The collective information from the flowchart, mindmap, and illustration establishes that mass accumulation in a variable density field is governed by the rule that density increases quadratically with distance from the origin. The mindmap provides the theoretical structure for this distance-dependent model, while the flowchart outlines a computational workflow using Python to derive analytical mass formulas for specific shapes like the cube, sphere, ellipsoid, and torus. Crucially, the illustration confirms the principle that because density grows with distance, the total mass calculation is dominated by the parts of an object at maximum distance from the center. This explains why a sphere captures significantly more mass than a cube and why mass concentrates in the outer shells of ellipsoids and the large outer rims of toruses. Together, these descriptions demonstrate that the geometric boundary of a container is the defining factor in how it accumulates mass within a non-uniform environment.
Total Mass in a Cube vs. a Sphere (TM-CS) | Cross-Disciplinary Perspective in MCP (Server)