Add MrGameEng.WorldGen: deterministic procedural world generation

Introduce a WorldGen module under Simulation with reusable helpers for
seed-based terrain heightmaps: PerlinNoise (deterministic 2D gradient
noise), FractalNoise (fBm over octaves), Falloff (island edge masks),
Heightmap (row-major grid with min-max normalize) and HeightmapGenerator
(settings to normalized heightmap). All deterministic from an integer
seed, allocation-free per sample, covered by xUnit tests.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/MrGameEng.Simulation/WorldGen/Falloff.cs

@@ -0,0 +1,32 @@
+namespace MrGameEng.WorldGen;
+
+/// <summary>
+/// Falloff masks that bias a heightmap toward water near the map edges, turning open noise into
+/// island-like continents. All methods are pure and deterministic.
+/// </summary>
+public static class Falloff
+{
+    /// <summary>
+    /// Island mask for normalized coordinates (<paramref name="nx"/>, <paramref name="ny"/>) in
+    /// <c>[-1, 1]</c> where (0,0) is the map centre. Returns 1 at the centre and falls toward 0 at
+    /// the edges; <paramref name="power"/> sets the coastline steepness (higher = sharper).
+    /// </summary>
+    public static float Island(float nx, float ny, float power = 3f)
+    {
+        // Chebyshev distance keeps the whole border ring low, so every edge becomes water.
+        var d = Math.Clamp(MathF.Max(MathF.Abs(nx), MathF.Abs(ny)), 0f, 1f);
+        return 1f - MathF.Pow(d, power);
+    }
+
+    /// <summary>
+    /// Island mask for a grid cell: maps (<paramref name="x"/>, <paramref name="y"/>) on a
+    /// <paramref name="width"/>×<paramref name="height"/> grid into <c>[-1, 1]</c> and evaluates
+    /// <see cref="Island(float, float, float)"/>.
+    /// </summary>
+    public static float EdgeFalloff(int x, int y, int width, int height, float power = 3f)
+    {
+        var nx = width <= 1 ? 0f : x / (float)(width - 1) * 2f - 1f;
+        var ny = height <= 1 ? 0f : y / (float)(height - 1) * 2f - 1f;
+        return Island(nx, ny, power);
+    }
+}

src/MrGameEng.Simulation/WorldGen/FractalNoise.cs

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+namespace MrGameEng.WorldGen;
+
+/// <summary>
+/// Fractal Brownian motion over a <see cref="PerlinNoise"/> source: sums several octaves of
+/// noise, each at a higher frequency (<see cref="Lacunarity"/>) and lower amplitude
+/// (<see cref="Persistence"/>), to build natural detail at multiple scales. The sum is
+/// normalized back into <c>[-1, 1]</c> regardless of octave count. Immutable and deterministic.
+/// </summary>
+public sealed class FractalNoise
+{
+    private readonly PerlinNoise _noise;
+
+    /// <summary>Number of noise layers summed (≥1). More octaves add finer detail.</summary>
+    public int Octaves { get; }
+
+    /// <summary>Base frequency applied to the first octave's sample coordinates.</summary>
+    public float Frequency { get; }
+
+    /// <summary>Amplitude multiplier between octaves (0..1, typically 0.5): lower is smoother.</summary>
+    public float Persistence { get; }
+
+    /// <summary>Frequency multiplier between octaves (typically 2): higher adds detail faster.</summary>
+    public float Lacunarity { get; }
+
+    /// <summary>Builds an fBm sampler over a Perlin field seeded by <paramref name="seed"/>.</summary>
+    public FractalNoise(
+        int seed,
+        int octaves = 4,
+        float frequency = 1f,
+        float persistence = 0.5f,
+        float lacunarity = 2f
+    )
+    {
+        _noise = new PerlinNoise(seed);
+        Octaves = Math.Max(1, octaves);
+        Frequency = frequency;
+        Persistence = persistence;
+        Lacunarity = lacunarity;
+    }
+
+    /// <summary>Samples the summed octaves at (<paramref name="x"/>, <paramref name="y"/>); result is in <c>[-1, 1]</c>.</summary>
+    public float Sample(float x, float y)
+    {
+        var amplitude = 1f;
+        var frequency = Frequency;
+        var sum = 0f;
+        var totalAmplitude = 0f;
+        for (var i = 0; i < Octaves; i++)
+        {
+            sum += amplitude * _noise.Sample(x * frequency, y * frequency);
+            totalAmplitude += amplitude;
+            amplitude *= Persistence;
+            frequency *= Lacunarity;
+        }
+
+        return totalAmplitude > 0f ? sum / totalAmplitude : 0f;
+    }
+}

src/MrGameEng.Simulation/WorldGen/Heightmap.cs

@@ -0,0 +1,64 @@
+namespace MrGameEng.WorldGen;
+
+/// <summary>
+/// A dense row-major grid of height values. Plain data with indexed access — fill it from a
+/// <see cref="HeightmapGenerator"/> and read it from worldgen code. Values are arbitrary until
+/// <see cref="Normalize"/> rescales them into <c>[0, 1]</c>.
+/// </summary>
+public sealed class Heightmap
+{
+    /// <summary>Grid width in cells.</summary>
+    public int Width { get; }
+
+    /// <summary>Grid height in cells.</summary>
+    public int Height { get; }
+
+    /// <summary>Row-major values, length <see cref="Width"/>×<see cref="Height"/>.</summary>
+    public float[] Values { get; }
+
+    /// <summary>Creates an all-zero map of the given size.</summary>
+    public Heightmap(int width, int height)
+    {
+        Width = width;
+        Height = height;
+        Values = new float[width * height];
+    }
+
+    /// <summary>Height at (<paramref name="x"/>, <paramref name="y"/>).</summary>
+    public float this[int x, int y]
+    {
+        get => Values[y * Width + x];
+        set => Values[y * Width + x] = value;
+    }
+
+    /// <summary>Rescales all values into <c>[0, 1]</c> by min–max; a flat map becomes all zeros.</summary>
+    public void Normalize()
+    {
+        var min = float.MaxValue;
+        var max = float.MinValue;
+        foreach (var v in Values)
+        {
+            if (v < min)
+            {
+                min = v;
+            }
+
+            if (v > max)
+            {
+                max = v;
+            }
+        }
+
+        var range = max - min;
+        if (range <= float.Epsilon)
+        {
+            Array.Clear(Values);
+            return;
+        }
+
+        for (var i = 0; i < Values.Length; i++)
+        {
+            Values[i] = (Values[i] - min) / range;
+        }
+    }
+}

src/MrGameEng.Simulation/WorldGen/HeightmapGenerator.cs

@@ -0,0 +1,97 @@
+namespace MrGameEng.WorldGen;
+
+/// <summary>
+/// Parameters for <see cref="HeightmapGenerator"/>. Defaults give a single continent with a soft
+/// coastline; raise <see cref="Octaves"/>/<see cref="Frequency"/> for finer detail and
+/// <see cref="IslandStrength"/> for how strongly the edges are pushed underwater.
+/// </summary>
+public readonly record struct HeightmapSettings
+{
+    /// <summary>Integer seed — the whole map derives from it.</summary>
+    public int Seed { get; init; }
+
+    /// <summary>Number of feature cycles across the map at the base octave (higher = smaller features).</summary>
+    public float Frequency { get; init; }
+
+    /// <summary>Number of fBm octaves (≥1).</summary>
+    public int Octaves { get; init; }
+
+    /// <summary>fBm amplitude falloff per octave (0..1).</summary>
+    public float Persistence { get; init; }
+
+    /// <summary>fBm frequency growth per octave (typically 2).</summary>
+    public float Lacunarity { get; init; }
+
+    /// <summary>Island falloff blend in <c>[0, 1]</c>: 0 disables it, 1 applies it fully.</summary>
+    public float IslandStrength { get; init; }
+
+    /// <summary>Coastline steepness of the island mask (higher = sharper); see <see cref="Falloff.Island"/>.</summary>
+    public float IslandPower { get; init; }
+
+    /// <summary>Sensible defaults: one continent, 5 octaves, soft coastline.</summary>
+    public static HeightmapSettings Default =>
+        new()
+        {
+            Seed = 0,
+            Frequency = 3f,
+            Octaves = 5,
+            Persistence = 0.5f,
+            Lacunarity = 2f,
+            IslandStrength = 0.6f,
+            IslandPower = 3f,
+        };
+}
+
+/// <summary>
+/// Turns <see cref="HeightmapSettings"/> into a normalized <see cref="Heightmap"/>: fractal noise
+/// sampled per cell, optionally multiplied by an island falloff, then rescaled into <c>[0, 1]</c>.
+/// Fully deterministic — the same settings always produce the same map, so a world can be rebuilt
+/// from its seed alone. Owns no world data.
+/// </summary>
+public sealed class HeightmapGenerator
+{
+    private readonly HeightmapSettings _settings;
+    private readonly FractalNoise _noise;
+
+    /// <summary>Builds a generator for the given <paramref name="settings"/>.</summary>
+    public HeightmapGenerator(HeightmapSettings settings)
+    {
+        _settings = settings;
+        _noise = new FractalNoise(
+            settings.Seed,
+            settings.Octaves,
+            frequency: 1f,
+            settings.Persistence,
+            settings.Lacunarity
+        );
+    }
+
+    /// <summary>Generates a <paramref name="width"/>×<paramref name="height"/> normalized heightmap.</summary>
+    public Heightmap Generate(int width, int height)
+    {
+        var map = new Heightmap(width, height);
+        var scaleX = width <= 1 ? 0f : _settings.Frequency / (width - 1);
+        var scaleY = height <= 1 ? 0f : _settings.Frequency / (height - 1);
+        var island = Math.Clamp(_settings.IslandStrength, 0f, 1f);
+
+        for (var y = 0; y < height; y++)
+        {
+            for (var x = 0; x < width; x++)
+            {
+                // fBm in [-1,1] → [0,1].
+                var n = _noise.Sample(x * scaleX, y * scaleY) * 0.5f + 0.5f;
+                if (island > 0f)
+                {
+                    var mask = Falloff.EdgeFalloff(x, y, width, height, _settings.IslandPower);
+                    // Blend the raw height with its masked self by the island strength.
+                    n *= 1f - island + mask * island;
+                }
+
+                map[x, y] = n;
+            }
+        }
+
+        map.Normalize();
+        return map;
+    }
+}

src/MrGameEng.Simulation/WorldGen/PerlinNoise.cs

@@ -0,0 +1,78 @@
+namespace MrGameEng.WorldGen;
+
+/// <summary>
+/// Deterministic 2D Perlin (gradient) noise. Construct once per seed, then sample any number of
+/// points: <see cref="Sample"/> is allocation-free and returns smooth values in <c>[-1, 1]</c>
+/// that vary continuously across the plane. The permutation table is built from the integer
+/// seed, so the same seed always yields the same field — the basis for reproducible world
+/// generation. <see cref="Sample"/> is a pure read and safe to call concurrently.
+/// </summary>
+public sealed class PerlinNoise
+{
+    private readonly int[] _perm = new int[512];
+
+    /// <summary>Builds the noise field deterministically from <paramref name="seed"/>.</summary>
+    public PerlinNoise(int seed)
+    {
+        var p = new int[256];
+        for (var i = 0; i < 256; i++)
+        {
+            p[i] = i;
+        }
+
+        // Deterministic Fisher–Yates shuffle from the seed — never Random.Shared in simulation.
+        var random = new Random(seed);
+        for (var i = 255; i > 0; i--)
+        {
+            var j = random.Next(i + 1);
+            (p[i], p[j]) = (p[j], p[i]);
+        }
+
+        for (var i = 0; i < 512; i++)
+        {
+            _perm[i] = p[i & 255];
+        }
+    }
+
+    /// <summary>Samples the noise at (<paramref name="x"/>, <paramref name="y"/>); result is in <c>[-1, 1]</c>.</summary>
+    public float Sample(float x, float y)
+    {
+        var x0 = (int)MathF.Floor(x);
+        var y0 = (int)MathF.Floor(y);
+        var xi = x0 & 255;
+        var yi = y0 & 255;
+        var xf = x - x0;
+        var yf = y - y0;
+
+        var u = Fade(xf);
+        var v = Fade(yf);
+
+        var aa = _perm[_perm[xi] + yi];
+        var ab = _perm[_perm[xi] + yi + 1];
+        var ba = _perm[_perm[xi + 1] + yi];
+        var bb = _perm[_perm[xi + 1] + yi + 1];
+
+        var x1 = Lerp(Grad(aa, xf, yf), Grad(ba, xf - 1f, yf), u);
+        var x2 = Lerp(Grad(ab, xf, yf - 1f), Grad(bb, xf - 1f, yf - 1f), u);
+        return Lerp(x1, x2, v);
+    }
+
+    // Quintic ease curve (Perlin's improved fade): zero first and second derivatives at 0 and 1.
+    private static float Fade(float t) => t * t * t * (t * (t * 6f - 15f) + 10f);
+
+    private static float Lerp(float a, float b, float t) => a + t * (b - a);
+
+    // Dot product with one of 8 gradient directions chosen by the low bits of the hash.
+    private static float Grad(int hash, float x, float y) =>
+        (hash & 7) switch
+        {
+            0 => x + y,
+            1 => -x + y,
+            2 => x - y,
+            3 => -x - y,
+            4 => x,
+            5 => -x,
+            6 => y,
+            _ => -y,
+        };
+}