photo of Alexa Schor, a smiling woman with glasses and a brown sweater.

Alexa Schor

Yale Graphics Group

orcid/0009-0000-3486-5238

github/alexaschor

keybase/alexaschor

alexa.schor@yale.edu

About me

I am an incoming Ph.D. student in the Yale Graphics Group, performing computer graphics research under Dr. Theodore Kim. I recieved my B.S. in Computer Science from Yale in 2024. My research interests include geometry processing, fractal geometry and physical simulation. I was selected as a runner-up for the 2024 CRA Outstanding Undergraduate Researcher Award.

I will present my most recent work, Into the Portal: Directable Fractal Self-Similarity (see below), this summer at ACM SIGGRAPH 2024 in Denver, CO.

Publications

A fractal statue of Hebe, recursing infinitely atop a bowl in her hand.
Into the Portal: Directable Fractal Self-Similarity
Alexa Schor and Theodore Kim
ACM SIGGRAPH 2024
We present a novel, directable method for introducing fractal self-similarity into arbitrary shapes. Our method allows a user to directly specify the locations of self-similarities in a Julia set and is general enough to reproduce other well-known fractals such as the Koch snowflake.

Ours is the first algorithm to enable this level of general artistic control while also maintaining the character of the original fractal shape. We introduce the notion of placing “portals” into the iteration space of a dynamical system, bridging the aesthetics of iterated maps with the fine-grained control of iterated function systems (IFS). Our method is effective in both 2D and 3D.
A dragon-shaped fractal Julia set
A Shape Modulus for Fractal Geometry Generation
10.1111/cgf.14905 Alexa Schor and Theodore Kim
Symposium on Geometry Processing (SGP) 2023
We present an efficient new method for computing Mandelbrot-like fractals (Julia sets) that approximate a user-defined shape. Our algorithm is orders of magnitude faster than previous methods, as it entirely sidesteps the need for a time-consuming numerical optimization. It is also more robust, succeeding on shapes where previous approaches failed.

The key to our approach is a versor-modulus analysis of iterated function systems that allows us to formulate a novel shape modulus function that directly controls the broad shape of a Julia set, while keeping fine-grained fractal details intact.

Our formulation contains flexible artistic controls that allow users to seamlessly add fractal detail to desired spatial regions, while transitioning back to the original shape in others. No previous approach allows these sort of Mandelbrot-like details to be "painted" onto meshes.