OpenPeerAI
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ChaosSIM

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-# ChaosSim Test Results
-**Test Date**: November 25, 2025
-**Tested By**: Development Team
-**Framework Version**: 1.0.0
-**Platform**: Wolfram Mathematica 13.x
----
-## Test Environment
-- **Operating System**: Windows 11
-- **Wolfram Version**: 13.0+
-- **Memory**: 16GB RAM recommended
-- **Processor**: Multi-core processor (4+ cores recommended)
----
-## Unit Tests
-### 1. Bernoulli Number Functions
-#### Test: `BernoulliChaosWeight[n]`
-**Expected Behavior**: Returns absolute value of nth Bernoulli number, returns 0.001 for B₀=0
-```mathematica
-(* Test cases *)
-BernoulliChaosWeight[0]  (* Expected: 0.001 *)
-BernoulliChaosWeight[2]  (* Expected: 0.166667 *)
-BernoulliChaosWeight[4]  (* Expected: 0.0333333 *)
-```
-**Status**: ✅ PASS
-**Notes**: Correctly handles zero Bernoulli numbers and returns normalized weights
-#### Test: `SimulateBernoulliChaos[iterations, complexity]`
-**Expected Behavior**: Generates chaos sequence of specified length with values in [0, 1]
-```mathematica
-(* Generate 100 iterations *)
-data = SimulateBernoulliChaos[100, 10];
-Length[data]  (* Expected: 100 *)
-Min[data] >= 0 && Max[data] <= 1  (* Expected: True *)
-```
-**Status**: ✅ PASS
-**Output Range**: [0, 1]
-**Sequence Length**: Matches input parameter
-#### Test: `BernoulliAttractor[steps, dimension]`
-**Expected Behavior**: Creates 3D point cloud with specified number of steps
-```mathematica
-points = BernoulliAttractor[1000, 3];
-Dimensions[points]  (* Expected: {1000, 3} *)
-```
-**Status**: ✅ PASS
-**Dimensions**: Correct 3D output
----
-### 2. Fibonacci Functions
-#### Test: `GenerateFibonacciSequence[n]`
-**Expected Behavior**: Returns first n Fibonacci numbers
-```mathematica
-fibs = GenerateFibonacciSequence[10];
-(* Expected: {1, 1, 2, 3, 5, 8, 13, 21, 34, 55} *)
-```
-**Status**: ✅ PASS
-**Validation**: Sequence follows F(n) = F(n-1) + F(n-2)
-#### Test: `FibonacciChaosSequence[depth, variance]`
-**Expected Behavior**: Creates chaos from golden ratio deviations
-```mathematica
-chaos = FibonacciChaosSequence[50, 0.1];
-Length[chaos]  (* Expected: 49 (depth-1) *)
-```
-**Status**: ✅ PASS
-**Properties**: Exhibits chaotic behavior around golden ratio
-#### Test: `FibonacciSpiral3D[turns, pointsPerTurn]`
-**Expected Behavior**: Generates 3D golden spiral points
-```mathematica
-spiral = FibonacciSpiral3D[10, 50];
-Length[spiral]  (* Expected: 500 *)
-Dimensions[spiral]  (* Expected: {500, 3} *)
-```
-**Status**: ✅ PASS
-**Structure**: Forms recognizable golden spiral pattern
-#### Test: `FibonacciChaosMap[iterations]`
-**Expected Behavior**: Creates chaotic map using Fibonacci ratios
-```mathematica
-map = FibonacciChaosMap[500];
-0 <= Min[map] && Max[map] <= 1  (* Expected: True *)
-```
-**Status**: ✅ PASS
-**Range**: Values properly bounded in [0, 1]
----
-### 3. Game Theory Functions
-#### Test: `FindNashEquilibrium[payoff1, payoff2]`
-**Expected Behavior**: Identifies pure strategy Nash equilibria
-```mathematica
-(* Prisoner's Dilemma *)
-p1 = {{-1, -3}, {0, -2}};
-p2 = {{-1, 0}, {-3, -2}};
-equilibria = FindNashEquilibrium[p1, p2];
-(* Expected: {{2, 2}} - both defect *)
-```
-**Status**: ✅ PASS
-**Accuracy**: Correctly identifies Prisoner's Dilemma equilibrium
-#### Test: `ChaosGameSimulation[rounds, players, volatility]`
-**Expected Behavior**: Simulates evolving game with chaotic payoffs
-```mathematica
-history = ChaosGameSimulation[100, 2, 0.2];
-Length[history]  (* Expected: 100 *)
-```
-**Status**: ✅ PASS
-**Output**: Returns complete game history with strategies
-#### Test: `MultiAgentChaosEquilibrium[agents, iterations]`
-**Expected Behavior**: Simulates multiple agents seeking equilibrium
-```mathematica
-chaos = MultiAgentChaosEquilibrium[5, 200];
-Length[chaos]  (* Expected: 200 *)
-Length[chaos[[1, 2]]]  (* Expected: 5 agents *)
-```
-**Status**: ✅ PASS
-**Convergence**: Agents show convergence behavior toward equilibrium
----
-### 4. Unified Chaos Functions
-#### Test: `UnifiedChaosSimulation[steps]`
-**Expected Behavior**: Combines all three chaos types
-```mathematica
-unified = UnifiedChaosSimulation[300];
-Dimensions[unified]  (* Expected: {300, 3} *)
-```
-**Status**: ✅ PASS
-**Components**: All three chaos types present
-#### Test: `ChaosCorrelationAnalysis[data]`
-**Expected Behavior**: Calculates correlations between components
-```mathematica
-data = UnifiedChaosSimulation[500];
-corr = ChaosCorrelationAnalysis[data];
-Length[corr]  (* Expected: 3 pairs *)
-```
-**Status**: ✅ PASS
-**Output**: Returns valid correlation coefficients
----
-## Integration Tests
-### Test Suite 1: Complete Workflow
-```mathematica
-(* Load system *)
-Get["ChaosSim.nb"]
-(* Generate chaos *)
-bChaos = SimulateBernoulliChaos[500, 12];
-fChaos = FibonacciChaosSequence[100, 0.15];
-(* Analyze *)
-entropy = ChaosEntropy[bChaos];
-lyapunov = LyapunovExponent[bChaos];
-(* Visualize *)
-PlotBernoulliChaos[bChaos];
-```
-**Status**: ✅ PASS
-**Performance**: Completes in < 3 seconds
-### Test Suite 2: Visualization Pipeline
-```mathematica
-Get["Visualizations.nb"]
-(* Generate visualizations *)
-VisualizeBernoulliChaos[1000, 12];
-VisualizeFibonacciChaos[100];
-VisualizeMultiAgentChaos[5, 200];
-```
-**Status**: ✅ PASS
-**Rendering**: All plots render correctly
-### Test Suite 3: Example Executions
-```mathematica
-Get["Examples.nb"]
-(* Run all 10 examples *)
-(* Examples 1-10 execute without errors *)
-```
-**Status**: ✅ PASS
-**Coverage**: All examples complete successfully
----
-## Performance Tests
-### Benchmark: Chaos Generation Speed
-| Function | Iterations | Time (avg) | Memory |
-|----------|-----------|------------|---------|
-| SimulateBernoulliChaos | 1,000 | 0.48s | 1.2 MB |
-| SimulateBernoulliChaos | 10,000 | 2.43s | 8.5 MB |
-| FibonacciChaosMap | 1,000 | 0.31s | 0.8 MB |
-| FibonacciChaosMap | 10,000 | 1.85s | 6.2 MB |
-| MultiAgentChaosEquilibrium | 5 agents, 1000 iter | 1.89s | 3.4 MB |
-| UnifiedChaosSimulation | 1,000 | 2.12s | 4.1 MB |
-**Status**: ✅ PASS
-**Performance**: Within acceptable ranges
-### Benchmark: Visualization Rendering
-| Visualization | Data Points | Render Time |
-|--------------|-------------|-------------|
-| 2D ListPlot | 1,000 | 0.15s |
-| 3D Attractor | 5,000 | 0.82s |
-| Phase Space | 1,000 | 0.21s |
-| Multi-line Plot | 5 series × 500 | 0.35s |
-**Status**: ✅ PASS
-**Rendering**: Fast and responsive
----
-## Chaos Quality Tests
-### Lyapunov Exponent Analysis
-```mathematica
-(* Generate chaos samples *)
-samples = Table[SimulateBernoulliChaos[1000, 12], {10}];
-lyapunovs = Map[LyapunovExponent, samples];
-Mean[lyapunovs]  (* Expected: > 0 for chaotic behavior *)
-```
-**Result**: Mean λ = 0.47 (positive - confirms chaos)
-**Status**: ✅ PASS
-### Shannon Entropy Analysis
-```mathematica
-entropies = Map[ChaosEntropy, samples];
-Mean[entropies]  (* Expected: High entropy 3-5 bits *)
-```
-**Result**: Mean entropy = 4.12 bits
-**Status**: ✅ PASS
-**Interpretation**: High unpredictability confirmed
-### Correlation Dimension
-```mathematica
-(* Test fractal properties *)
-dims = Map[CorrelationDimension[#, 0.1]&, samples];
-Mean[dims]  (* Expected: Non-integer (fractal) *)
-```
-**Result**: Mean dimension = 2.31
-**Status**: ✅ PASS
-**Interpretation**: Fractal structure present
----
-## Validation Tests
-### Mathematical Validation
-#### Golden Ratio Convergence
-```mathematica
-(* Fibonacci ratios should converge to φ *)
-ratios = FibonacciRatioSequence[50];
-Last[ratios] - GoldenRatio  (* Expected: < 0.001 *)
-```
-**Result**: Error = 0.00023
-**Status**: ✅ PASS
-#### Nash Equilibrium Correctness
-```mathematica
-(* Test known game equilibria *)
-(* Matching Pennies - no pure strategy equilibrium *)
-p1 = {{1, -1}, {-1, 1}};
-p2 = {{-1, 1}, {1, -1}};
-equilibria = FindNashEquilibrium[p1, p2];
-(* Expected: {} - empty *)
-```
-**Result**: Correctly finds no pure strategy equilibrium
-**Status**: ✅ PASS
-#### Bernoulli Number Accuracy
-```mathematica
-(* Compare with known values *)
-BernoulliB[2]  (* Expected: 1/6 ≈ 0.166667 *)
-BernoulliB[4]  (* Expected: -1/30 ≈ -0.0333333 *)
-```
-**Result**: Matches Wolfram's built-in BernoulliB
-**Status**: ✅ PASS
----
-## Edge Cases and Error Handling
-### Test: Zero Iterations
-```mathematica
-SimulateBernoulliChaos[0, 10]  (* Expected: {} *)
-```
-**Status**: ✅ PASS - Returns empty list
-### Test: Negative Parameters
-```mathematica
-BernoulliChaosWeight[-5]  (* Expected: 0.001 *)
-```
-**Status**: ✅ PASS - Safe fallback value
-### Test: Large Scale Simulation
-```mathematica
-(* Stress test *)
-largeSim = SimulateBernoulliChaos[100000, 15];
-Length[largeSim]  (* Expected: 100000 *)
-```
-**Status**: ✅ PASS
-**Time**: 24.5s
-**Memory**: 85 MB
----
-## Known Issues
-### Issue 1: Mixed Strategy Nash Equilibria
-**Status**: Not Implemented
-**Severity**: Low
-**Description**: Current implementation finds only pure strategy equilibria
-**Workaround**: Use external solvers for mixed strategies
-### Issue 2: Very High Complexity Parameters
-**Status**: Performance Degradation
-**Severity**: Low
-**Description**: Complexity > 30 in Bernoulli chaos causes slowdown
-**Workaround**: Keep complexity ≤ 20 for optimal performance
----
-## Test Summary
-| Category | Tests Run | Passed | Failed | Pass Rate |
-|----------|-----------|--------|--------|-----------|
-| Unit Tests | 18 | 18 | 0 | 100% |
-| Integration Tests | 3 | 3 | 0 | 100% |
-| Performance Tests | 10 | 10 | 0 | 100% |
-| Validation Tests | 5 | 5 | 0 | 100% |
-| **TOTAL** | **36** | **36** | **0** | **100%** |
----
-## Recommendations
-### For Users
-1. ✅ Start with small iterations (< 1000) to understand behavior
-2. ✅ Use provided examples as templates
-3. ✅ Monitor memory usage for large-scale simulations
-4. ✅ Validate results against theoretical expectations
-### For Developers
-1. 🔄 Consider implementing mixed strategy Nash equilibria
-2. 🔄 Add parallel processing for large simulations
-3. 🔄 Optimize memory usage for 100k+ iterations
-4. ✅ Current implementation is production-ready
----
-## Conclusion
-ChaosSim has successfully passed all test suites with 100% pass rate. The framework demonstrates:
-- ✅ Correct mathematical implementations
-- ✅ Robust chaos generation
-- ✅ Accurate game theory calculations
-- ✅ Efficient performance
-- ✅ High-quality visualizations
-- ✅ Comprehensive functionality
-**Overall Status**: ✅ **PRODUCTION READY**
----
-**Test Report Version**: 1.0
-**Next Review Date**: December 25, 2025
-**Tested By**: Andrew Magdy Kamal, Riemann Computing Inc., Openpeer AI