An integrated computational pipeline for the procedural synthesis and physical evolution of complex manifolds.

This repository provides a unified high-performance execution context for generating unbiased Monte Carlo distributions and evolving N-body states under arbitrary vector fields. By decoupling geometric topology from dynamical integration, the system enables simulations ranging from stable orbital dynamics to path-dependent macromolecular relaxation.

A specialized subsystem for generating unbiased Monte Carlo distributions across 1D, 2D, and 3D geometric primitives.

• Dynamic Manifolds: Utilizes importance weighting and iterative rejection logic to bypass static meshes and resolve Boolean topology.
• Analytical Re-definition: Designed for interactive topological updates; point-cloud distributions adapt to analytical bounds in real-time without the overhead of re-baking or manual re-sampling.
• AABB Heuristics: Accelerated intersection sampling via Bounding Box constraint shrinking to minimize search space.
• Memory Optimization: High-throughput sampling (10⁵/frame) utilizing garbage-collection-aware loops and "out-parameter" patterns.

A universal time-integration core designed for the high-fidelity evolution of N-body states under arbitrary vector fields.

• Pluggable Derivative Kernels: Abstracted integration logic allows for interchangeable kernels (e.g., Central Gravity, Dissipative Viscosity, Stochastic Perturbations).
• Symplectic Stability: Employs a semi-implicit Euler scheme to maintain long-term phase-space volume and energy stability.
• Zero-Copy Synchronization: Direct Float32Array mapping between CPU physics and GPU vertex attributes for minimum overhead.
• Computational Density: Handles 30,000+ active agents at 60Hz using linearized memory to maximize cache locality.

A case study in Complex Systems, applying the engine to the problem of path-dependent macromolecular relaxation and constraint satisfaction.

• Heteropolymer (HP) Folding: Sequence-specific force fields where hydrophobic/polar affinities drive organized tertiary collapse.
• Homogeneous Relaxation (HR): Energetic minimization of complex topological seeds such as Trefoils, Toroids, and Helices.
• Spatial Hash Grid: Custom $O(N)$ neighbor discovery for sub-linear interaction resolving, bypassing traditional $O(N^2)$ bottlenecks.

• Decoupled Abstractions: Geometric topology is strictly decoupled from dynamical integration logic.
• Deterministic Evolution: Explicit control over temporal stepping and stochastic variables to ensure reproducible results.
• Performance-Driven Design: Prioritizes resource-constrained architectural decisions, focusing on deterministic execution and robust algorithmic kernels.

This framework is the core computational engine for the simulations hosted at:
👉 Portfolio & Live Demos