This is a computational physics project, not an AI tool. The name "Anatropic" refers to anisotropic entropy production in cosmological structure formation. It has no relation to Anthropic (the AI company).
Metal-accelerated cosmological hydrodynamics for the τ framework
Anatropic is a GPU-accelerated adaptive mesh refinement (AMR) code designed to simulate structure formation in the τ framework — a modified gravity theory where the Khronon field's DBI kinetic term produces scale-dependent sound speed c_s²(k) → 0 at sub-galactic scales, enabling Jeans fragmentation at sub-kpc scales.
The τ framework (Huang 2026) connects:
- Running G: G(r) = G_N[1 + 2k_*r/π] (Kumar 2025, Gubitosi+ 2024)
- Khronon = GDM equivalence (Blanchet & Skordis 2024)
- Scale-dependent sound speed: c_s²(k) = (μ₀/k)² where μ₀ = H₀/c
When c_s → 0 at galactic scales, the Jeans length λ_J = √(πc_s²c²/(Gρ)) shrinks to sub-kpc, potentially producing density fluctuations observable in gravitational lensing.
Our 1D and 2D simulations of the Khronon Jeans instability reveal:
- When c_s → 0, all modes become simultaneously Jeans-unstable (dust limit)
- Growth rates converge to the free-fall rate ω_J = √(4πGρ₀) independent of wavelength
- 2D simulations produce filamentary structure (nodes, filaments, voids) — a self-similar multi-scale fragmentation pattern
- Power spectrum: P(k) ~ k⁻²·², a broad continuum with no preferred scale
Live demo → anatropic.pages.dev
Three-panel WebGL comparison (volume ray marching + voxel rendering) of ψDM, Khronon, and CDM morphologies. Switch between render modes with tabs.
Note: The 3D visualization shows topology only (filamentary vs periodic vs discrete), not physical amplitude. Real dark matter perturbations are δρ/ρ ~ 1–10% and are invisible — detectable only through gravitational lensing residuals.
- Phase 1 (current): Python prototype — 1D/2D Euler + Poisson solver
- Phase 2 (planned): Apple Metal compute shaders for 3D GPU acceleration
- Phase 3 (planned): Full AMR with τ-EOS
| Module | Description | Status |
|---|---|---|
anatropic.euler |
Godunov hydro solver (HLLE Riemann) | Phase 1 |
anatropic.gravity |
FFT Poisson solver (self-gravity) | Phase 1 |
anatropic.eos |
τ-EOS: c_s²(k) = (μ₀/k)² | Phase 1 |
anatropic.metal |
Metal compute shader backend | Phase 2 |
anatropic.amr |
Adaptive mesh refinement | Phase 3 |
Before running new physics, Anatropic is validated against:
- Sod shock tube (exact solution)
- Linear Jeans instability growth rate (analytical)
- Acoustic wave propagation
- GAMER test problem results (cross-code comparison)
- Python 3.9+
- numpy, scipy, matplotlib
- (Phase 2) macOS 13+ with Apple Silicon for Metal acceleration
- Kumar 2025 (arXiv:2509.05246): Running G from QFT
- Gubitosi et al. 2024 (arXiv:2403.00531): SPARC validation
- Blanchet & Skordis 2024 (arXiv:2404.06584): Khronon = GDM
- Thomas, Kopp & Skordis 2016 (arXiv:1601.05097): GDM constraints
- Skordis & Złośnik 2021 (PRL 127, 161302): AeST theory
- Schive et al. 2018 (arXiv:1712.07070): GAMER-2
BSD 3-Clause
Sheng-Kai Huang (akai@fawstudio.com)