Physics Nature Is Weird

Materials shaped like fractals can store a ton more quantum data on their edges than regular shapes.

April 2, 2026

Original Paper

Fractal hierarchy enables exponential scaling of topological boundary states

Limin Song, Zhichan Hu, Ziteng Wang, Domenico Bongiovanni, Liqin Tang, Daohong Song, Roberto Morandotti, Jingjun Xu, Hrvoje Buljan, Zhigang Chen

arXiv · 2604.00814

The Takeaway

By building lattices using self-repeating patterns like the Koch snowflake, researchers found that the number of protected paths for light or electricity grows explosively rather than linearly. This allows for massive amounts of information to be packed into extremely compact, fractal-based hardware.

From the abstract

Exponential growth describes an extremely rapid process ubiquitous across mathematics and diverse physical, biological, and technological systems. Here, we introduce a class of fractal-inspired lattices that combine long-range periodic order with self-similar hierarchy, establishing a structural motif that enables exponential scaling of topological boundary states. We demonstrate this phenomenon in (i) a quasi-one-dimensional lattice chain constructed from Koch-curve unit cells and (ii) a two-di