Add real-time BPM detection and display to HUD and title

Implement real-time BPM (beats per minute) estimation in AudioAnalyzer by tracking beat intervals and smoothing the result. Display the current BPM in both the window title and the on-screen HUD. Update AudioFeatures to include a Bpm field. Adjust HUD layout to accommodate the new BPM information.

FractalVisualizer/Audio/AudioAnalyzer.cs

@@ -1,4 +1,5 @@
 using System;
+using System.Collections.Generic;
 using System.Diagnostics;
 using System.Numerics;
 using System.Threading;
@@ -32,6 +33,11 @@ public sealed class AudioAnalyzer : IDisposable
     private float _smoothedHigh;
     private float _smoothedBeat;
     private float _energyBaseline;
+    private float _smoothedBpm;
+    private float _lastBeatTimeSeconds = -10f;
+    private bool _beatGateOpen = true;
+    private readonly Queue<float> _beatIntervals = new();
+    private const int MaxBeatIntervals = 8;
 
     private Snapshot _latestSnapshot;
     private bool _disposed;
@@ -217,6 +223,31 @@ public sealed class AudioAnalyzer : IDisposable
         _smoothedHigh = Smooth(_smoothedHigh, highEnergy, 0.30f, 0.08f);
         _smoothedBeat = MathF.Max(beat, _smoothedBeat * 0.85f);
 
+        float now = (float)_clock.Elapsed.TotalSeconds;
+        bool beatHit = beat > 0.62f && _beatGateOpen;
+        if (beatHit)
+        {
+            float delta = now - _lastBeatTimeSeconds;
+            if (delta > 0.22f && delta < 2.0f)
+            {
+                _beatIntervals.Enqueue(delta);
+                while (_beatIntervals.Count > MaxBeatIntervals)
+                {
+                    _beatIntervals.Dequeue();
+                }
+            }
+
+            _lastBeatTimeSeconds = now;
+            _beatGateOpen = false;
+        }
+        else if (beat < 0.20f)
+        {
+            _beatGateOpen = true;
+        }
+
+        float bpmInstant = CalculateBpm();
+        _smoothedBpm = Smooth(_smoothedBpm, bpmInstant, 0.18f, 0.04f);
+
         AudioFeatures features = new()
         {
             Level = _smoothedLevel,
@@ -224,8 +255,9 @@ public sealed class AudioAnalyzer : IDisposable
             Mid = _smoothedMid,
             High = _smoothedHigh,
             Beat = _smoothedBeat,
+            Bpm = _smoothedBpm,
             Spectrum = spectrum,
-            TimeSeconds = (float)_clock.Elapsed.TotalSeconds
+            TimeSeconds = now
         };
 
         Volatile.Write(ref _latestSnapshot, new Snapshot(features));
@@ -264,6 +296,29 @@ public sealed class AudioAnalyzer : IDisposable
         return a + ((b - a) * t);
     }
 
+    private float CalculateBpm()
+    {
+        if (_beatIntervals.Count == 0)
+        {
+            return 0f;
+        }
+
+        float sum = 0f;
+        foreach (float interval in _beatIntervals)
+        {
+            sum += interval;
+        }
+
+        float avg = sum / _beatIntervals.Count;
+        if (avg <= 1e-5f)
+        {
+            return 0f;
+        }
+
+        float bpm = 60f / avg;
+        return Math.Clamp(bpm, 40f, 220f);
+    }
+
     private void ThrowIfDisposed()
     {
         if (_disposed)