Generate an explanatory visualization of the following algorithm. Strive to create an interactive visualization that illustrates and demonstrates how the algorithm functions. Use animations, transitions and strive for an engaging as well as demonstrative demo:
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| <html lang="en"> | |
| <head> | |
| <meta charset="UTF-8"> | |
| <meta name="viewport" content="width=device-width, initial-scale=1.0"> | |
| <title>SRC Algorithm Visualizer</title> | |
| <script src="https://cdn.tailwindcss.com"></script> | |
| <script src="https://unpkg.com/feather-icons"></script> | |
| <script src="https://cdn.jsdelivr.net/npm/feather-icons/dist/feather.min.js"></script> | |
| <script src="https://cdnjs.cloudflare.com/ajax/libs/animejs/3.2.1/anime.min.js"></script> | |
| <style> | |
| body { | |
| background: linear-gradient(135deg, #0f172a, #1e293b); | |
| color: #f1f5f9; | |
| font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; | |
| } | |
| .hilbert-space { | |
| background: rgba(15, 23, 42, 0.7); | |
| border: 1px solid #334155; | |
| box-shadow: 0 0 20px rgba(99, 102, 241, 0.2); | |
| } | |
| .prime-state { | |
| transition: all 0.5s ease; | |
| } | |
| .active-state { | |
| box-shadow: 0 0 15px #818cf8; | |
| transform: scale(1.1); | |
| } | |
| .resonance-path { | |
| stroke-dasharray: 1000; | |
| stroke-dashoffset: 1000; | |
| } | |
| .entropy-graph { | |
| background: rgba(30, 41, 59, 0.8); | |
| } | |
| .control-panel { | |
| background: rgba(15, 23, 42, 0.9); | |
| backdrop-filter: blur(10px); | |
| } | |
| .algorithm-step { | |
| transition: all 0.3s ease; | |
| } | |
| .current-step { | |
| background: rgba(99, 102, 241, 0.2); | |
| border-left: 3px solid #818cf8; | |
| } | |
| </style> | |
| </head> | |
| <body class="min-h-screen"> | |
| <!-- Header --> | |
| <header class="py-6 px-4 sm:px-6 lg:px-8 border-b border-slate-700"> | |
| <div class="max-w-7xl mx-auto flex flex-col md:flex-row justify-between items-center"> | |
| <div> | |
| <h1 class="text-3xl font-bold text-indigo-300">Symbolic Resonance Collapse</h1> | |
| <p class="text-slate-400 mt-1">Visualization of P = NP Proof</p> | |
| </div> | |
| <div class="mt-4 md:mt-0 flex items-center space-x-4"> | |
| <div class="bg-indigo-900/30 px-4 py-2 rounded-lg"> | |
| <span class="text-indigo-300 font-mono">P = NP</span> | |
| </div> | |
| <div class="text-sm text-slate-400"> | |
| Sebastian Schepis, 2025 | |
| </div> | |
| </div> | |
| </div> | |
| </header> | |
| <!-- Main Content --> | |
| <main class="max-w-7xl mx-auto py-8 px-4 sm:px-6 lg:px-8"> | |
| <div class="grid grid-cols-1 lg:grid-cols-3 gap-8"> | |
| <!-- Visualization Panel --> | |
| <div class="lg:col-span-2"> | |
| <div class="hilbert-space rounded-xl p-6"> | |
| <div class="flex justify-between items-center mb-6"> | |
| <h2 class="text-xl font-semibold text-indigo-200">Prime-Encoded Hilbert Space</h2> | |
| <div class="flex space-x-2"> | |
| <button id="resetBtn" class="px-3 py-1 bg-slate-700 hover:bg-slate-600 rounded-lg text-sm"> | |
| Reset | |
| </button> | |
| <button id="startBtn" class="px-3 py-1 bg-indigo-600 hover:bg-indigo-500 rounded-lg text-sm"> | |
| Start Simulation | |
| </button> | |
| </div> | |
| </div> | |
| <!-- Hilbert Space Visualization --> | |
| <div class="relative h-96 rounded-lg border border-slate-600 bg-slate-900/50 overflow-hidden"> | |
| <div id="hilbertCanvas" class="w-full h-full relative"> | |
| <!-- Prime states will be dynamically added here --> | |
| </div> | |
| <!-- Resonance path --> | |
| <svg class="absolute top-0 left-0 w-full h-full pointer-events-none"> | |
| <path id="resonancePath" class="resonance-path" fill="none" stroke="#818cf8" stroke-width="2"></path> | |
| </svg> | |
| </div> | |
| <!-- System Status --> | |
| <div class="mt-6 grid grid-cols-1 md:grid-cols-3 gap-4"> | |
| <div class="bg-slate-800/50 p-4 rounded-lg"> | |
| <div class="text-sm text-slate-400">Current State</div> | |
| <div id="currentState" class="text-lg font-mono text-indigo-300">|Ψ₀⟩</div> | |
| </div> | |
| <div class="bg-slate-800/50 p-4 rounded-lg"> | |
| <div class="text-sm text-slate-400">Entropy</div> | |
| <div id="entropyValue" class="text-lg font-mono text-green-300">S₀</div> | |
| </div> | |
| <div class="bg-slate-800/50 p-4 rounded-lg"> | |
| <div class="text-sm text-slate-400">Time Step</div> | |
| <div id="timeStep" class="text-lg font-mono text-yellow-300">t = 0</div> | |
| </div> | |
| </div> | |
| </div> | |
| <!-- Entropy Graph --> | |
| <div class="hilbert-space rounded-xl p-6 mt-8"> | |
| <h2 class="text-xl font-semibold text-indigo-200 mb-4">Entropy Convergence</h2> | |
| <div class="entropy-graph rounded-lg p-4 h-64"> | |
| <canvas id="entropyChart" width="800" height="200"></canvas> | |
| </div> | |
| </div> | |
| </div> | |
| <!-- Control Panel --> | |
| <div class="control-panel rounded-xl p-6 h-fit"> | |
| <h2 class="text-xl font-semibold text-indigo-200 mb-4">Algorithm Steps</h2> | |
| <div class="space-y-4"> | |
| <div class="algorithm-step p-4 rounded-lg current-step" data-step="0"> | |
| <div class="flex items-start"> | |
| <div class="flex-shrink-0 h-6 w-6 rounded-full bg-indigo-500 flex items-center justify-center text-xs font-bold">1</div> | |
| <div class="ml-3"> | |
| <h3 class="font-medium text-white">Prime-Encoded Hilbert Space</h3> | |
| <p class="mt-1 text-sm text-slate-400">Define HP over prime-number eigenstates |p⟩ for Boolean variables</p> | |
| </div> | |
| </div> | |
| </div> | |
| <div class="algorithm-step p-4 rounded-lg" data-step="1"> | |
| <div class="flex items-start"> | |
| <div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">2</div> | |
| <div class="ml-3"> | |
| <h3 class="font-medium text-white">SAT Representation</h3> | |
| <p class="mt-1 text-sm text-slate-400">Encode SAT instance Φ into symbolic state |Ψ₀⟩ ∈ H⊗nP</p> | |
| </div> | |
| </div> | |
| </div> | |
| <div class="algorithm-step p-4 rounded-lg" data-step="2"> | |
| <div class="flex items-start"> | |
| <div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">3</div> | |
| <div class="ml-3"> | |
| <h3 class="font-medium text-white">Symbolic Operators</h3> | |
| <p class="mt-1 text-sm text-slate-400">Define Hamiltonian ĤΦ and Resonance Operator R̂</p> | |
| </div> | |
| </div> | |
| </div> | |
| <div class="algorithm-step p-4 rounded-lg" data-step="3"> | |
| <div class="flex items-start"> | |
| <div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">4</div> | |
| <div class="ml-3"> | |
| <h3 class="font-medium text-white">System Evolution</h3> | |
| <p class="mt-1 text-sm text-slate-400">Evolve |Ψ(t)⟩ using symbolic Schrödinger equation</p> | |
| </div> | |
| </div> | |
| </div> | |
| <div class="algorithm-step p-4 rounded-lg" data-step="4"> | |
| <div class="flex items-start"> | |
| <div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">5</div> | |
| <div class="ml-3"> | |
| <h3 class="font-medium text-white">Entropy Minimization</h3> | |
| <p class="mt-1 text-sm text-slate-400">S(t) decreases as system approaches stable state</p> | |
| </div> | |
| </div> | |
| </div> | |
| <div class="algorithm-step p-4 rounded-lg" data-step="5"> | |
| <div class="flex items-start"> | |
| <div class="flex-shrink-0 h-6 w-6 rounded-full bg-slate-700 flex items-center justify-center text-xs font-bold">6</div> | |
| <div class="ml-3"> | |
| <h3 class="font-medium text-white">Polynomial Convergence</h3> | |
| <p class="mt-1 text-sm text-slate-400">System reaches |Ψ*⟩ in O(nᵏ) symbolic time</p> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| <!-- Parameters --> | |
| <div class="mt-8"> | |
| <h3 class="font-medium text-white mb-3">Simulation Parameters</h3> | |
| <div class="space-y-4"> | |
| <div> | |
| <label class="block text-sm text-slate-400 mb-1">Variables (n)</label> | |
| <input type="range" min="3" max="10" value="5" id="varCount" class="w-full"> | |
| <div class="text-right text-sm text-slate-400" id="varCountValue">5</div> | |
| </div> | |
| <div> | |
| <label class="block text-sm text-slate-400 mb-1">Clauses (m)</label> | |
| <input type="range" min="3" max="15" value="7" id="clauseCount" class="w-full"> | |
| <div class="text-right text-sm text-slate-400" id="clauseCountValue">7</div> | |
| </div> | |
| <div> | |
| <label class="block text-sm text-slate-400 mb-1">Decay Constant (λ)</label> | |
| <input type="range" min="0.1" max="2" step="0.1" value="0.5" id="decayConstant" class="w-full"> | |
| <div class="text-right text-sm text-slate-400" id="decayValue">0.5</div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| </div> | |
| <!-- Explanation Section --> | |
| <div class="mt-12 hilbert-space rounded-xl p-8"> | |
| <h2 class="text-2xl font-bold text-indigo-200 mb-6">How Symbolic Resonance Collapse Works</h2> | |
| <div class="grid grid-cols-1 md:grid-cols-2 gap-8"> | |
| <div> | |
| <h3 class="text-lg font-semibold text-white mb-3">The Framework</h3> | |
| <p class="text-slate-300 mb-4"> | |
| The SRC framework redefines computation as an entropic resonance process in a quantum-inspired | |
| Hilbert space over prime-number eigenstates. Instead of combinatorial search, NP-complete problems | |
| converge to solution states through entropy-driven alignment. | |
| </p> | |
| <p class="text-slate-300"> | |
| SAT instances are modeled as symbolic wavefunctions undergoing entropy minimization, with clause | |
| interactions acting as quantum-like operators in a resonance field. | |
| </p> | |
| </div> | |
| <div> | |
| <h3 class="text-lg font-semibold text-white mb-3">Key Insights</h3> | |
| <ul class="space-y-2 text-slate-300"> | |
| <li class="flex items-start"> | |
| <i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i> | |
| <span>Computation as coherence alignment rather than enumeration</span> | |
| </li> | |
| <li class="flex items-start"> | |
| <i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i> | |
| <span>Polynomial convergence through symbolic gradient descent</span> | |
| </li> | |
| <li class="flex items-start"> | |
| <i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i> | |
| <span>Entropy minimization drives system to stable states</span> | |
| </li> | |
| <li class="flex items-start"> | |
| <i data-feather="check-circle" class="text-green-400 mt-1 mr-2 flex-shrink-0"></i> | |
| <span>No local minima for satisfiable instances</span> | |
| </li> | |
| </ul> | |
| </div> | |
| </div> | |
| </div> | |
| </main> | |
| <script> | |
| // Initialize Feather Icons | |
| feather.replace(); | |
| // DOM Elements | |
| const hilbertCanvas = document.getElementById('hilbertCanvas'); | |
| const entropyChart = document.getElementById('entropyChart').getContext('2d'); | |
| const currentStateEl = document.getElementById('currentState'); | |
| const entropyValueEl = document.getElementById('entropyValue'); | |
| const timeStepEl = document.getElementById('timeStep'); | |
| const startBtn = document.getElementById('startBtn'); | |
| const resetBtn = document.getElementById('resetBtn'); | |
| const varCount = document.getElementById('varCount'); | |
| const clauseCount = document.getElementById('clauseCount'); | |
| const decayConstant = document.getElementById('decayConstant'); | |
| const varCountValue = document.getElementById('varCountValue'); | |
| const clauseCountValue = document.getElementById('clauseCountValue'); | |
| const decayValue = document.getElementById('decayValue'); | |
| const algorithmSteps = document.querySelectorAll('.algorithm-step'); | |
| // Simulation state | |
| let simulationRunning = false; | |
| let currentTime = 0; | |
| let entropyData = []; | |
| let currentState = '|Ψ₀⟩'; | |
| let primeStates = []; | |
| let animationTimeline = null; | |
| // Update parameter displays | |
| varCount.addEventListener('input', () => { | |
| varCountValue.textContent = varCount.value; | |
| }); | |
| clauseCount.addEventListener('input', () => { | |
| clauseCountValue.textContent = clauseCount.value; | |
| }); | |
| decayConstant.addEventListener('input', () => { | |
| decayValue.textContent = decayConstant.value; | |
| }); | |
| // Initialize visualization | |
| function initVisualization() { | |
| hilbertCanvas.innerHTML = ''; | |
| primeStates = []; | |
| // Create prime-number eigenstates | |
| const primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]; | |
| const n = parseInt(varCount.value); | |
| for (let i = 0; i < n; i++) { | |
| const prime = primes[i]; | |
| const state = document.createElement('div'); | |
| state.className = 'prime-state absolute w-16 h-16 rounded-full flex items-center justify-center text-white font-bold border-2 border-indigo-400'; | |
| state.style.left = `${20 + (i % 3) * 30}%`; | |
| state.style.top = `${20 + Math.floor(i / 3) * 30}%`; | |
| state.style.backgroundColor = `rgba(${50 + i * 20}, ${60 + i * 15}, ${200 + i * 5}, 0.7)`; | |
| state.textContent = `|${prime}⟩`; | |
| state.dataset.prime = prime; | |
| state.dataset.index = i; | |
| hilbertCanvas.appendChild(state); | |
| primeStates.push(state); | |
| } | |
| // Reset state displays | |
| currentStateEl.textContent = '|Ψ₀⟩'; | |
| entropyValueEl.textContent = 'S₀'; | |
| timeStepEl.textContent = 't = 0'; | |
| entropyData = [{time: 0, entropy: 100}]; | |
| drawEntropyChart(); | |
| } | |
| // Draw entropy convergence chart | |
| function drawEntropyChart() { | |
| entropyChart.clearRect(0, 0, entropyChart.canvas.width, entropyChart.canvas.height); | |
| if (entropyData.length === 0) return; | |
| // Draw grid | |
| entropyChart.strokeStyle = '#334155'; | |
| entropyChart.lineWidth = 1; | |
| // Vertical grid lines | |
| for (let i = 0; i <= 10; i++) { | |
| const x = (i / 10) * entropyChart.canvas.width; | |
| entropyChart.beginPath(); | |
| entropyChart.moveTo(x, 0); | |
| entropyChart.lineTo(x, entropyChart.canvas.height); | |
| entropyChart.stroke(); | |
| } | |
| // Horizontal grid lines | |
| for (let i = 0; i <= 5; i++) { | |
| const y = (i / 5) * entropyChart.canvas.height; | |
| entropyChart.beginPath(); | |
| entropyChart.moveTo(0, y); | |
| entropyChart.lineTo(entropyChart.canvas.width, y); | |
| entropyChart.stroke(); | |
| } | |
| // Draw entropy curve | |
| entropyChart.strokeStyle = '#4ade80'; | |
| entropyChart.lineWidth = 3; | |
| entropyChart.beginPath(); | |
| for (let i = 0; i < entropyData.length; i++) { | |
| const x = (entropyData[i].time / 100) * entropyChart.canvas.width; | |
| const y = entropyChart.canvas.height - (entropyData[i].entropy / 100) * entropyChart.canvas.height; | |
| if (i === 0) { | |
| entropyChart.moveTo(x, y); | |
| } else { | |
| entropyChart.lineTo(x, y); | |
| } | |
| } | |
| entropyChart.stroke(); | |
| } | |
| // Animate the simulation | |
| function animateSimulation() { | |
| if (!simulationRunning) return; | |
| currentTime++; | |
| timeStepEl.textContent = `t = ${currentTime}`; | |
| // Update entropy | |
| const newEntropy = Math.max(0, 100 - currentTime * 5); | |
| entropyValueEl.textContent = `S(t) = ${newEntropy.toFixed(1)}`; | |
| entropyData.push({time: currentTime, entropy: newEntropy}); | |
| drawEntropyChart(); | |
| // Animate prime states | |
| primeStates.forEach((state, index) => { | |
| // Simulate phase changes | |
| const phase = (currentTime + index) % 4; | |
| const phases = ['0', 'π/2', 'π', '3π/2']; | |
| // Update visual state | |
| anime({ | |
| targets: state, | |
| scale: [1, 1.1, 1], | |
| backgroundColor: [ | |
| state.style.backgroundColor, | |
| `rgba(${100 + index * 15}, ${120 + index * 10}, ${220 + index * 5}, 0.9)`, | |
| state.style.backgroundColor | |
| ], | |
| duration: 1000, | |
| easing: 'easeInOutQuad' | |
| }); | |
| // Add active class temporarily | |
| state.classList.add('active-state'); | |
| setTimeout(() => { | |
| state.classList.remove('active-state'); | |
| }, 1000); | |
| }); | |
| // Update current state | |
| if (currentTime < 10) { | |
| currentStateEl.textContent = '|Ψ(t)⟩'; | |
| } else if (currentTime < 20) { | |
| currentStateEl.textContent = '|Ψ*⟩'; | |
| // Highlight final step | |
| algorithmSteps.forEach(step => step.classList.remove('current-step')); | |
| algorithmSteps[5].classList.add('current-step'); | |
| } | |
| // Update algorithm steps | |
| if (currentTime >= 5 && currentTime < 10) { | |
| algorithmSteps.forEach(step => step.classList.remove('current-step')); | |
| algorithmSteps[3].classList.add('current-step'); | |
| } else if (currentTime >= 10 && currentTime < 15) { | |
| algorithmSteps.forEach(step => step.classList.remove('current-step')); | |
| algorithmSteps[4].classList.add('current-step'); | |
| } | |
| // Continue animation or stop | |
| if (currentTime < 25) { | |
| setTimeout(animateSimulation, 800); | |
| } else { | |
| simulationRunning = false; | |
| startBtn.textContent = 'Restart Simulation'; | |
| } | |
| } | |
| // Event Listeners | |
| startBtn.addEventListener('click', () => { | |
| if (!simulationRunning) { | |
| simulationRunning = true; | |
| startBtn.textContent = 'Running...'; | |
| animateSimulation(); | |
| } | |
| }); | |
| resetBtn.addEventListener('click', () => { | |
| simulationRunning = false; | |
| currentTime = 0; | |
| startBtn.textContent = 'Start Simulation'; | |
| initVisualization(); | |
| // Reset algorithm steps | |
| algorithmSteps.forEach(step => step.classList.remove('current-step')); | |
| algorithmSteps[0].classList.add('current-step'); | |
| }); | |
| // Initialize on load | |
| window.addEventListener('load', () => { | |
| initVisualization(); | |
| // Animate introduction | |
| anime({ | |
| targets: '.prime-state', | |
| scale: [0, 1], | |
| opacity: [0, 1], | |
| delay: anime.stagger(200), | |
| duration: 1000, | |
| easing: 'easeOutElastic' | |
| }); | |
| }); | |
| </script> | |
| </body> | |
| </html> | |