CRR Physical Systems: Mathematical Physics in Motion
Coherence: 0.245 •
Particles: 400 •
Memory: 0.156
Phase transitions: 0 •
Reconstruction: 0.78
Physical Systems Simulations
Explore interactive toy CRR simulations demonstrating physical phenomena across scales; from quantum mechanics to cosmology. Each simulation provides hands-on exploration of dynamical systems, phase transitions, and emergent behaviours. These are provided as proof of concept only and are intended for users to reflect on the role of markovian and non-markovian memory in complex systems over time.
Physics & Cosmology
| Simulation | Description | Why It Might Matter |
|---|---|---|
| Atom | Interactive atomic structure model with electron orbital dynamics. CRR implementation: Coherence C(t) accumulates as deviation from ground state energy; rupture δ(t-t₀) triggers quantum jumps between orbital shells following Fermi's Golden Rule; regeneration uses Boltzmann weighting exp(C/Ω) to determine transition probabilities. Wave-particle duality emerges from tanh(C/C_crit) mixing parameter. We share this as a computational model of interest, noting that CRR memory dynamics can be modelled at this scale | Quantum systems exhibit both continuous evolution and discrete jumps. Understanding how coherence relates to observable transitions. |
| Black Hole (Interactive) | Simplified black hole system with event horizon and accretion dynamics. CRR implementation: Coherence integrates matter-energy density in accretion disk; event horizon acts as rupture boundary (δ(r-R_s)) where spacetime forces discrete transitions; Hawking radiation represents regeneration flux weighted by black hole's accumulated mass history. | Black holes represent boundary conditions where spacetime geometry forces discontinuous transitions. Studying these systems may offer insights into fundamental limits of information and causality. We share this because we find it intriguing that black holes seem to share similar memory-based patterns to a surprising number of other physical and biological systems, including human beings! |
| Black Hole (Research) | Extended black hole simulation with comprehensive CRR mathematics. Implementation: Full coherence field calculations for orbiting matter; threshold-triggered rupture events at the event horizon; regeneration operator modelling quantum fluctuations producing Hawking radiation at temperature T_H = ℏc³/(8πGMk_B). | The interplay between matter accumulation, horizon physics, and quantum radiation presents a laboratory for studying irreversible processes and thermal equilibrium in gravitational systems. CRR as a coarse-grain approach for understanding how systems maintain identity by changing. |
| Dark Energy | Cosmological evolution with time-varying dark energy. CRR implementation: Coherence C(t) accumulates as cosmic age in Gyr; vacuum equation of state w(t) evolves as function of C/Ω ratio; phantom crossing occurs when coherence reaches critical threshold; regeneration term modifies dark energy density ρ_Λ(t) exponentially with accumulated coherence. | Recent observational data suggest possible deviations from cosmological constant behaviour. Models that incorporate memory effects in the vacuum may contribute to understanding accelerated expansion and the universe's ultimate fate. The CRR offers a coarse-grain understanding - it is modelled here to demonstrate the principle of systems maintaining identity by changing. |
| Gravitational waves | Gravitational Waves. CRR implementation: Coherence C(t) accumulates as orbital phase through inspiral via C(t) = ∫ω(τ)dτ following post-Newtonian evolution f(τ) ∝ τ⁻³/⁸; rupture δ(t_merger) marks the irreversible topology change from binary to single black hole; regeneration R(t) describes quasi-normal mode ringdown with damping τ_QNM determined by the memory kernel exp(C/Ω). The precision parameter Ω derives from mass ratio symmetry: Z₂ symmetric binaries (q=1) have Ω = 1/π ≈ 0.318, while broken symmetry increases Ω. QNM frequencies use Berti et al. fits; final state parameters from NR fits (Healy et al.). See crr_gravitational_waves.py for complete derivations. | Gravitational waves from binary black hole mergers naturally decompose into CRR's three phases. The inspiral chirp represents coherence accumulation as C approaches C* = Ω⁻¹. The merger is a true δ-function rupture—instantaneous, irreversible, scale-invariant. The ringdown represents regeneration toward equilibrium, with τ_QNM ∝ Ω⁻¹ confirming symmetric mergers decay faster. The CRR-BH correspondence yields C = S = 4πM², Ω = T = 1/(8πM), recovering the Sekino-Susskind scrambling time exactly: t_scr = Ω⁻¹log(C). The ringdown is the scrambling process made audible. |
| Sun Simulation (V1) Sun Simulation (V2) |
Two complementary solar simulations demonstrating stellar dynamics. CRR implementation: Nuclear coherence (C_nuclear) accumulates from fusion reactions over stellar lifetime; magnetic coherence follows ~11-year cycles. Rupture events include: solar flares (magnetic reconnection, δ-impulses with τ=5s), coronal mass ejections (plasma expulsion with extended regeneration), and magnetic field reversals (complete coherence reset). Regeneration operator rebuilds corona and magnetic structure with memory of past configurations. We share this to show how even the sun can be thought of, in a coarse-grain way, as a memory-bearing system! | |
| The Sun exhibits both steady fusion processes and catastrophic magnetic events. Understanding how systems reduce free energy variation through time and reach critical thresholds may be of benefit to systems thinkers. | ||
| Thermodynamics | Thermodynamic CRR system with non-Markovian dynamics. CRR implementation: Coherence C accumulates as potential energy at rate L₀=0.6 J/time; rupture δ(t-t₀) activates when C≥threshold, transferring heat Q=C×1.5; regeneration R[χ] extracts work through memory integral ∫φ(τ)·exp(C/Ω)·Θ(t-τ)dτ with causal Heaviside constraint. Demonstrates perfect energy conservation (0.000% error). | Non-Markovian thermodynamics with memory effects remains compatible with fundamental conservation laws. This might have implications for understanding far-from-equilibrium processes and energy harvesting in complex systems. Maybe. |
| Sandpile Modelling | Self-organised criticality via Bak-Tang-Wiesenfeld cellular automaton. CRR implementation: Coherence C_n = ∫(z-z_c/2)dt for each site accumulates height deviation; rupture occurs when grain count z≥4, triggering avalanche; regeneration distributes grains to neighbours weighted by exp(C_n/Ω). System self-organises to critical state C→C* with power-law avalanche distribution P(s)~s^(-1.27). | Self-organised critical systems appear across nature—from earthquakes to neural avalanches. Understanding how systems naturally evolve towards critical states may inform prediction of cascading failures and phase transitions. |
Basic Phase Transitions & Interactive Models
| Simulation | Description | Why It Might Matter |
|---|---|---|
| Kettle | Water boiling with molecular dynamics and hydrogen bonding. CRR implementation: Coherence measured through hydrogen bond network stability and thermal equilibrium; rupture δ(t-t₀) occurs at phase transition threshold (100°C) breaking liquid coherence into chaotic steam; regeneration models atmospheric dispersion and convection currents with memory of thermal history. | Phase transitions involve crossing discrete thresholds where coherent structures rupture. Everyday phenomena like boiling provide accessible examples of how accumulated thermal energy triggers sudden reorganisation. We share this as a simple pedagogical model to show how coherence builds over time until rupture/phase transition thresholds are met |
| Ice | Crystallisation dynamics with nucleation and growth. CRR implementation: Coherence C(x,t) tracks local molecular organisation through temperature-dependent coupling; nucleation sites emerge when coherence exceeds threshold (rupture points); regeneration operator propagates crystalline order spatially using exp(C/Ω) weighting, with Heaviside causality ensuring crystal grows from established regions. Notice how cohernece also increases in this system, as the system forms a stabilised structure over time. This is why we think of CRR in terms of identity transforming through time, at all scales. | Freezing demonstrates how local interactions produce long-range order. Understanding nucleation and crystal growth informs materials science, protein folding, and pattern formation in natural systems. |
| Zippo Lighter | Interactive lighter with realistic combustion mechanics. CRR implementation: Fuel vapour coherence field tracks butane concentration and mixing; spark field accumulates ignition energy through flint friction; rupture occurs when ignition_energy>threshold AND fuel_density>0.3, triggering flame; regeneration maintains flame through memory-weighted fuel consumption with wind/movement perturbations causing coherence loss. | Combustion requires precise conditions—fuel density, ignition energy, and spatial coherence. Small variations determine whether reactions propagate or extinguish, illustrating sensitivity to initial conditions in chemical systems. We like the emergent effects from gas escaping, and the natural "non-markovian" look of the flame! |
| Atmosphere | Molecular-scale atmospheric model with N₂, O₂, CO₂ interactions. CRR implementation: Atmospheric coherence field (80 elements) tracks gas mixture organisation; field evolves via temperature/pressure/humidity coupling; molecular collisions create rupture events redistributing momentum; regeneration processes restore equilibrium distributions through Brownian dynamics. | Atmospheric chemistry involves countless molecular collisions producing emergent properties like pressure and temperature. Such systems bridge microscopic randomness and macroscopic regularity. |
| Holographic | Thin-film interference and holographic projection. CRR implementation: Multi-layer optical path differences create interference patterns; coherence accumulates constructively/destructively across viewing angles; colour regeneration computed through wavelength-dependent phase shifts (400-700nm range); memory effects produce viewing-angle-dependent iridescence. | Wave interference creates stable patterns from continuous oscillations. Holography demonstrates how distributed information can encode three-dimensional structure—concepts relevant to both optics and theoretical physics. Upload an image to "rupture" the coherence field and see some stunning holographic effects! |
| Bubbles | Soap bubble physics with film drainage and rupture. CRR implementation: Coherence L=f_film·f_age·f_structure·f_kinetic accumulates film stability factors; rupture δ(t-t₀) triggers when C| Soap films exist at minimal energy configurations until perturbations exceed stability thresholds. Their dynamics illustrate how structures persist through continuous adjustment until catastrophic failure occurs. We know this isn't an NVidia level demonstration, but we found it intriguing! |
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Markovian Agents in Non-Markovian Fields (ML Applications)
| Simulation | Description | Why It Might Matter |
|---|---|---|
| Room Navigation | Multi-room exploration with key collection and goal-finding. CRR implementation: Agent maintains spatial coherence field C(x,y) through visited locations; local rupture detection via loop threshold breaks exploration cycles; global rupture resets after goal achievement; regeneration operator R[χ] weights actions by spatial memory integral ∫φ(x,τ)·exp(C/Ω)dτ. Intelligence I(t)=tanh(C_global/Ω) emerges from accumulated experience. | Intelligent behaviour can emerge from simple principles without explicit programming. Spatial memory accumulated through exploration enables efficient navigation—relevant for robotics, autonomous systems, and understanding biological navigation. |
| Fish Schooling | Single-agent learning with predators and food. CRR implementation: Memory trace accumulates position history (max 500 timesteps); coherence C grows via learning density L=reward-baseline; rupture occurs when C>threshold, triggering behavioural reset; regeneration R calculates movement bias from memory-weighted historical states. Avoidance/seeking strength scales with tanh(C/Ω) intelligence factor. | Animals adapt continuously to changing environments through memory and learning. Understanding how individual agents balance exploration, exploitation, and threat avoidance may inform reinforcement learning and swarm intelligence. |
| Maze Pathfinding | Goal-directed maze navigation with emergent intelligence. CRR implementation: Global coherence C_global and per-cell coherence fields C(x,y) accumulate from learning density L(reward); spatial memory stores field signals with coherence-weighted history; action selection combines goal distance heuristic with regeneration momentum R·direction; intelligence I=C_global/Ω modulates exploration/exploitation trade-off. Rupture on threshold crossing or timeout. | Pathfinding in unknown environments requires balancing memory, exploration, and goal pursuit. Emergent intelligence from accumulated coherence may offer alternatives to traditional planning algorithms in uncertain domains. |