How to resolve the algorithm Mandelbrot set step by step in the Emacs Lisp programming language

Published on 12 May 2024 09:40 PM
#Emacs lisp

How to resolve the algorithm Mandelbrot set step by step in the Emacs Lisp programming language

Table of Contents

Problem Statement

Generate and draw the Mandelbrot set.

Note that there are many algorithms to draw Mandelbrot set and there are many functions which generate it .

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Mandelbrot set step by step in the Emacs Lisp programming language

Source code in the emacs programming language

; === Mandelbrot ============================================

(setq mandel-size (cons 76 34))
(setq xmin -2)
(setq xmax .5)
(setq ymin -1.2)
(setq ymax 1.2)
(setq max-iter 20)

(defun mandel-iter-point (x y)
  "Run the actual iteration for each point."
  (let ((xp 0)
        (yp 0)
        (it 0)
        (xt 0))
    (while (and (< (+ (* xp xp) (* yp yp)) 4) (< it max-iter))
      (setq xt (+ (* xp xp) (* -1 yp yp) x))
      (setq yp (+ (* 2 xp yp) y))
      (setq xp xt)
      (setq it (1+ it)))
    it))

(defun mandel-iter (p)
  "Return string for point based on whether inside/outside the set."
  (let ((it (mandel-iter-point (car p) (cdr p))))
    (if (= it max-iter) "*" "-")))

(defun mandel-pos (x y)
  "Convert screen coordinates to input coordinates."
  (let ((xp (+ xmin (* (- xmax xmin) (/ (float x) (car mandel-size)))))
        (yp (+ ymin (* (- ymax ymin) (/ (float y) (cdr mandel-size))))))
       (cons xp yp)))

(defun mandel ()
  "Plot the Mandelbrot set."
  (dotimes (y (cdr mandel-size))
    (dotimes (x (car mandel-size))
      (if (= x 0)
        (insert(format "\n%s" (mandel-iter (mandel-pos x y))))
        (insert(format "%s" (mandel-iter (mandel-pos x y))))))))

(mandel)


; === Graphical Mandelbrot ============================================

(setq mandel-size (cons 320 300))
(setq xmin -2)
(setq xmax .5)
(setq ymin -1.2)
(setq ymax 1.2)
(setq max-iter 20)

(defun mandel-iter-point (x y)
  "Run the actual iteration for each point."
  (let ((xp 0)
        (yp 0)
        (it 0)
        (xt 0))
    (while (and (< (+ (* xp xp) (* yp yp)) 4) (< it max-iter))
      (setq xt (+ (* xp xp) (* -1 yp yp) x))
      (setq yp (+ (* 2 xp yp) y))
      (setq xp xt)
      (setq it (1+ it)))
    it))

(defun mandel-iter (p)
  "Return string for point based on whether inside/outside the set."
  (let ((it (mandel-iter-point (car p) (cdr p))))
    (if (= it max-iter) "*" (if (cl-oddp it) "+" "-"))))

(defun mandel-pos (x y)
  "Convert screen coordinates to input coordinates."
  (let ((xp (+ xmin (* (- xmax xmin) (/ (float x) (car mandel-size)))))
        (yp (+ ymin (* (- ymax ymin) (/ (float y) (cdr mandel-size))))))
       (cons xp yp)))

(defun string-to-image (str)
  "Convert image data string to XPM image."
  (create-image (concat (format "/* XPM */
static char * mandel[] = {
\"%i %i 3 1\",
\"+      c #ff0000\",
\"-      c #0000ff\",
\"*      c #000000\"," (car mandel-size) (cdr mandel-size))
    str "};") 'xpm t))

(defun mandel-pic ()
  "Plot the Mandelbrot set."
  (setq all "")
  (dotimes (y (cdr mandel-size))
    (setq line "")
    (dotimes (x (car mandel-size))
      (setq line (concat line (mandel-iter (mandel-pos x y)))))
    (setq all (concat all "\"" line "\",\n")))
  (insert-image (string-to-image all)))

(mandel-pic)

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