A simple glsl function that checks if a point is part of the mandelbrot set.

mandelbrot.glsl

// Mandelbrot Set
bool mandelbrot(vec2 c, int iter)
{
	// Initialize Z
	vec2 z = vec2(0.0);

	// Iterate function (z = z ^ 2 + c)
	for(int i = 0; i < iter; i++)
	{
		// Check if our point diverged
		if(length(z) > 4.0){return false;}

		// Compute the next point in the orbit
		z = vec2((z.x*z.x)-(z.y*z.y), z.x*z.y*2.0) + c;
	}

	// The point never diverged, it's part of the Mandelbrot Set
	return true;
}