Hideki Tsuiki

Statement

When I found H-fractal (Hexagonal bipyramid imaginary cube fractal) and T-fractal (Triangular antiprismoid imaginary cube fractal), I was attracted by their beauty, in particular, the way their projected images change. Recently, I succeeded in characterizing the directions from which these objects are projected to positively-measured fractals, and I was also moved by the beauty of this result. I wondered how I can convey this beauty to a wider audience, and I came up with the idea of making precise models of these fractals with 3D-printers, make YouTube videos of them, and link a paper in the comment of the video.

Films

The three objects in this film are fractal imaginary cubes, which are fractal objects with square projections along three orthogonal directions. They have, not only squares but also many other beautiful fractal shadows which are changing continuously under sunshine. Though they change continuously, their Lebesgue measure change discontinuously, and they have positive measure only when they are projected from some particular directions as explained in this video. See the details in https://arxiv.org/abs/2205.13065.