This work describes a novel building block system for tangible interaction design, GaussBricks, which enables real-time constructive tangible interactions on portable displays. Given its simplicity, the mechanical design of the magnetic building blocks facilitates the construction of configurable forms. The form constructed by the magnetic building blocks, which are connected by the magnetic joints, allows users to stably manipulate with various elastic force feedback mechanisms. With an analog Hall-sensor grid mounted to its back, a portable display determines the geometrical configuration and detects various user interactions in real time. This work also introduce several methods to enable shape changing, multi-touch input, and display capabilities in the construction. The proposed building block system enriches how individuals interact with the portable displays physically.