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;; complex_dynamics.lisp - functions to plot Julia and mandelbrot sets
;;
;; Copyright (C) 2006 Jaime E. Villate <villate@fe.up.pt>
;;
;; This program is free software; you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation; either version 2 of the License, or
;; (at your option) any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with this program; if not, write to the Free Software
;; Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
;; MA 02110-1301, USA.
;;
;; $Id: complex_dynamics.lisp,v 1.1 2007/04/01 22:46:42 villate Exp $
(in-package :maxima)
;; Function hsv2rgb transforms a color specification triplet
;; (hue,saturation,value), into RGB values. Hue should be an integer (angle
;; in degrees), while saturation and value should be floating-point numbers
;; between 0 and 1.
;; The RGB values returned are six hexadecimal digits: two digits for R,
;; followed by two digits for G and two digits for B.
(defun hsv2rgb(hue sat val)
(let (v rgb h i f u p q r)
(setq v (* val 255))
(if (= sat 0)
(setq rgb (+ v (* 256 (+ v (* 256 v))))) ; achromatic case
(progn
(setq h (/ (mod hue 360) 60)) ; 0<= h <6
(setq i (truncate h)) ; largest integer <= h
(setq f (- h i)) ; fractional part of h
(setq u (round v)) ; u, p, q and r are all
(setq p (round (* v (- 1 sat)))) ; integers between 0
(setq q (round (* v (- 1 (* sat f))))) ; and 255
(setq r (round (* v (- 1 (* sat (- 1 f))))))
(cond
((eql i 0) (setq rgb (+ p (* 256 (+ r (* 256 u)))))) ; red
((eql i 1) (setq rgb (+ p (* 256 (+ u (* 256 q)))))) ; yellow
((eql i 2) (setq rgb (+ r (* 256 (+ u (* 256 p)))))) ; green
((eql i 3) (setq rgb (+ u (* 256 (+ q (* 256 p)))))) ; cyan
((eql i 4) (setq rgb (+ u (* 256 (+ p (* 256 r)))))) ; blue
((eql i 5) (setq rgb (+ q (* 256 (+ p (* 256 u))))))))) ; magenta
(format nil "~6,'0x" (round rgb))))
;; Function $mandelbrot creates an XPM graphic file with the Mandelbrot set
;; on the region: xmin < x <xmax, ymin < y <ymax.
;; The input argument m must be a positive integer, which defines the number
;; of iterations to be made, before considering a point as part of the set.
(defun $mandelbrot(&rest options)
(let (a b c d e colorbytes colorcodes colors line num
dx dy x xmax xmin y ymax ymin
(xcenter 0.0) (ycenter 0.0) (radius 2.0)
(m 12) (nx 400) (ny 400) (file "mandelbrot.xpm")
(huerange 360) (hue0 -60) (sat 0.76) (val 0.96) (color "000000")
($numer t) (optname nil)
(letters "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"))
(dolist (option options)
(setf optname (second option))
(cond
((eql optname '$size)
(if (> (length option) 3)
(progn (setq nx (third option)) (setq ny (fourth option)))
(progn (setq nx (third option)) (setq ny nx))))
((eql optname '$levels) (setq m (third option)))
((eql optname '$huerange) (setq huerange (third option)))
((eql optname '$hue) (setq hue0 (third option)))
((eql optname '$saturation) (setq sat (third option)))
((eql optname '$value) (setq val (third option)))
((eql optname '$color)
(setq color (hsv2rgb (third option) (fourth option) (fifth option))))
((eql optname '$center)
(setq xcenter (coerce-float (third option)))
(setq ycenter (coerce-float (fourth option))))
((eql optname '$radius) (setq radius (coerce-float (third option))))
((eql optname '$filename)
(setq file (format nil "~a.xpm"
(print-invert-case (stripdollar (third option))))))))
(setq xmin (- xcenter radius))
(setq xmax (+ xcenter radius))
(setq ymin (- ycenter radius))
(setq ymax (+ ycenter radius))
(setq dx (/ (float (- xmax xmin)) nx)) ; x displacement per pixel
(setq dy (/ (float (- ymax ymin)) ny)) ; y displacement per pixel
;; setup color tables
(if (> m 52) (setq colorbytes 2) (setq colorbytes 1))
(setq colors (list color))
(setq colorcodes
(cond ((eql colorbytes 1) '(".")) ((eql colorbytes 2) '(".."))))
(dotimes (i m)
(push (hsv2rgb (+ hue0 (* huerange (- 1 (/ i (- m 1))))) sat val) colors)
(push (cond
((eql colorbytes 1) (string (char letters i)))
((eql colorbytes 2) (format nil "~a~a" (char letters (floor i 50))
(char letters (mod i 50)))))
colorcodes))
(with-open-file (st file :direction :output :if-exists :supersede)
;; print XPM file header
(format st "/* XPM */~%static char *mandelbrot[] = {~%")
(format st "\"~a ~a ~a ~a\",~%" nx ny (+ m 1) colorbytes)
;; print colors table
(dotimes (i (+ m 1))
(format st "\"~a c #~a\",~%" (nth i colorcodes) (nth i colors)))
;; iteration through all grid points
(dotimes (i ny)
(setq y (+ ymin (* (- ny (+ i 1)) dy)))
(setq line "")
(dotimes (j nx)
(setq x (+ xmin (* j dx)))
(setq a 0) (setq b 0)
(setq num m)
(dotimes (l m)
(setq c (* a a))
(setq d (* b b))
(setq e (* 2 a b))
(when (> (+ c d) 4) (progn (setq num l) (return)))
(setq a (+ x (- c d)))
(setq b (+ y e)))
(setq line (concatenate 'string line (nth num colorcodes))))
(if (= i (- ny 1))
(format st "\"~a\"~%" line) (format st "\"~a\",~%" line)))
(format st "};~%"))
(format t "File ~a was created.~%" file)))
;; Function $julia creates an XPM graphic file with the Julia set for the
;; point (x,y) of the complex plane, on the region: xmin < x <xmax,
;; ymin < y <ymax.
;; The input argument m must be a positive integer, which defines the number
;; of iterations to be made, before considering a point as part of the set.
(defun $julia(x y &rest options)
(let (a b b0 c d e colorbytes colorcodes colors line num
dx dy xmax xmin ymax ymin
(xcenter 0.0) (ycenter 0.0) (radius 2.0)
(m 12) (nx 400) (ny 400) (file "julia.xpm")
(huerange 360) (hue0 -60) (sat 0.76) (val 0.96) (color "000000")
($numer t) (optname nil)
(letters "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"))
(dolist (option options)
(setf optname (second option))
(cond
((eql optname '$size)
(if (> (length option) 3)
(progn (setq nx (third option)) (setq ny (fourth option)))
(progn (setq nx (third option)) (setq ny nx))))
((eql optname '$levels) (setq m (third option)))
((eql optname '$huerange) (setq huerange (third option)))
((eql optname '$hue) (setq hue0 (third option)))
((eql optname '$saturation) (setq sat (third option)))
((eql optname '$value) (setq val (third option)))
((eql optname '$color)
(setq color (hsv2rgb (third option) (fourth option) (fifth option))))
((eql optname '$center)
(setq xcenter (coerce-float (third option)))
(setq ycenter (coerce-float (fourth option))))
((eql optname '$radius) (setq radius (coerce-float (third option))))
((eql optname '$filename)
(setq file (format nil "~a.xpm"
(print-invert-case (stripdollar (third option))))))))
(setq xmin (- xcenter radius))
(setq xmax (+ xcenter radius))
(setq ymin (- ycenter radius))
(setq ymax (+ ycenter radius))
(setq dx (/ (float (- xmax xmin)) nx)) ; x displacement per pixel
(setq dy (/ (float (- ymax ymin)) ny)) ; y displacement per pixel
;; setup color tables
(if (> m 52) (setq colorbytes 2) (setq colorbytes 1))
(setq colors (list color))
(setq colorcodes
(cond ((eql colorbytes 1) '(".")) ((eql colorbytes 2) '(".."))))
(dotimes (i m)
(push (hsv2rgb (+ hue0 (* huerange (- 1 (/ i (- m 1))))) sat val) colors)
(push (cond
((eql colorbytes 1) (string (char letters i)))
((eql colorbytes 2) (format nil "~a~a" (char letters (floor i 50))
(char letters (mod i 50)))))
colorcodes))
(with-open-file (st file :direction :output :if-exists :supersede)
;; print XPM file header
(format st "/* XPM */~%static char *mandelbrot[] = {~%")
(format st "\"~a ~a ~a ~a\",~%" nx ny (+ m 1) colorbytes)
;; print colors table
(dotimes (i (+ m 1))
(format st "\"~a c #~a\",~%" (nth i colorcodes) (nth i colors)))
;; iteration through all grid points
(dotimes (i ny)
(setq b0 (+ ymin (* (- ny (+ i 1)) dy)))
(setq line "")
(dotimes (j nx)
(setq a (+ xmin (* j dx)))
(setq b b0)
(setq num m)
(dotimes (l m)
(setq c (* a a))
(setq d (* b b))
(setq e (* 2 a b))
(when (> (+ c d) 4) (progn (setq num l) (return)))
(setq a (+ x (- c d)))
(setq b (+ y e)))
(setq line (concatenate 'string line (nth num colorcodes))))
(if (= i (- ny 1))
(format st "\"~a\"~%" line) (format st "\"~a\",~%" line)))
(format st "};~%"))
(format t "File ~a was created.~%" file)))
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