// Minimal Mandelbrot with slow timed zoom to a preset boundary location.
// --- Presets ---
const vec2  ZOOM_TARGET     = vec2(-0.743643887, 0.131825904); // Seahorse Valley
const float ZOOM_DURATION   = 60.0;      // seconds to complete zoom (iTime=0..duration)
const float ZOOM_FACTOR_END = 1e-3;      // final scale relative to full-view (smaller => deeper)
const int   MAX_ITER_START  = 200;       // iterations at start (full view)
const int   MAX_ITER_END    = 1000;      // iterations at end (deep zoom)

// HSV to RGB, h in [0,1], s,v in [0,1]
vec3 hsv2rgb(vec3 c)
{
    vec3 p = abs(fract(c.x + vec3(0.0, 1.0/3.0, 2.0/3.0)) * 6.0 - 3.0);
    return c.z * mix(vec3(1.0), clamp(p - 1.0, 0.0, 1.0), c.y);
}

// ROYGBIV palette: hue sweep at full saturation/value
vec3 rainbow(float t)
{
    return vec3(fract(t), 1.0, 1.0); // HSV
}

void mainImage( out vec4 fragColor, in vec2 fragCoord )
{
    // Normalized pixel coordinates (0..1)
    vec2 uv = fragCoord / iResolution.xy;

    // --- View mapping (full-set rectangle) ---
    // Initial full view bounds (classic): x∈[-2.5, 1.0], y∈[-1.0, 1.0]
    const vec2 INIT_MIN = vec2(-2.5, -1.0);
    const vec2 INIT_MAX = vec2( 1.0,  1.0);
    const vec2 INIT_CENTER = 0.5 * (INIT_MIN + INIT_MAX);
    const vec2 INIT_HALF   = 0.5 * (INIT_MAX - INIT_MIN); // (1.75, 1.0)

    // --- Time-based zoom/pan ---
    float t = clamp(iTime / ZOOM_DURATION, 0.0, 1.0);

    // Geometric interpolation for scale (smooth visual zoom)
    float logEnd = log(ZOOM_FACTOR_END);
    float scale  = exp(mix(0.0, logEnd, t));  // 1.0 -> ZOOM_FACTOR_END

    // Linear interpolation of center from initial to target
    vec2 center = mix(INIT_CENTER, ZOOM_TARGET, t);

    // Current bounds
    vec2 halfSpan = INIT_HALF * scale;
    vec2 minP = center - halfSpan;
    vec2 maxP = center + halfSpan;

    // Map uv to complex plane coordinate c
    vec2 c = mix(minP, maxP, uv);

    // Iteration budget interpolation
    int MAX_ITER = int(mix(float(MAX_ITER_START), float(MAX_ITER_END), t) + 0.5);

    // --- Mandelbrot iteration: z_{n+1} = z_n^2 + c ---
    vec2 z = vec2(0.0);
    int i;
    for (i = 0; i < MAX_ITER; ++i)
    {
        // z = (zx + i zy)^2 + c = (zx^2 - zy^2) + i(2 zx zy) + c
        vec2 z2 = vec2(z.x*z.x - z.y*z.y, 2.0*z.x*z.y) + c;
        z = z2;
        if (dot(z, z) > 4.0) break; // escape radius^2
    }

    // Color: inside = black, outside = rainbow by normalized iteration
    vec3 col = (i == MAX_ITER)
        ? vec3(0.0)
        : hsv2rgb(rainbow(float(i) / float(MAX_ITER)));

    fragColor = vec4(col, 1.0);
}