Multiport interferometers based on integrated beamsplitter meshes have recently captured interest as a platform for many emerging technologies. In this paper, we present a novel architecture for multiport interferometers based on the sine–cosine fractal decomposition of a unitary matrix. Our architecture is unique in that it is self-similar, enabling the construction of modular multi-chiplet devices. Due to this modularity, our design enjoys improved resilience to hardware imperfections as compared to conventional multiport interferometers. Additionally, the structure of our circuit enables systematic truncation, which is key in reducing the hardware footprint of the chip as well as compute time in training optical neural networks, while maintaining full connectivity. Numerical simulations show that truncation of these meshes gives robust performance even under large fabrication errors. This design is a step forward in the construction of large-scale programmable photonics, removing a major hurdle in scaling up to practical machine learning and quantum computing applications.