(defun mandelbrot (size filename)
        (let ((img (make-8-bit-gray-image size size)))
                (declare (type 8-bit-gray-image img))
                (loop for i from 1 to (1- size) do
                        (loop for j from 1 to (1- size) do ;these two loops go through all pixels of the image
                                (labels ((mb-set (x y nit) ;nit is the number of the iteration
                                                (if (or (> (+ (* x x) (* y y)) 2) (> nit 1000)) ;this bit of code checks if the modulo of z is >2
                                                        (setf (pixel img i j) (round(/ 255.0 (1+ nit)))) ;if it is, this bit sets the current pixel to the appropriate shade of grey
                                                        (mb-set (+ (- (* x x) (* y y)) (/ (- j (round (/ size 2.0))) 50.0)) (+ (* 2 x y) (/ (- j (round (/ size 2.0))) 50.0)) (1+ nit)) ;if not, this bit sends new information into the next iteration
                                                )
                                        ))
                                                (mb-set 0.0 0.0 0)
                                )
                        )
                )
                (write-jpeg-file filename img)
        )
)