Visualizations.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* Visualizations.nb - ChaosSim Visualization Suite *)
(* Advanced plotting and visualization for chaotic systems *)

(* ::Title:: *)
(*ChaosSim Visualizations*)


(* ::Section:: *)
(*Setup and Initialization*)


(* Load main ChaosSim functions *)
Get[FileNameJoin[{NotebookDirectory[], "ChaosSim.nb"}]]

Print["Visualization suite initialized."]


(* ::Section:: *)
(*Bernoulli Number Chaos Visualizations*)


(* ::Subsection:: *)
(*Time Series Plots*)


VisualizeBernoulliChaos[iterations_Integer: 1000, complexity_Integer: 12] := Module[
  {data, plot1, plot2, plot3},
  
  data = SimulateBernoulliChaos[iterations, complexity];
  
  (* Time series plot *)
  plot1 = ListPlot[data,
    PlotStyle -> {Blue, PointSize[Small]},
    PlotLabel -> Style["Bernoulli Chaos Time Series", Bold, 16],
    AxesLabel -> {Style["Iteration", 14], Style["State Value", 14]},
    ImageSize -> Large,
    GridLines -> Automatic,
    GridLinesStyle -> LightGray
  ];
  
  (* Phase space plot *)
  plot2 = ListPlot[
    Partition[data, 2, 1],
    PlotStyle -> {Red, PointSize[Tiny]},
    PlotLabel -> Style["Bernoulli Phase Space", Bold, 16],
    AxesLabel -> {Style["x(t)", 14], Style["x(t+1)", 14]},
    ImageSize -> Large,
    AspectRatio -> 1
  ];
  
  (* Histogram *)
  plot3 = Histogram[data,
    PlotLabel -> Style["Bernoulli Chaos Distribution", Bold, 16],
    AxesLabel -> {Style["State Value", 14], Style["Frequency", 14]},
    ImageSize -> Large,
    ChartStyle -> Blue
  ];
  
  GraphicsGrid[{{plot1}, {plot2}, {plot3}}, ImageSize -> Full]
]


(* 3D Bernoulli Attractor *)
VisualizeBernoulliAttractor3D[steps_Integer: 2000] := Module[
  {points, plot},
  
  points = BernoulliAttractor[steps, 3];
  
  plot = ListPointPlot3D[points,
    PlotStyle -> Directive[PointSize[Tiny], ColorFunction -> "Rainbow"],
    BoxRatios -> {1, 1, 1},
    ImageSize -> Large,
    PlotLabel -> Style["Bernoulli 3D Chaos Attractor", Bold, 16],
    AxesLabel -> {Style["X", 14], Style["Y", 14], Style["Z", 14]},
    ViewPoint -> {1.3, -2.4, 2.0},
    Background -> Black,
    Boxed -> True
  ];
  
  plot
]


(* Animated Bernoulli chaos evolution *)
AnimateBernoulliChaos[maxIterations_Integer: 500] := Animate[
  Module[{data},
    data = SimulateBernoulliChaos[n, 12];
    ListPlot[data,
      PlotStyle -> {Blue, PointSize[Medium]},
      PlotLabel -> Style[StringTemplate["Bernoulli Chaos: `` iterations"][n], Bold, 14],
      PlotRange -> {{0, maxIterations}, {0, 1}},
      ImageSize -> Large,
      AspectRatio -> 0.6
    ]
  ],
  {n, 10, maxIterations, 10}
]


(* ::Section:: *)
(*Fibonacci Chaos Visualizations*)


(* ::Subsection:: *)
(*Golden Ratio and Spiral Patterns*)


VisualizeFibonacciChaos[depth_Integer: 100] := Module[
  {data, spiralData, plot1, plot2, plot3},
  
  data = FibonacciChaosSequence[depth, 0.15];
  spiralData = FibonacciSpiral3D[15, 80];
  
  (* Chaos sequence plot *)
  plot1 = ListLinePlot[data,
    PlotStyle -> {Orange, Thick},
    PlotLabel -> Style["Fibonacci Chaos Sequence", Bold, 16],
    AxesLabel -> {Style["Index", 14], Style["Value", 14]},
    ImageSize -> Large,
    Filling -> Axis,
    FillingStyle -> Opacity[0.3, Orange]
  ];
  
  (* Golden ratio convergence *)
  plot2 = ListLinePlot[
    Table[GoldenRatioApproximation[n], {n, 2, depth}],
    PlotStyle -> {Green, Thick},
    PlotLabel -> Style["Golden Ratio Convergence", Bold, 16],
    AxesLabel -> {Style["Fibonacci Index", 14], Style["Ratio", 14]},
    GridLines -> {{}, {GoldenRatio}},
    GridLinesStyle -> Directive[Red, Dashed],
    ImageSize -> Large
  ];
  
  (* 3D Spiral *)
  plot3 = ListPointPlot3D[spiralData,
    PlotStyle -> Directive[PointSize[Small]],
    ColorFunction -> Function[{x, y, z}, ColorData["SunsetColors"][z]],
    BoxRatios -> {1, 1, 0.5},
    PlotLabel -> Style["Fibonacci Golden Spiral", Bold, 16],
    ImageSize -> Large,
    Background -> GrayLevel[0.95]
  ];
  
  GraphicsGrid[{{plot1, plot2}, {plot3, ""}}, ImageSize -> Full]
]


(* Fibonacci chaos map bifurcation *)
FibonacciBifurcationDiagram[iterations_Integer: 200, samples_Integer: 50] := Module[
  {data, points},
  
  points = Flatten[
    Table[
      Module[{seq},
        seq = FibonacciChaosMap[iterations];
        Table[{i/samples, seq[[j]]}, {j, iterations - 100, iterations}]
      ],
      {i, 1, samples}
    ],
    1
  ];
  
  ListPlot[points,
    PlotStyle -> {Black, PointSize[Tiny]},
    PlotLabel -> Style["Fibonacci Chaos Bifurcation", Bold, 16],
    AxesLabel -> {Style["Parameter", 14], Style["State", 14]},
    ImageSize -> Large,
    AspectRatio -> 0.7
  ]
]


(* ::Section:: *)
(*Nash Equilibrium Visualizations*)


(* ::Subsection:: *)
(*Game Theory and Multi-Agent Systems*)


VisualizeNashEquilibrium[payoff1_List, payoff2_List] := Module[
  {equilibria, heatmap1, heatmap2, combined},
  
  equilibria = FindNashEquilibrium[payoff1, payoff2];
  
  (* Heatmap for player 1 payoffs *)
  heatmap1 = ArrayPlot[payoff1,
    ColorFunction -> "TemperatureMap",
    PlotLabel -> Style["Player 1 Payoff Matrix", Bold, 14],
    FrameLabel -> {Style["Player 2 Strategy", 12], Style["Player 1 Strategy", 12]},
    ImageSize -> Medium,
    PlotLegends -> Automatic
  ];
  
  (* Heatmap for player 2 payoffs *)
  heatmap2 = ArrayPlot[payoff2,
    ColorFunction -> "TemperatureMap",
    PlotLabel -> Style["Player 2 Payoff Matrix", Bold, 14],
    FrameLabel -> {Style["Player 2 Strategy", 12], Style["Player 1 Strategy", 12]},
    ImageSize -> Medium,
    PlotLegends -> Automatic
  ];
  
  (* Display equilibria *)
  Print[Style["Nash Equilibria Found: ", Bold], equilibria];
  
  GraphicsRow[{heatmap1, heatmap2}, ImageSize -> Full]
]


(* Chaos game simulation visualization *)
VisualizeChaosGame[rounds_Integer: 150] := Module[
  {history, strategies, equilibriaCount, plot1, plot2},
  
  history = ChaosGameSimulation[rounds, 2, 0.25];
  
  (* Extract strategy evolution *)
  strategies = history[[All, 2]];
  equilibriaCount = Length /@ history[[All, 3]];
  
  (* Strategy evolution plot *)
  plot1 = ListLinePlot[
    {strategies[[All, 1]], strategies[[All, 2]]},
    PlotStyle -> {{Blue, Thick}, {Red, Thick}},
    PlotLabel -> Style["Strategy Evolution in Chaos Game", Bold, 16],
    AxesLabel -> {Style["Round", 14], Style["Strategy", 14]},
    PlotLegends -> {"Player 1", "Player 2"},
    ImageSize -> Large
  ];
  
  (* Equilibria count over time *)
  plot2 = ListLinePlot[equilibriaCount,
    PlotStyle -> {Purple, Thick},
    PlotLabel -> Style["Number of Nash Equilibria Over Time", Bold, 16],
    AxesLabel -> {Style["Round", 14], Style["Equilibria Count", 14]},
    Filling -> Axis,
    FillingStyle -> Opacity[0.3, Purple],
    ImageSize -> Large
  ];
  
  GraphicsColumn[{plot1, plot2}, ImageSize -> Full]
]


(* Multi-agent chaos equilibrium *)
VisualizeMultiAgentChaos[agents_Integer: 6, iterations_Integer: 150] := Module[
  {chaos, stateEvolution, fitnessEvolution, plot1, plot2},
  
  chaos = MultiAgentChaosEquilibrium[agents, iterations];
  
  (* Extract state and fitness data *)
  stateEvolution = chaos[[All, 2]];
  fitnessEvolution = chaos[[All, 3]];
  
  (* Agent state evolution *)
  plot1 = ListLinePlot[
    Table[stateEvolution[[All, i]], {i, 1, agents}],
    PlotStyle -> Table[ColorData[97][i], {i, 1, agents}],
    PlotLabel -> Style["Multi-Agent State Evolution", Bold, 16],
    AxesLabel -> {Style["Iteration", 14], Style["Agent State", 14]},
    PlotLegends -> Table[StringTemplate["Agent ``"][i], {i, 1, agents}],
    ImageSize -> Large
  ];
  
  (* Fitness landscape *)
  plot2 = ListPlot3D[
    Table[{chaos[[i, 1]], j, stateEvolution[[i, j]]}, 
      {i, 1, Min[100, iterations]}, {j, 1, agents}],
    ColorFunction -> "Rainbow",
    PlotLabel -> Style["Agent Fitness Landscape", Bold, 16],
    AxesLabel -> {Style["Iteration", 12], Style["Agent", 12], Style["State", 12]},
    ImageSize -> Large,
    Mesh -> None
  ];
  
  GraphicsColumn[{plot1, plot2}, ImageSize -> Full]
]


(* ::Section:: *)
(*Unified Chaos Visualization*)


(* ::Subsection:: *)
(*Combined System Analysis*)


VisualizeUnifiedChaos[steps_Integer: 500] := Module[
  {data, correlations, plot1, plot2, plot3},
  
  data = UnifiedChaosSimulation[steps];
  correlations = ChaosCorrelationAnalysis[data];
  
  (* 3D phase space *)
  plot1 = ListPointPlot3D[data,
    PlotStyle -> Directive[PointSize[Small]],
    ColorFunction -> Function[{x, y, z}, ColorData["Rainbow"][z]],
    BoxRatios -> {1, 1, 1},
    PlotLabel -> Style["Unified Chaos Phase Space", Bold, 16],
    AxesLabel -> {Style["Bernoulli", 12], Style["Fibonacci", 12], Style["Nash", 12]},
    ImageSize -> Large,
    ViewPoint -> {1.5, -2.0, 1.5}
  ];
  
  (* Component time series *)
  plot2 = ListLinePlot[
    {data[[All, 1]], data[[All, 2]], data[[All, 3]]},
    PlotStyle -> {{Blue, Thick}, {Orange, Thick}, {Green, Thick}},
    PlotLabel -> Style["Chaos Components Over Time", Bold, 16],
    AxesLabel -> {Style["Step", 14], Style["Value", 14]},
    PlotLegends -> {"Bernoulli", "Fibonacci", "Nash"},
    ImageSize -> Large
  ];
  
  (* Correlation matrix *)
  plot3 = BarChart[correlations[[All, 2]],
    ChartLabels -> correlations[[All, 1]],
    PlotLabel -> Style["Component Correlations", Bold, 16],
    AxesLabel -> {None, Style["Correlation", 14]},
    ChartStyle -> "Pastel",
    ImageSize -> Large
  ];
  
  Print[Style["Correlation Analysis:", Bold]];
  Print[Grid[correlations, Frame -> All]];
  
  GraphicsGrid[{{plot1}, {plot2}, {plot3}}, ImageSize -> Full]
]


(* Interactive chaos explorer *)
ManipulateChaosParameters[] := Manipulate[
  Module[{data},
    data = SimulateBernoulliChaos[iterations, complexity];
    ListPlot[data,
      PlotStyle -> {colorScheme, PointSize[pointSize]},
      PlotLabel -> Style["Interactive Chaos Explorer", Bold, 16],
      ImageSize -> Large,
      AspectRatio -> 0.7
    ]
  ],
  {{iterations, 300, "Iterations"}, 50, 1000, 50},
  {{complexity, 10, "Complexity"}, 2, 20, 1},
  {{pointSize, 0.005, "Point Size"}, 0.001, 0.02, 0.001},
  {{colorScheme, Blue, "Color"}, {Blue, Red, Green, Orange, Purple}}
]


(* ::Section:: *)
(*Comparative Analysis Visualizations*)


CompareChaosTypes[iterations_Integer: 500] := Module[
  {bernoulli, fibonacci, nash, plot},
  
  bernoulli = SimulateBernoulliChaos[iterations, 12];
  fibonacci = FibonacciChaosMap[iterations];
  nash = MultiAgentChaosEquilibrium[5, iterations][[All, 2, 1]];
  
  plot = ListLinePlot[
    {bernoulli, fibonacci, nash},
    PlotStyle -> {
      {Blue, Thick, Opacity[0.7]},
      {Orange, Thick, Opacity[0.7]},
      {Green, Thick, Opacity[0.7]}
    },
    PlotLabel -> Style["Chaos Type Comparison", Bold, 18],
    AxesLabel -> {Style["Iteration", 14], Style["State Value", 14]},
    PlotLegends -> Placed[
      {Style["Bernoulli", 12], Style["Fibonacci", 12], Style["Nash Equilibrium", 12]},
      Right
    ],
    ImageSize -> Large,
    GridLines -> Automatic,
    GridLinesStyle -> LightGray
  ];
  
  plot
]


(* ::Section:: *)
(*Export and Reporting*)


ExportVisualization[graphic_, filename_String] := Module[{path},
  path = FileNameJoin[{NotebookDirectory[], filename}];
  Export[path, graphic, "PNG", ImageResolution -> 300];
  Print[Style[StringTemplate["Exported to: ``"][path], Bold, Green]];
]


GenerateFullReport[steps_Integer: 500] := Module[{},
  Print[Style["\n=== ChaosSim Full Visualization Report ===\n", Bold, 20, Blue]];
  
  Print[Style["1. Bernoulli Chaos Analysis:", Bold, 16]];
  VisualizeBernoulliChaos[steps, 12];
  
  Print[Style["\n2. Fibonacci Chaos Patterns:", Bold, 16]];
  VisualizeFibonacciChaos[100];
  
  Print[Style["\n3. Multi-Agent Nash Equilibrium:", Bold, 16]];
  VisualizeMultiAgentChaos[5, steps];
  
  Print[Style["\n4. Unified Chaos System:", Bold, 16]];
  VisualizeUnifiedChaos[steps];
  
  Print[Style["\n=== Report Complete ===\n", Bold, 20, Green]];
]


Print["Visualization functions loaded. Use GenerateFullReport[] to create complete analysis."]