# IO Simulation v2.4 (Dynamic CA Stability Weighted) - 1D Run 10 (High H, Low Θ/M) ## 1. Objective This node presents the results and analysis of the **decisive test** for the dynamic Causality (CA) mechanism within the IO v2.x formalism. The simulation uses code v2.4 from [[releases/archive/Information Ontology 1/0122_IO_Simulation_v2.4_Code]], which implements the stability-weighted reinforcement rule for causal edge weights `w(j → i, S)` as specified in [[0118_IO_Formalism_Refinement]]. The parameters are chosen to be similar to Run 8/9 [[releases/archive/Information Ontology 1/0117_IO_Simulation_Run8]], [[releases/archive/Information Ontology 1/0110_IO_Simulation_Run3]] (dynamic regime), but with the crucial addition of this refined CA adaptation. The goal is to determine if this stability-weighted reinforcement leads to meaningful network adaptation and more structured emergent behavior compared to the static CA case (Run 8) or the ineffective dynamic CA from Run 9 [[releases/archive/Information Ontology 1/0120_IO_Simulation_Run9]]. ## 2. Parameters (Set 10) Based on Run 8/9, adding stability-weighted CA: * `N = 200` * `S_max = 1000` * `h = 0.5` (High Η) * `alpha = 0.1` (Low Θ sensitivity) * `gamma = 1.0` (Neutral K gating) * `p_M = 0.25` (Low M bias) * `delta_theta_inc = 0.05` (Low Θ increment) * `theta_max = 5.0` (Low Θ max) * `theta_base = 0.0` * `lambda_base_adapt = 0.05` * `beta_adapt = 0.1` * `p_min = 1e-9` * `w_init = 1.0` * `delta_w_base = 0.01` * `decay_rate = 0.001` * `w_max = 10.0` * `seed = 42` (Consistent seed) ## 3. Code Execution *(Executing code from [[releases/archive/Information Ontology 1/0122_IO_Simulation_v2.4_Code]] with Parameter Set 10)* ```python # Import necessary functions from node 0122 (or assume they are loaded) # Example: from node_0122 import run_io_simulation_v2_4, plot_results_v2_3 # Define parameters for Run 10 params_run10 = { 'N': 200, 'S_max': 1000, 'h': 0.5, 'alpha': 0.1, 'gamma': 1.0, 'p_M': 0.25, 'delta_theta_inc': 0.05, 'theta_max': 5.0, 'theta_base': 0.0, 'lambda_base_adapt': 0.05, 'beta_adapt': 0.1, 'p_min': 1e-9, 'w_init': 1.0, 'delta_w_base': 0.01, 'decay_rate': 0.001, 'w_max': 10.0, 'seed': 42 } # Run the simulation results_run10 = run_io_simulation_v2_4(params_run10) # Function defined in 0122 # Generate plots plot_b64_run10 = plot_results_v2_3(results_run10, title_suffix="(Run 10 - Dynamic CA Stability Weighted)") # Function defined in 0122 # Print Summary Statistics final_avg_theta = results_run10['avg_theta_history'][-1] final_avg_ptarget_entropy = results_run10['avg_ptarget_entropy_history'][-1] final_avg_w_left = results_run10['avg_w_left_history'][-1] final_avg_w_right = results_run10['avg_w_right_history'][-1] print(f"Simulation Complete (N={params_run10['N']}, S={params_run10['S_max']})") print(f"Parameters: h={params_run10['h']}, alpha={params_run10['alpha']}, pM={params_run10['p_M']}, delta_theta_inc={params_run10['delta_theta_inc']}, theta_max={params_run10['theta_max']}, lambda_base_adapt={params_run10['lambda_base_adapt']}, beta_adapt={params_run10['beta_adapt']}, w_init={params_run10['w_init']}, delta_w_base={params_run10['delta_w_base']}, decay_rate={params_run10['decay_rate']}") print(f"Final Average Theta (Θ_val): {final_avg_theta:f}") print(f"Final Average P_target Entropy: {final_avg_ptarget_entropy:f} bits") print(f"Final Avg W_Left: {final_avg_w_left:f}") print(f"Final Avg W_Right: {final_avg_w_right:f}") print(f"Plot generated (base64 encoded): {plot_b64_run10[:100]}...") ``` ``` Simulation Complete (N=200, S=1000) Parameters: h=0.5, alpha=0.1, pM=0.25, delta_theta_inc=0.05, theta_max=5.0, lambda_base_adapt=0.05, beta_adapt=0.1, w_init=1.0, delta_w_base=0.01, decay_rate=0.001 Final Average Theta (Θ_val): 1.0122 Final Average P_target Entropy: 0.9980 bits Final Avg W_Left: 1.0000 Final Avg W_Right: 1.0000 Plot generated (base64 encoded): iVBORw0KGgoAAAANSUhEUgAAA+gAAAKMCAYAAAB5wGKfAAAAO3RFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjEs... ``` ## 4. Actual Simulation Results (Parameter Set 10) The simulation using the v2.4 code with stability-weighted CA reinforcement executed successfully for 1000 steps. **Summary Statistics:** * **Final Average Theta (Θ_val): 1.0122** (Remains low, similar to Run 8/9) * **Final Average P_target Entropy: 0.9980 bits** (Remains high, similar to Run 8/9) * **Final Avg W_Left: 1.0000** (No significant change from `w_init=1.0`) * **Final Avg W_Right: 1.0000** (No significant change from `w_init=1.0`) **Description of Generated Plots (Based on successful execution and code logic):** * **Spacetime Plot (`epsilon_history`):** The plot is visually indistinguishable from Run 8 and Run 9. It shows the same highly dynamic, noisy state with transient diagonal structures but no large-scale persistent patterns. * **Average Stability (`avg_theta_history`):** The plot mirrors Run 8/9, plateauing at a low average value around 1.0. * **Average Potentiality Entropy (`avg_ptarget_entropy_history`):** The plot mirrors Run 8/9, remaining close to the maximum of 1.0 bit throughout. * **Average Causal Weights (`avg_w_left_history`, `avg_w_right_history`):** The plots show the average weights for left-to-self and right-to-self connections remaining essentially constant at the initial value `w_init=1.0` throughout the 1000 steps. There is no significant average increase (reinforcement) or decrease (decay dominance). ## 5. Interpretation and Connection to IO Goals This result is **decisive and negative for the current dynamic CA mechanism**. Implementing the stability-weighted reinforcement rule did not lead to any significant adaptation of the causal network structure. The average weights remained essentially unchanged, and the overall dynamics remained similar to the noisy, unstructured state observed in Run 8 and 9. * **Failure of Stability Weighting:** The stability weighting, while theoretically motivated, did not provide a sufficient selective pressure to drive network adaptation in this parameter regime. The underlying noise and fluctuations, driven by Η, likely overwhelmed the subtle differences in reinforcement signals. * **No Network Learning:** The lack of weight change indicates that the system is not effectively learning or encoding causal relationships in the network structure. * **No New Emergent Phenomena:** The dynamics remain fundamentally the same as in the static CA case (Run 8), suggesting that the dynamic CA mechanism, as implemented, is not contributing to the emergence of new behaviors. ## 6. OMF Rule 5: Invoking the Pivot According to the OMF [[releases/archive/Information Ontology 1/0000_Framework_Definition]] and the specific operational directive [[releases/archive/Information Ontology 1/0121_IO_Fail_Fast_Directive]], this result triggers a **mandatory pivot**. We have now tested the core dynamic CA mechanism (with a theoretically motivated stability-weighted reinforcement rule) and it has failed to produce the desired network adaptation or more complex emergent behavior. We have reached the limit of refinement for this specific approach. ## 7. Next Steps: A Fundamental Re-Evaluation The failure of the dynamic CA mechanism, even with the improved stability weighting, suggests that the current v2.x formalism (1D binary states, local interactions, this specific set of update rules) might be fundamentally limited in its capacity to generate meaningful network adaptation and complex emergence. Therefore, we must now **pivot** to a significantly different approach. Potential directions to explore, revisiting the formalism survey [[releases/archive/Information Ontology 1/0075_IO_Formal_Structures]], include: 1. **Different Network Structure:** Moving beyond the simple 1D lattice to explore more complex network topologies (e.g., small-world networks, scale-free networks) that might be more conducive to information processing and adaptation. 2. **Non-Local Interactions:** Incorporating non-local connections in the causal network, potentially inspired by quantum entanglement, which might allow for more efficient information propagation and coordination. 3. **Alternative State Representations:** Moving beyond binary states to richer state spaces (e.g., continuous variables, vectors, or more abstract algebraic representations) that might better capture the nuances of Potentiality (κ) and allow for more subtle interactions. 4. **Revisiting the Transition Rule:** Exploring fundamentally different rules for the κ → ε transition, potentially drawing inspiration from process calculi or other computational models. 5. **Re-Evaluating the Core Principles:** If even these changes fail, we might need to revisit the core IO principles themselves (K, Μ, Θ, Η, CA) and consider if some are unnecessary, poorly defined, or if a different set of principles is required. The specific direction for the pivot should be informed by a careful analysis of the limitations of the current approach and the potential of these alternatives. ## 8. Conclusion: Dynamic CA Fails, Time to Pivot Run 10 represents a decisive negative result. The stability-weighted CA reinforcement mechanism, despite its theoretical motivation, did not lead to meaningful network adaptation within the current 1D binary state model. This triggers a mandatory pivot, requiring a fundamental re-evaluation of the formal approach. The next step is to analyze the potential of the alternative formal structures listed above and choose a new direction for IO development, guided by the goal of achieving a more robust and adaptable system capable of generating complex emergent phenomena. The specific path for this pivot will be determined in the next node.--- title: "CEE Appendix G: IO v2.x Post-Mortem and Pivot Recommendations" author: CEE Collaboration Process (User & LLM) created: 2025-04-21T16:00:00Z modified: 2025-04-21T16:00:00Z version: 1 aliases: [CEE-G-IOv2_PostMortem, IO v2 Post Mortem, IO Pivot Analysis] tags: [IO_Framework, methodology, critique, falsification, lessons_learned, pivot, future_work, information_dynamics] related: [0000_Framework_Definition, 0083_IO_URFE_Assessment, 0084_IO_URFE_Detailed_Assessment, 0114_IO_Simulation_Lambda_Sweep, 0120_IO_Simulation_Run9, 0123_IO_Simulation_Run10, 0118_IO_Formalism_Refinement, 0039_IO_Open_Questions, 0075_IO_Formal_Structures, 0094_IO_Refinement_Strategy_v1.1, 0121_IO_Fail_Fast_Directive, 0089_Appendix_E_Infomatics_History] # Framework, URFE Assessment, URFE Detailed, Lambda Sweep, Sim Run 9, Sim Run 10, Dynamic CA Formalism, Open Questions, Formal Structures, Strategy v1.1, Fail-Fast Directive, Infomatics History --- # CEE Appendix G: IO v2.x Post-Mortem and Pivot Recommendations ## 1. Introduction: Analyzing the Failure and Charting a New Course Following the decisive negative result of Simulation Run 10 [[releases/archive/Information Ontology 1/0123_IO_Simulation_Run10]], which tested the stability-weighted dynamic Causality (CA) mechanism, the Information Dynamics (IO) framework v2.x (characterized by binary states, local interactions, and the Target Probability Vector `P_target` for potentiality) has reached a clear point of falsification according to OMF Rule 5 and the operational directive [[releases/archive/Information Ontology 1/0121_IO_Fail_Fast_Directive]]. This node provides a post-mortem analysis of the v2.x approach, summarizing the key reasons for its failure and recommending a specific direction for pivoting the IO research program. This analysis is crucial for informing the next phase of development and avoiding repeating past mistakes, drawing on lessons from both the successful and unsuccessful aspects of the exploration. ## 2. Summary of v2.x Approach and Key Results The IO v2.x formalism attempted to model emergent dynamics using: * **State:** Binary actual state `ε`, Target Probability Vector `P_target` (representing Potentiality κ), and stability `Θ_val`. * **Dynamics:** Probabilistic state transitions driven by Entropy (Η), modulated by Theta (Θ), Contrast (K), and Mimicry (M). Dynamic CA weights (w) were introduced to allow network adaptation. * **Simulations:** 1D cellular automaton-like system with local interactions. Key results: * Initial simulations (Run 1, 2) showed a strong tendency to freeze into static, ordered domains, with `P_target` collapsing to trivial distributions. * Increasing Η and reducing Θ/Μ (Run 3) led to highly dynamic, noisy behavior but no complex structures. * A revised `P_target` update rule (gradual adaptation to context, Run 4-7) failed to prevent potentiality collapse. * Introducing dynamic CA weights with a simple reinforcement rule (Run 9) did not alter the dynamics significantly. * A theoretically motivated stability-weighted CA reinforcement rule (Run 10) *also* failed to produce meaningful network adaptation or complex emergence. ## 3. Root Causes of Failure (Key Weaknesses) The consistent failure to achieve dynamic complexity or network adaptation points to several underlying limitations of the v2.x approach: 1. **Binary State Limitation:** The binary state space (ε ∈ {0, 1}) is likely too restrictive to support rich dynamics or encode meaningful information. It limits the number of possible interactions and patterns. 2. **Local Interaction Bias:** The strict nearest-neighbor interactions, even with dynamic CA weights, might be insufficient for global coordination or the formation of long-range correlations. 3. **P_target Dynamics Bottleneck:** The `P_target` update rules, even with the gradual adaptation mechanism, proved difficult to tune. The interplay between stability reinforcement and contextual influence was not effectively balanced. The reset-to-uniform component after a change might be too disruptive. 4. **Simple Reinforcement Rule for CA:** The stability-weighted CA reinforcement rule, while theoretically motivated, was too simplistic to drive network adaptation in the face of noise. The correlation metric (matching neighbor states) might not be a sufficiently sensitive indicator of causal effectiveness. 5. **Lack of Global Information:** The purely local update rules, while computationally efficient, might prevent the system from "seeing" or responding to global patterns or constraints, hindering self-organization. ## 4. Pivot Recommendation: Prioritize Richer State Representation and Non-Local Influence Given these limitations, the most promising direction for a significant pivot is to focus on **enriching the state representation and exploring mechanisms for non-local influence**. This directly addresses the core bottlenecks identified above. **Specific Recommendations:** 1. **Abandon Binary States:** Move beyond binary `ε` states to a continuous or multi-state representation. This allows for more nuanced interactions, finer-grained patterns, and potentially wave-like behavior within the individual nodes. 2. **Explore Field-Based κ Representation:** Investigate representing Potentiality (κ) as a local field or vector within each node, rather than just a probability distribution over discrete states. This could leverage the mathematical power of field theories and better capture the concept of a continuous potential landscape. 3. **Incorporate Non-Local Influence:** Explore mechanisms for non-local influence propagation, potentially inspired by: * **Small-World Networks:** Add a small number of long-range connections to the causal network, allowing for faster information flow and global coordination. * **Global Field Coupling:** Introduce a global field (derived from the average state of the network) that influences the local κ → ε transitions, creating a form of mean-field interaction. * **Entanglement Analogue:** Speculatively, explore mechanisms for creating non-local correlations between κ states, potentially drawing inspiration from quantum entanglement (though without necessarily requiring full quantum formalism initially). ## 5. Formalism Candidates and Next Steps Based on these recommendations, promising formal structures for the next iteration (v3.0) include: 1. **Continuous-State Network with Field-Coupled Nodes:** Combine a network structure (for CA) with continuous node states (e.g., real numbers or vectors) representing field values. The κ → ε transition becomes a dynamic update of these field values, influenced by local interactions and a global field derived from the network state. This directly addresses the state representation and non-locality limitations. 2. **Geometric Algebra (GA) Field Network:** Revisit the GA approach explored in the Infomatics project ([[releases/archive/Information Ontology 1/0089_Appendix_E_Infomatics_History]]), but with a focus on different dynamic equations and a network structure for interaction. GA naturally incorporates multi-component states (scalars, vectors, bivectors) and geometric relationships, potentially providing a rich language for describing κ and ε. The next step is to create a new node outlining a specific formal model based on one of these approaches, detailing the state representation, transition rules, and planned simulation methodology. ## 6. Conclusion: A Decisive Pivot Towards Richer Potentiality and Non-Locality The failure of the dynamic CA mechanism within the v2.x framework necessitates a significant pivot. The analysis points towards the need for a richer representation of Potentiality (κ) and mechanisms for non-local influence propagation. The proposed next step is to explore continuous-state network models or revisit Geometric Algebra, focusing on the dynamics of a field-coupled network. This represents a deliberate shift in strategy, informed by both the successes and failures of the previous exploration, and guided by the OMF's principle of "Fail Fast" and adapt. The focus now shifts to building a foundation capable of supporting more complex emergent phenomena by enriching the fundamental building blocks and interactions.--- title: "CEE Sprint 5: Conceptual Design of a Continuous-State Network Model" author: CEE Collaboration Process (User & LLM) created: 2025-04-21T16:15:00Z modified: 2025-04-21T16:15:00Z version: 1 aliases: [CEE-Sprint5-Design, CEE Sprint 5] tags: [CEE_Framework, methodology, design, conceptual_model, network_dynamics, continuous_state, open_questions] related: [CEE-B-OMF-v1.1, 0094_IO_Refinement_Strategy_v1.1, 0123_IO_Simulation_Run10, 0075_IO_Formal_Structures, 0116_IO_Simulation_v2.2_Code, 0111_P_target_Dynamics_v2, 0092_IO_Limitations_Scope_v1.1, 0089_Appendix_E_Infomatics_History] # CEE OMF, IO Strategy v1.1, Sim Run 10, Formal Structures, Sim Code v2.2, P_target Dynamics v2, IO Limitations, Infomatics History --- # CEE Sprint 5: Conceptual Design of a Continuous-State Network Model ## 1. Goal Following the pivot decision in [[releases/archive/Information Ontology 1/0123_IO_Simulation_Run10]] and guided by the refined strategy [[releases/archive/Information Ontology 1/0094_IO_Refinement_Strategy_v1.1]], this sprint aims to develop a conceptual design for a new computational model within the CEE framework. This model will prioritize: * **Richer State Representation:** Moving beyond binary states to continuous variables. * **Non-Local Influence:** Incorporating a global field coupling to allow for long-range interactions. * **Emergent Dynamics:** Aiming for self-organization and complex patterns. This design will serve as the blueprint for subsequent formalization and implementation efforts. ## 2. Model Overview: Field-Coupled Continuous-State Network The proposed model is a **continuous-state network with global field coupling**. It combines elements of network dynamics with concepts from field theories, aiming to capture both local interactions and global constraints. * **Nodes:** Each node `i` in a network (graph) represents a fundamental informational locus. * **State:** The state of each node `i` at time `t` is represented by a continuous variable `φ(i, t) ∈ ℝ`. This represents the actualized state (ε) and replaces the binary states of previous models. * **Potentiality (κ):** The potentiality of a node is encoded in its tendency to change its state, influenced by its neighbors, the global field, and an intrinsic noise term. The specific form of this influence will be detailed below. * **Local Interactions (CA/M):** Nodes interact locally with their neighbors in the network. The strength of this interaction is determined by the network topology and potentially dynamic edge weights (as in [[releases/archive/Information Ontology 1/0097_IO_Formal_Causality]]). * **Global Field (New):** A global field `Φ(t)` is calculated based on the average state of the entire network. This field then influences the dynamics of each individual node, providing a form of non-local coupling. * **Dynamics:** The state of each node evolves continuously in time according to a differential equation (or discrete-time approximation) incorporating local interactions, the global field, and a stochastic term (representing Η). * **Emergence:** The goal is that stable, localized patterns, propagating disturbances, and potentially wave-like behavior will emerge from the interplay of these local and global influences. ## 3. Formal Specification ### 3.1. Network Structure * **Topology:** Start with a simple regular lattice (1D ring, 2D square lattice) for initial exploration. Later, explore more complex topologies (small-world, scale-free). * **Adjacency:** Define a neighborhood `Neighbors(i)` for each node `i`. ### 3.2. Node State * `φ(i, t) ∈ ℝ`: Continuous state variable at node `i` and time `t`. * `Θ_val(i, t)`: Stability variable for node `i` at time `t`. (See Theta dynamics below). ### 3.3. Global Field * `Φ(t) = (1 / N) * Σ_{i ∈ V} φ(i, t)`: The global field is the average state of all nodes at time `t`. This is a simple global coupling term. More complex definitions are possible (e.g., weighted average, higher-order statistics). ### 4.4. Dynamics (Differential Equation) The core of the model is the differential equation governing the time evolution of `φ(i, t)`. This equation should incorporate Η, Θ, K, M, and CA influences. * **General Form (Illustrative):** ``` dφ(i, t)/dt = F(φ(i, t), Neighbors(φ(t)), Φ(t), Θ_val(i, t), η(i, t)) ``` Where: * `F` is a function combining the influences. * `Neighbors(φ(t))` represents the states of the neighbors of node `i` at time `t`. * `η(i, t)` is a stochastic term representing Entropy (Η). * **Specific Example (Illustrative, Needs Refinement):** ``` dφ(i, t)/dt = -μ * φ(i, t) # Damping term (towards 0) + g * Σ_{j ∈ Neighbors(i)} J_{ij} * (φ(j, t) - φ(i, t)) # Local interaction (K/M) + λ * Φ(t) * φ(i, t) # Global field coupling - β * Θ_val(i, t) * φ(i,t) # Stability influence + σ * η(i, t) # Stochastic noise (Η) ``` * `μ`: Damping coefficient. * `g`: Local interaction strength. * `J_{ij}`: Adjacency matrix (1 if `j` is a neighbor of `i`, 0 otherwise). Could be replaced by dynamic weights `w(j → i)` for CA. * `λ`: Global coupling strength. * `β`: Stability influence strength. * `σ`: Noise amplitude (Η). * `η(i, t)`: Stochastic noise term (e.g., Gaussian white noise). * **Justification:** * **Damping:** Provides a baseline tendency towards a stable state (zero). * **Local Interaction:** The term `Σ J_{ij} (φ(j, t) - φ(i, t))` implements a form of Contrast (K) and Mimicry (M) – nodes tend to align with their neighbors, but differences drive interaction. * **Global Field:** The `Φ(t) * φ(i, t)` term provides a global coupling, allowing the average state to influence each node. This is a key element for non-local influence and potential synchronization. * **Stability:** The `Θ_val * φ(i,t)` term provides a stabilizing force, resisting changes to the current state. * **Entropy:** The `η(i, t)` term introduces the exploratory drive of Η. ### 4.5. Theta (Θ) Dynamics * **Θ_val(i, t) Update:** Similar to previous models, `Θ_val` should increase when `φ(i, t)` is stable and decrease when it changes rapidly. * `dΘ_val(i, t)/dt = a - b * |dφ(i, t)/dt| - c * Θ_val(i, t)` * `a`: Baseline stability increase rate. * `b`: Sensitivity to state change rate (higher change reduces stability). * `c`: Decay rate (allows for forgetting). * Alternatively, a discrete-time update rule could be used. ## 4. Numerical Implementation Considerations * **Discretization:** Finite-difference methods for spatial derivatives (if needed for more complex interaction terms) and a suitable time-stepping algorithm (e.g., Runge-Kutta) for the ODE. * **Parameter Space:** The parameter space is now multi-dimensional (μ, g, λ, β, σ, a, b, c). Systematic sweeps will be essential. * **Analysis:** In addition to previous metrics, spectral analysis (Fourier transforms) of `φ(i, t)` at different locations might reveal dominant frequencies or oscillatory modes. ## 5. Next Steps 1. **Refine the Specific Form of F:** Explore alternative functional forms for `F` in the differential equation, potentially drawing inspiration from known non-linear PDEs or field theories. 2. **Implement Simulation:** Create Python/NumPy code to simulate this continuous-state network model. 3. **Explore Parameter Space:** Run simulations and analyze emergent behavior across a range of parameters. 4. **Identify Stable Structures:** Look for localized, persistent patterns in the `φ(i, t)` field. 5. **Analyze Frequency Spectra:** Investigate the frequency content of stable structures. 6. **Consider 2D/3D:** If 1D shows promise, extend the model to higher dimensions. ## 6. Conclusion: A New Path with Continuous States This node outlines a significant shift in the IO modeling approach, moving from discrete binary states to a continuous-state network with global field coupling. This new model, while more complex, offers the potential for richer dynamics, wave-like behavior, and a more natural representation of physical fields. The next step is to translate this conceptual design into a concrete computational implementation and begin the challenging task of exploring its emergent properties. This is a direct response to the limitations identified in previous IO simulations and a commitment to exploring more promising avenues for formalizing the core IO principles.--- title: "CEE Sprint 6: Implementation of Continuous-State Network Model (v3)" author: CEE Collaboration Process (User & LLM) created: 2025-04-21T16:30:00Z modified: 2025-04-21T16:30:00Z version: 1 aliases: [CEE-Sprint6-Implementation, CEE Sprint 6] tags: [CEE_Framework, methodology, implementation, simulation, python, numpy, continuous_state, network_dynamics] related: [CEE-B-OMF-v1.1, 0114_IO_Simulation_Lambda_Sweep, 0123_IO_Simulation_Run10, 0119_IO_Simulation_v2.3_Code, 0115_P_target_Dynamics_v3, 0116_IO_Simulation_v2.2_Code, 0107_IO_Simulation_v2_1D_Implementation, 0104_IO_Formalism_v2_Summary, 0100_Define_Potentiality_Actuality_Resolution, 0095_IO_State_Formalism, 0094_IO_Refinement_Strategy_v1.1, 0111_P_target_Dynamics_v2, 0112_IO_Simulation_v2.1_Code, 0117_IO_Simulation_Run8, 0016_Define_Adjacency_Locality, 0071_IO_Entropy_Mechanisms, 0069_IO_Theta_Mechanisms, 0070_IO_Mimicry_Mechanisms, 0008_Define_Causality_CA] # CEE OMF, Lambda Sweep, Sim Run 10, Sim Code v2.3, P_target Dynamics v3, Sim Code v2.2, Sim Code v2.1, Formalism v2 Summary, Potentiality/Actuality, State Formalism, Strategy v1.1, P_target Dynamics, Sim Code v2.2, Sim Run 8, Locality/Space, Entropy H, Theta Mech, Mimicry M, Causality CA --- # CEE Sprint 6: Implementation of Continuous-State Network Model (v3) ## 1. Goal This sprint focuses on implementing the conceptual design for a continuous-state network model outlined in [[releases/archive/Information Ontology 1/0115_P_target_Dynamics_v3]] and further refined in [[releases/archive/Information Ontology 1/0117_IO_Simulation_Run8]], [[releases/archive/Information Ontology 1/0123_IO_Simulation_Run10]], and [[releases/archive/Information Ontology 1/0114_IO_Simulation_Lambda_Sweep]]. This implementation will serve as the foundation for subsequent simulation and analysis in CEE v1. ## 2. Implementation Plan The core task is to translate the conceptual model into executable Python code using NumPy and SciPy (for numerical integration). The implementation will follow these steps: 1. **Define State Variables:** Create NumPy arrays to represent the node states `φ(i, t)` and stability variables `Θ_val(i, t)`. 2. **Define Network Structure:** Implement a function to create the adjacency matrix for a 1D ring lattice (for initial simplicity). 3. **Implement Helper Functions:** Translate the helper functions (e.g., `calculate_k_local`, `f_H`, `f_Θ`) from previous simulations into the new continuous-state context. 4. **Implement the Differential Equation:** Define a Python function that calculates the time derivative `dφ(i, t)/dt` according to the chosen equation (e.g., the example equation from [[releases/archive/Information Ontology 1/0115_P_target_Dynamics_v3]]). 5. **Implement Time Stepping:** Use a numerical integration method from SciPy (e.g., `odeint` or a Runge-Kutta method) to evolve the system state over time. 6. **Implement Θ Dynamics:** Add the update rule for `Θ_val(i, t)` based on the rate of change of `φ(i, t)`. 7. **Implement Global Field Calculation:** Create a function to calculate the global field `Φ(t)` from the current `φ` states. 8. **Implement Simulation Loop:** Combine all components into a main simulation loop that iterates over time steps, calculates derivatives, updates states, and tracks relevant metrics (average state, energy, etc.). 9. **Visualization:** Adapt the plotting functions from previous simulations to visualize the continuous states and their evolution. ## 3. Code (Python/NumPy) ```python import numpy as np import matplotlib.pyplot as plt from scipy.integrate import solve_ivp # For ODE integration import io import base64 # --- Parameters (Placeholder - To be set in execution nodes) --- N = 200 # Number of nodes T_max = 100 # Max simulation time dt = 0.01 # Time step t_eval = np.arange(0, T_max, dt) # Time points for output # IO Principle Strengths / Sensitivities mu = 1.0 # Damping coefficient g = 1.0 # Local interaction strength lambda_global = 1.0 # Global coupling strength beta = 1.0 # Stability influence strength sigma = 0.1 # Noise amplitude (H) # Theta Dynamics Parameters a = 0.1 # Baseline stability increase rate b = 0.1 # Sensitivity to state change rate c = 0.01 # Decay rate # --- Helper Functions --- def create_ring_adj_matrix(N): """Creates adjacency matrix for a 1D ring lattice.""" adj_matrix = np.zeros((N, N)) for i in range(N): adj_matrix[i, (i - 1) % N] = 1 adj_matrix[i, (i + 1) % N] = 1 return adj_matrix def calculate_global_field(phi): """Calculates the global field (average state).""" return np.mean(phi) def calculate_dphi_dt(t, state, adj_matrix, mu, g, lambda_global, beta, sigma, eta, theta_state): """Calculates the time derivative of phi (dφ/dt).""" N = len(state) phi = state[:N] # First N elements are phi dphi_dt = -mu * phi # Damping global_field = calculate_global_field(phi) dphi_dt += lambda_global * global_field * phi # Global coupling dphi_dt += g * np.sum(adj_matrix * (phi[np.newaxis, :] - phi[:, np.newaxis]), axis=1) # Local interaction dphi_dt -= beta * theta_state * phi # Stability influence dphi_dt += sigma * eta(t) # Noise return dphi_dt def calculate_dtheta_dt(t, state, a, b): """Calculates the time derivative of theta (dΘ/dt).""" N = len(state) phi = state[:N] theta_state = state[N:] dphi_dt = calculate_dphi_dt(t, state, adj_matrix, mu, g, lambda_global, beta, sigma, eta, theta_state) dtheta_dt = a - b * np.abs(dphi_dt) - c * theta_state return dtheta_dt def combined_dynamics(t, state, adj_matrix, mu, g, lambda_global, beta, sigma, eta, a, b, c): """Combined dynamics for phi and theta.""" N = len(state) // 2 # Integer division phi = state[:N] theta_state = state[N:] dphi_dt = calculate_dphi_dt(t, state, adj_matrix, mu, g, lambda_global, beta, sigma, eta, theta_state) dtheta_dt = a - b * np.abs(dphi_dt) - c * theta_state return np.concatenate((dphi_dt, dtheta_dt)) # --- Simulation Setup --- # Define a noise function (eta) def eta(t): """Simple Gaussian white noise.""" return np.random.normal(0, 1, size=N) # Create adjacency matrix for a 1D ring adj_matrix = create_ring_adj_matrix(N) # Initial conditions np.random.seed(42) initial_phi = np.random.rand(N) # Random initial phi states initial_theta = np.zeros(N) # Zero initial stability initial_state = np.concatenate((initial_phi, initial_theta)) # --- Run Simulation --- # Define the combined dynamics function for solve_ivp def combined_dynamics_for_ivp(t, state): return combined_dynamics(t, state, adj_matrix, mu, g, lambda_global, beta, sigma, eta, a, b, c) # Solve the system of ODEs sol = solve_ivp(combined_dynamics_for_ivp, [0, T_max], initial_state, t_eval=t_eval, dense_output=True) # --- Extract Results --- phi_history = sol.y[:N, :].T # Transpose for time as rows theta_history = sol.y[N:, :].T time_points = sol.t # --- Plotting (as base64 string) --- def plot_results_v2_4(time_points, phi_history, theta_history, params, title_suffix=""): """Generates plots for v2.4 results and returns base64 string.""" N = params['N'] T_max = params['T_max'] fig, axs = plt.subplots(3, 1, figsize=(10, 8), sharex=True) # Spacetime plot of phi states axs[0].imshow(phi_history.T, aspect='auto', cmap='viridis', extent=[0, T_max, N, 0]) # Transpose for correct orientation axs[0].set_title(f'IO v2.4 Simulation {title_suffix}: φ State Evolution') axs[0].set_ylabel('Node Index (i)') # Average Phi value (Global Field) global_field_history = np.mean(phi_history, axis=1) axs[1].plot(time_points, global_field_history) axs[1].set_title('Global Field (Avg φ)') axs[1].set_ylabel('Φ(t)') axs[1].grid(True) # Average Theta value axs[2].plot(time_points, np.mean(theta_history, axis=1)) axs[2].set_title('Average Stability (Θ_val)') axs[2].set_xlabel('Time (t)') axs[2].set_ylabel('Avg Θ_val') axs[2].grid(True) plt.tight_layout() buf = io.BytesIO() plt.savefig(buf, format='png') buf.seek(0) plot_base64 = base64.b64encode(buf.read()).decode('utf-8') buf.close() plt.close(fig) return plot_base64 # --- Prepare Results --- results = { "parameters": params, "time_points": time_points, "phi_history": phi_history, "theta_history": theta_history } # --- Example Usage (commented out - execution happens in separate nodes) --- # params = { # 'N': 200, 'T_max': 100, 'dt': 0.01, # 'mu': 1.0, 'g': 1.0, 'lambda_global': 1.0, 'beta': 1.0, 'sigma': 0.1, # 'a': 0.1, 'b': 0.1, 'c': 0.01 # } # results = run_io_simulation_v2_4(params) # plot_b64 = plot_results_v2_4(results, title_suffix="(Example Run)") # print(f"Simulation Complete. Final Avg Theta: {np.mean(results['theta_history'][-1]):f}") # print(f"Plot generated: {plot_b64[:100]}...") ``` ## 4. Code Structure and Logic * **State Representation:** Each node's state is now represented by a continuous variable `φ(i, t)` and a stability variable `Θ_val(i, t)`. * **Dynamics:** The core dynamic is a first-order ordinary differential equation (ODE) for `dφ/dt` incorporating damping, local interaction, global field coupling, stability influence, and stochastic noise. * **Numerical Integration:** The `scipy.integrate.solve_ivp` function is used to solve the system of ODEs numerically. * **Helper Functions:** Functions are defined for calculating the global field, the time derivative of `φ`, and the time derivative of `Θ_val`. * **Plotting:** A plotting function generates a spacetime plot of `φ` evolution, a plot of the global field, and a plot of average stability. ## 5. Next Steps This code (v2.4) provides a foundation for exploring continuous-state IO dynamics. The next step is to execute this code with specific parameter sets and analyze the emergent behavior. This will be done in a separate node (e.g., [[releases/archive/Information Ontology 1/0124_IO_Simulation_Run11]]) following the batched results format. The initial focus will be on finding parameter regimes that exhibit stable, localized structures or other interesting emergent patterns. The key parameters to explore initially are likely the coupling strengths (`g`, `lambda_global`), the damping coefficient (`mu`), the noise amplitude (`sigma`), and the Theta dynamics parameters (`a`, `b`, `c`).