#version 100
precision highp float;

uniform float u_time;
uniform vec2 u_resolution;
uniform float u_zoom;
uniform vec2 u_center; // Unused if using perturbation?

uniform sampler2D u_ref_orbit; // Stores Reference Z (Real=Luminance, Imag=Alpha)

// Sliders
uniform float u_exponent; // Perturbation usually assumes Z^2. 
uniform vec2 u_z_start;
uniform vec2 u_c_offset;

// Complex Math helpers
vec2 complex_mul(vec2 a, vec2 b) {
    return vec2(a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x);
}

vec2 complex_sq(vec2 a) {
    return vec2(a.x*a.x - a.y*a.y, 2.0*a.x*a.y);
}

void main() {
    // Current pixel coordinate relative to screen center
    vec2 p = (gl_FragCoord.xy - u_resolution.xy * 0.5) / u_resolution.y;
    
    // Delta C (Difference from Reference Point)
    vec2 dc = p / u_zoom;
    
    // Apply C Offset from sliders (as Delta C)
    dc += u_c_offset; 

    // Initial Delta Z
    vec2 dz = vec2(0.0);
    
    float iter = 0.0;
    float max_iter = 1000.0; 
    
    for (float i = 0.0; i < 1000.0; i++) {
        // Fetch Reference Z from Texture
        vec4 ref = texture2D(u_ref_orbit, vec2((i + 0.5) / 1024.0, 0.5));
        
        // Decode Range [0, 1] -> [-4, 4]
        // Z = Val * 8 - 4
        // Use R and G channels (was R and A)
        vec2 Zn = vec2(ref.r * 8.0 - 4.0, ref.g * 8.0 - 4.0);
        
        // dz = 2*Zn*dz + dz^2 + dc
        vec2 two_Zn_dz = complex_mul(2.0 * Zn, dz);
        vec2 dz_sq = complex_sq(dz);
        
        dz = two_Zn_dz + dz_sq + dc; // Perturbation formula
        
        // Check Escape: |Zn + dz|^2 > 4
        vec2 current_z = Zn + dz;
        if (dot(current_z, current_z) > 4.0) {
            iter = i;
            break;
        }
    }
    
    // Coloring
    float t = iter / max_iter;
    
    // Standard Black Interior
    if (iter >= 999.0) {
        gl_FragColor = vec4(0.0, 0.0, 0.0, 1.0);
    } else {
        // Original "Generic" Palette
        gl_FragColor = vec4(sqrt(t), t*t, sin(t * 3.14), 1.0);
    }
}