Modern hardware is increasingly complex, requiring increasing effort to understand in order to carefully engineer systems for optimal performance and effective utilization. Moreover, established design principles and assumptions are not portable to modern hardware because: 1) Non-Uniform Memory Access (NUMA) architectures are becoming increasingly complex and diverse across CPU vendors; Chiplet-based architecture provides hierarchical NUMA instead of flat-NUMA topology, while heterogeneous compute cores (e.g., Apple Silicon) and on-chip accelerators (e.g., Intel sapphire rapids) are also normalized in materializing the vision for workload- and requirement-specific compute scheduling. 2) Increasing IO bandwidth (e.g., arrays of NVMe drives approaching memory bandwidth) is a double-edged sword; having high-bandwidth IO can interfere with the concurrent memory access bandwidth as the IO target is also memory; hence IO itself consumes memory bandwidth. 3) Interference modeling is becoming more complex in modern hierarchical NUMA and on-chip heterogeneous architectures due to topology obliviousness. Therefore, systems designs need to be hardware topology-aware, which requires understanding the bottlenecks and data flow characteristics, and then adapting scheduling over the given hardware topology. Modern hardware promises performance by providing powerful and complex yet non-intuitive computing models which require tuning specifically for target hardware or risk under-utilizing the hardware. Therefore, system designers need to understand, carefully engineer, and adapt to the target hardware to avoid unnecessarily hitting bottlenecks in the hardware topology. In this paper, we propose the Chaosity framework, which enables system designers to systematically analyze, benchmark, and understand complex system topologies, their bandwidth characteristics, and interference of effects of data access paths, including memory and PCIe-based IO. Chaosity aims to provide critical insights into system designs and workload schedulers for modern NUMA hierarchies.