Fractal Rendering in Emacs

Taking advantage of Emacs’ image-mode and the handy Netpbm format it’s possible to generate and render images inside Emacs using Elisp. This function will generate a Sierpinski carpet and display the result in a buffer.

(defun sierpinski (s)
  (pop-to-buffer (get-buffer-create "*sierpinski*"))
  (fundamental-mode) (erase-buffer)
  (labels ((fill-p (x y)
                   (cond ((or (zerop x) (zerop y)) "0")
                         ((and (= 1 (mod x 3)) (= 1 (mod y 3))) "1")
                         (t (fill-p (/ x 3) (/ y 3))))))
    (insert (format "P1\n%d %d\n" s s))
    (dotimes (y s) (dotimes (x s) (insert (fill-p x y) " "))))

It’s best called with powers of three,

(sierpinski (expt 3 5))

This one should look quite familiar. Using the same technique,

(defun mandelbrot ()
  (pop-to-buffer (get-buffer-create "*mandelbrot*"))
  (let ((w 400) (h 300) (d 32))
    (fundamental-mode) (erase-buffer)
    (set-buffer-multibyte nil)
    (insert (format "P6\n%d %d\n255\n" w h))
    (dotimes (y h)
      (dotimes (x w)
        (let* ((cx (* 1.5 (/ (- x (/ w 1.45)) w 0.45)))
               (cy (* 1.5 (/ (- y (/ h 2.0)) h 0.5)))
               (zr 0) (zi 0)
               (v (dotimes (i d d)
                    (if (> (+ (* zr zr) (* zi zi)) 4) (return i)
                      (psetq zr (+ (* zr zr) (- (* zi zi)) cx)
                             zi (+ (* (* zr zi) 2) cy))))))
          (insert-char (floor (* 256 (/ v 1.0 d))) 3))))

Tweak it with a colormap,

(defun colormap (v)
  "Given a value between 0 and 1.0, insert a P6 color."
  (dotimes (i 3)
    (insert-char (floor (* 256 (min 0.99 (sqrt (* (- 3 i) v))))) 1)))

One of the project ideas on my mental back-burner of things I’ll never get to is to create a little graphics library for Elisp. It would use a technique like this to pull it off. Assuming support was compiled in, Emacs can even render SVGs to a buffer, so creating a rich graphics library wouldn’t be difficult at all. Plus, unlike bare Elisp, it would be fast.

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Chris Wellons