#!/bin/bash # # Developed by Fred Weinhaus 12/6/2016 .......... revised 12/6/2016 # # ------------------------------------------------------------------------------ # # Licensing: # # Copyright © Fred Weinhaus # # My scripts are available free of charge for non-commercial use, ONLY. # # For use of my scripts in commercial (for-profit) environments or # non-free applications, please contact me (Fred Weinhaus) for # licensing arrangements. My email address is fmw at alink dot net. # # If you: 1) redistribute, 2) incorporate any of these scripts into other # free applications or 3) reprogram them in another scripting language, # then you must contact me for permission, especially if the result might # be used in a commercial or for-profit environment. # # My scripts are also subject, in a subordinate manner, to the ImageMagick # license, which can be found at: http://www.imagemagick.org/script/license.php # # ------------------------------------------------------------------------------ # #### # # USAGE: juliaset [-d dimensions] [-c constant ][-z zoom] [-m middle] # [-C colors] outfile # USAGE: juliaset [-h or -help] # # OPTIONS: # # -d dimensions WxH of output; integers>0; default="400x400" # -c constant fixed complex constant, c=(creal+i*cimag) used in # the julia set expression; comma separate pair: # "creal,cimag" where creal is the real part and # cimag is the imaginary part; the absolute value of c, # |c| = sqrt(realc^2 - imagc^2) <= 2; # default="-0.7,0.27015" # -z zoom zoom value; float>0; default=1 (nominal size); # larger values zoom in and smaller values zoom out # -m middle middle (center) location for pattern; mx,my; comma # separate pair of integers within the output image; # default is W/2,H/2 # -C colors list of colors to make up the color map; at least two # colors must be provided; the first color will be used # as the background color; default="white blueviolet # blue cyan green1 yellow orange red" ### # # NAME: JULIASET # # PURPOSE: To create a julia set fractal image. # # DESCRIPTION: JULIASET creates a julia set fractal image. The fractal is # defined in the complex plane by iterating the expression, z^2 + c, where # z=(x+i*y), i=sqrt(-1) and c=(creal+i*cimag) is a fixed complex value. # The fractal may be zoomed in at any center coordinate within the WxH. The # output image is colored by a color map according to the number of iterations # needed to converge at each pixel. The background color (first color in the # list) represents reaching the maximum number of iterations, which is 255. # Otherwise, smaller number correspond more to the left in the color map and # larger colors correspond to more to the right in the color map. # # OPTIONS: # # -d dimensions ... DIMENSIONS are the width and height of the output image # expressed as WxH. Values are integers>0. The default="400x400". # # -c constant ... CONSTANT is the fixed complex constant in the julia set # expression where c=(creal+i*cimag) is expressed as a comma separate pair: # "creal,cimag". Here creal is the real part and cimag is the imaginary part. # The absolute value of c, |c| = sqrt(realc^2 - imagc^2) <= 2. # The default="-0.7,0.27015" # # -z zoom ... ZOOM value. Values are floats>0. The default=1 (nominal size). # Larger values zoom in and smaller values zoom out. # # -m middle ... MIDDLE (center) location for the fractal pattern expressed as # comma separated pair of integers, cx,cy, within the WxH. The default is # W/2,H/2. # # -C colors ... COLORS is the list of space delimited colors that makes up # the horizontal 1D color map. At least two colors must be provided. The # default="white blueviolet blue cyan green1 yellow orange red". Any valid # IM (opaque) colors are allowed. # # NOTE: this script may be slow due to having to iterate up to 255 times at # each pixels. Time run from a couple of seconds up to about 15 seconds for # for a 400x400 sized image. The larger the zoom, the slower it will be. # # REFERENCES: # http://jonisalonen.com/2013/lets-draw-the-mandelbrot-set/ # https://rosettacode.org/wiki/Julia_set # https://en.wikipedia.org/wiki/Julia_set # http://lodev.org/cgtutor/juliamandelbrot.html # # CAVEAT: No guarantee that this script will work on all platforms, # nor that trapping of inconsistent parameters is complete and # foolproof. Use At Your Own Risk. # ###### # # set default values dimensions="400x400" realc=-0.7 imagc=0.27015 zoom=1 middle="" colors="white blueviolet blue cyan green1 yellow orange red" # set directory for temporary files dir="." # suggestions are dir="." or dir="/tmp" tmpL="$dir/juliaset_$$.miff" trap "rm -f $tmpL; exit 0" 0 trap "rm -f $tmpL; exit 1" 1 2 3 15 # set up functions to report Usage and Usage with Description PROGNAME=`type $0 | awk '{print $3}'` # search for executable on path PROGDIR=`dirname $PROGNAME` # extract directory of program PROGNAME=`basename $PROGNAME` # base name of program usage1() { echo >&2 "" echo >&2 "$PROGNAME:" "$@" sed >&2 -e '1,/^####/d; /^###/g; /^#/!q; s/^#//; s/^ //; 4,$p' "$PROGDIR/$PROGNAME" } usage2() { echo >&2 "" echo >&2 "$PROGNAME:" "$@" sed >&2 -e '1,/^####/d; /^######/g; /^#/!q; s/^#*//; s/^ //; 4,$p' "$PROGDIR/$PROGNAME" } # function to report error messages errMsg() { echo "" echo $1 echo "" usage1 exit 1 } # function to test for minus at start of value of second part of option 1 or 2 checkMinus() { test=`echo "$1" | grep -c '^-.*$'` # returns 1 if match; 0 otherwise [ $test -eq 1 ] && errMsg "$errorMsg" } # test for correct number of arguments and get values if [ $# -eq 0 ] then # help information echo "" usage2 exit 0 elif [ $# -gt 11 ] then errMsg "--- TOO MANY ARGUMENTS WERE PROVIDED ---" else while [ $# -gt 0 ] do # get parameter values case "$1" in -help) # help information echo "" usage2 exit 0 ;; -d) # dimensions shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID DIMENSIONS SPECIFICATION ---" checkMinus "$1" dimensions=`expr "$1" : '\([0-9]*x[0-9]*\)'` [ "$dimensions" = "" ] && errMsg "--- DIMENSIONS=$dimensions MUST BE AN X-Delimited PAIR OF NON-NEGATIVE INTEGERS (with no sign) ---" ;; -c) # constant shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID CONSTANT SPECIFICATION ---" #checkMinus "$1" constant=`expr "$1" : '\([-.0-9]*,[-.0-9]*\)'` [ "$constant" = "" ] && errMsg "--- CONSTANT=$constant MUST BE A COMMA DELIMITED PAIR OF POSITIVE OR NEGATIVE FLOATS ---" ;; -z) # zoom shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID ZOOM SPECIFICATION ---" checkMinus "$1" zoom=`expr "$1" : '\([.0-9]*\)'` [ "$zoom" = "" ] && errMsg "--- ZOOM=$zoom MUST BE A NON-NEGATIVE FLOATING POINT VALUE (with no sign) ---" test=`echo "$zoom <= 0" | bc` [ $test -eq 1 ] && errMsg "--- ZOOM=$zoom MUST BE A POSITIVE FLOATING POINT VALUE ---" ;; -m) # middle shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID MIDDLE SPECIFICATION ---" checkMinus "$1" middle=`expr "$1" : '\([0-9]*,[0-9]*\)'` [ "$middle" = "" ] && errMsg "--- MIDDLE=$middle MUST BE A COMMA DELIMITED PAIR OF NON-NEGATIVE INTEGERS (with no sign) ---" ;; -C) # colors shift # to get the next parameter # test if parameter starts with minus sign errorMsg="--- INVALID COLORS SPECIFICATION ---" checkMinus "$1" colors="$1" [ "$colors" = "" ] && errMsg "--- COLORS=$colors MUST BE A PROPER LIST OF COLOR VALUES ---" ;; -) # STDIN and end of arguments break ;; -*) # any other - argument errMsg "--- UNKNOWN OPTION ---" ;; *) # end of arguments break ;; esac shift # next option done # # get infile and outfile outfile="$1" fi # test that outfile provided [ "$outfile" = "" ] && errMsg "--- NO OUTPUT FILE SPECIFIED ---" # get width and height wd=`echo "$dimensions" | cut -dx -f1` ht=`echo "$dimensions" | cut -dx -f2` [ $wd -le 0 ] && errMsg "--- INVALID WIDTH PROVIDED ---" [ $ht -le 0 ] && errMsg "--- INVALID HEIGHT PROVIDED ---" # get constants if [ "$constant" != "" ]; then realc=`echo "$constant" | cut -d, -f1` imagc=`echo "$constant" | cut -d, -f2` fi # test for valid c test=`convert xc: -format "%[fx:($realc*$realc - $imagc*$imagc)<=4?1:0]" info:` [ $test -eq 0 ] && errMsg "--- INVALID VALUES FOR CONSTANT ---" # get middle if [ "$middle" = "" ]; then [ "$xoff" = "" ] && xoff=`convert xc: -format "%[fx:$wd/2]" info:` [ "$yoff" = "" ] && yoff=`convert xc: -format "%[fx:$ht/2]" info:` else xoff=`echo "$middle" | cut -d, -f1` yoff=`echo "$middle" | cut -d, -f1` fi [ $xoff -lt 0 -o $xoff -gt $wd ] && errMsg "--- INVALID X MIDDLE PROVIDED ---" [ $yoff -lt 0 -o $yoff -gt $ht ] && errMsg "--- INVALID Y MIDDLE PROVIDED ---" # create color lut colorArr=($colors) numcolors=${#colorArr[*]} str="" for ((i=0; iheight) { aspectw = (width/height); aspecth = 1; } else if (height>width) { aspectw = 1; aspecth = (height/width); } else { aspectw = 1; aspecth = 1; } for (row=0;row