#version 100
precision highp float;

uniform float u_time;
uniform vec2 u_resolution;
uniform float u_zoom;
uniform vec2 u_center;

// Sliders
uniform float u_exponent;
uniform vec2 u_z_start;
uniform vec2 u_c_offset;

void main() {
    // Current pixel coordinate in 0..1
    vec2 st = gl_FragCoord.xy / u_resolution.xy;
    st.x *= u_resolution.x / u_resolution.y; // Aspect ratio correction
    
    // Center the coords:
    vec2 c_uv = (gl_FragCoord.xy - u_resolution.xy * 0.5) / u_resolution.y;
    
    // Apply Zoom and Pan
    vec2 c = (c_uv / u_zoom) + u_center;
    
    // Apply C Offset from sliders (allows Julia-like effects)
    c += u_c_offset;

    // Initial Z
    vec2 z = u_z_start;
    
    float iter = 0.0;
    float max_iter = 100.0 + log(u_zoom) * 20.0;
    
    for (float i = 0.0; i < 500.0; i++) {
        if (i > max_iter) break;
        
        // Generalized Z^n
        // Convert to Polar: r, theta
        float r = length(z);
        float theta = atan(z.y, z.x);
        
        // Z^n = r^n * (cos(n*theta) + i*sin(n*theta))
        float rn = pow(r, u_exponent);
        float nt = theta * u_exponent;
        
        float x = rn * cos(nt) + c.x;
        float y = rn * sin(nt) + c.y;
        
        if ((x * x + y * y) > 4.0) {
            iter = i;
            break;
        }
        z.x = x;
        z.y = y;
    }
    
    // Coloring
    float t = iter / max_iter;
    if (iter == 0.0) {
        gl_FragColor = vec4(0.0, 0.0, 0.0, 1.0);
    } else {
        // More colorful palette
        gl_FragColor = vec4(
            0.5 + 0.5 * cos(3.0 + t * 10.0 + u_time),
            0.5 + 0.5 * cos(3.0 + t * 10.0 + 2.0),
            0.5 + 0.5 * cos(3.0 + t * 10.0 + 4.0),
            1.0
        );
    }
}