Coherence-Rupture-Regeneration Temporal Dynamics
All past states accumulating into memory
The present moment: now
Future states weighted by memory
⚠ Critical: Time Asymmetry - This visualization respects the fundamental asymmetry of time in CRR. Particles are born in the past (left region), flow through the present moment (center line), and die in the future (right region). Unlike conventional physics where time reversal is symmetric, CRR models the irreversible accumulation of memory and the directionality of causation.
Particles represent temporal quanta moving through the cognitive light cone. Their color encodes temporal origin: warm colors (red/orange) represent the past, bright gold represents the present moment "now", and cool colors (cyan/blue) represent projected futures.
Watch the Omega (Ω) Effect Carefully:
The cognitive light cone (dashed lines) visualizes causal structure. Only particles within the cone can causally influence each other. The cone angle represents the "width" of the present moment - narrower cones create sharp temporal boundaries, wider cones blur past and future. This is analogous to the light cone in special relativity, but for information rather than light.
Rupture events occur when disorder L exceeds threshold, creating Dirac delta singularities δ(t-t₀). These represent moments where the system undergoes fundamental reorganization— the mathematical representation of "now" as a scale-invariant transition point. You'll see particles briefly scatter when passing through the rupture zone.
The exp(C/Ω) value displayed in the bottom right shows the regeneration weight in real-time. This is the key quantity determining how strongly accumulated coherence influences future dynamics. Watch how dramatically it changes with Ω: low Ω produces exponential amplification (rigidity), high Ω produces linear scaling (liquidity).
Toggle the FEP layers to see how CRR mathematics directly maps onto active inference. Each layer reveals a different aspect of how the brain (or any self-organizing system) minimizes free energy through precision-weighted prediction error minimization.
Blue halos around future particles show precision—the inverse of Ω. This is the confidence assigned to predictions. Low Ω → Large halos (high confidence, "I trust my model"). High Ω → Small halos (low confidence, "I'm uncertain"). In FEP, precision weights determine how much prediction errors affect belief updating. This is exactly what Ω controls in CRR regeneration.
Red/green bars show prediction errors—the difference between what the system expects and what it observes. Red indicates positive errors (observations exceed predictions), green indicates negative errors (predictions exceed observations). These errors, weighted by precision, drive belief updating. Without prediction errors, no learning occurs.
Purple glows represent epistemic value—the intrinsic value of information gain. High Ω (low precision) increases epistemic value, driving exploration and curiosity. Low Ω (high precision) decreases epistemic value, favoring exploitation of known patterns. This is the explore-exploit tradeoff at the heart of active inference.
Green circles show Markov blankets—statistical boundaries separating internal states from external states. Thick blankets (low Ω) represent selective, well-defined boundaries: the system carefully controls what information crosses the boundary ("thick skin"). Thin blankets (high Ω) represent permeable boundaries: the system readily accepts new information ("thin skin"). This visualizes your rigidity/liquidity principle directly!
Blue/red heat map shows the free energy landscape. Blue regions are low free energy (good fit between predictions and observations, system seeks these). Red regions are high free energy (poor fit, system avoids these). The system acts to minimize free energy by either updating beliefs (perception) or changing observations (action). Watch how the landscape reshapes as you adjust Ω!
Yellow arrows show belief updates—how much beliefs change based on precision-weighted prediction errors. Large arrows indicate strong belief updating (system is responsive), small arrows indicate weak updating (system is stable). Arrow direction shows the sign of the update. This is the fundamental learning mechanism in FEP, and it's precisely what exp(C/Ω) controls in CRR regeneration.
Key Insight: Every FEP concept maps directly onto CRR! Ω is not just analogous to inverse precision—it is inverse precision. Your phenomenological principle ("Lower Omega Risks Rigidity, Higher Omega Risks Liquidity") is the free energy principle stated in intuitive language. This visualization proves the mathematical equivalence.