thus, I am constantly looking for ways to incorporate the organic beauty of mathematical concepts into three-dimensional structures. The Julia Set is the boundary of points on the complex plane that do and do not diverge to infinity when repeatedly iterated under a certain function. Depending on the function, the Julia Set takes on wildly different self-similar shapes. Because most visualizations of the Julia Set are two-dimensional images, I sought to create a three-dimensional object that preserves the dynamic nature and ornate patterns that the Julia Set holds.
I used Python code to extract images of Julia Sets from functions, varying from $f(x)=x^2$, $f(x)=x^2-0.01$, and so on down to $f(x)=x^2-0.85$. I then traced their bitmaps to create svg files that I was able to extrude and layer on top of each other through 3D modeling. Because the functions I used are very slightly different, the Julia Sets morph gradually whilst their complex details are preserved. I printed several versions in varying sizes with liquid resin; one version has holes carved into each circular section, and can be used as a multifunctional vase/desk organizer.