This function only looks at the calculation process for a given pixel. You need to repeat this function for every pixel in your frame.
Contact me if you do not know how to implement this code in your program or need additional code.

//Screen width and height:
final int WIDTH, HEIGHT;

//Coordinates:
double xLoc, yLoc, zoom;

//Iteration limit:
int maxIterations;

private Color mandelbrot(int x, int y) {

//Adjusts the coordinate system to screen size:
x -= this.WIDTH / 2;
y -=this.HEIGHT / 2;
double real = (double) x / (this.WIDTH / 2);
double imaginary = (double) y / (this.HEIGHT / 2);

//Moves and zooms in to given x/y-location and zoom:
real = real * this.zoom + this.xLoc;
imaginary = imaginary * this.zoom + this.yLoc;

//Stores the original complex number:
double tempReal = real;
double tempImaginary = imaginary;
int n = 0;
while (n < this.maxIterations) {
double oldTemporary = tempReal;
//The following calculation is explained right here.
real = (real * real - imaginary * imaginary) + tempReal;
imaginary = (2 * oldTemporary * imaginary) + tempImaginary;

//Stops the calculation if the formula is going to infinity
if (Math.abs(real + imaginary) > 16) {
break;
}
n++;
}

if (n == this.maxIterations) {
//Returns a black color when the complex number is in the Mandelbrot set:
return new Color(0);
} else {
//Returns a color with individual hue when the complex number is not in the Mandelbrot set:
float hue = ((float) n / (float) this.maxIterations);
return Color.getHSBColor(hue, 1.0f, 1.0f);
}
}