;;-----------------=={ Julia Set Fractal }==------------------;;
;;                                                            ;;
;;  The function will create a representation of the Julia    ;;
;;  set by iteration of the function:                         ;;
;;                                                            ;;
;;    f(z) = z^2 + c                                          ;;
;;                                                            ;;
;;  Where 'z' & 'c' are complex numbers. The fractal colour   ;;
;;  is determined by the number of iterations (less than a    ;;
;;  predetermined maximum iteration number) before the        ;;
;;  norm of the complex number generated by the above         ;;
;;  function reaches a limit.                                 ;;
;;                                                            ;;
;;  'c' is the constant for each calculation, this            ;;
;;  distinguishes the Julia set from the Mandelbrot set       ;;
;;  (in which 'c' is set to the complex values of each point) ;;
;;  For this reason, there are infinitely many Julia fractals,;;
;;  but only one Mandelbrot fractal.                          ;;
;;                                                            ;;
;;  More interestingly, there exists a Julia fractal for      ;;
;;  every point of the Mandelbrot fractal.                    ;;
;;------------------------------------------------------------;;
;;  Note:                                                     ;;
;;  --------                                                  ;;
;;  Fractal calculation is CPU intensive and may take a       ;;
;;  long time to generate the result. Reduce the iteration    ;;
;;  limit and image size & resolution to decrease calculation ;;
;;  time.                                                     ;;
;;------------------------------------------------------------;;
;;  Author: Lee Mac, Copyright © 2011 - www.lee-mac.com       ;;
;;------------------------------------------------------------;;

(defun c:jfract ( / a b c i im[c] lim re[c] res x xmax xmin y ymax ymin )
    (setvar 'PDMODE 0)
    (setq
        lim 255     ;; Iteration Limit

        xmin -0.60  ;; }
        xmax -0.30  ;; | Image
        ymin -0.35  ;; | Size
        ymax -0.05  ;; }

        res 0.0025  ;; Image Resolution

        Re[c] 0.285 ;; Real Coefficient of Julia Constant
        Im[c] 0.01  ;; Imaginary Coefficient of Julia Constant
    )
    (setq x (- xmin res))
    (while (<= (setq x (+ x res)) xmax)
        (setq y (- ymin res))
        (while (<= (setq y (+ y res)) ymax)
            (setq
                i 0
                a x
                b y
            )
            (while
                (and
                    (< (+ (* a a) (* b b)) 4.)
                    (<= (setq i (1+ i)) lim)
                )
                (setq
                    c (* 2.0 a b)
                    a (+ (- (* a a) (* b b)) Re[c])
                    b (+ c Im[c])
                )
            )
            (entmake
                (list
                   '(0 . "POINT")
                    (list 10 x y)
                    (cons 62 (1+ (rem (+ 30 i) 255)))
                )
            )
        )
    )
    (princ)
)