To simulate both external multiverse gravitational pulls and a "Big Bounce" implosion, the engine must override standard Newtonian gravity with custom mathematical models. Here is the core logic and mathematical documentation for implementation.
1. External Gravitational Influence (The "Dark Flow")
To simulate the gravitational pull of a neighboring universe or external massive structure, you must modify the standard N body acceleration equations. Instead of particles only interacting with each other, they are subjected to an external gravitational potential gradient $\nabla \Phi {ext}$.
The Math:
For a particle $i$ with mass $m i$ and position vector $\mathbf{r} i$, the total acceleration is the sum of local gravitational forces plus the external multi universe force:
$\mathbf{a} i = \sum {j \neq i} G \frac{m j}{\vert{}\mathbf{r} i \mathbf{r} j\vert{}^3} (\mathbf{r} j \mathbf{r} i) \nabla \Phi {ext}(\mathbf{r} i, t)$
The Logic (C99 Physics Solver):
In a solver like REBOUND, you implement this by attaching a custom force callback to the simulation loop before the integrator steps forward.