############################################################################
#
#	File:     mandel2.icn
#
#	Subject:  Program to draw the Mandelbrot set
#
#	Author:   Roger Hare
#
#	Date:     June 17, 1994
#
############################################################################
#
#   This file is in the public domain.
#
############################################################################
#
# This program draws portions of the Mandelbrot set according to the values
# input # on the command line. The method is that described in the articles by
# Dewdney # in the Computer Recreations column of Scientific American in August
# '85, # October '87 and February '89.
#
# I have problems with colours (not enough of 'em!), so I have used alternated
# black and white. Those with decent X-terminals will be able to do far
# better than me.
#
# The program certainly doesn't display images as striking as those seen 
# in publications. Perhaps the scaling of the value of k needs to be
# different? All suggestions gratefully received.
#
# It is possible to speed things up by displaying the points row by row
# rather than randomly, but as the program is resident in the 100 cycle
# iteration most of the time, this is only ~5% speed-up. Not really
# worth it.
#
# One of Dewdney's articles mentions other methods to speed things up - I 
# will search out the algorithms one of these days...
#
# Usage is - xmand startr startc size n &
#
# where:
#
# startr, startc are the co-ordinates of the lower left hand corner of the
#  area of the complex plane to be displayed
# size is the size of the (square) area of the complex plane to be displayed
# n is the number of pixels into which size is to be divided for display
#  purposes
#
# For example - xmand -1.5 -1.25 2.5 400 &
# 
# will display the Mandelbrot set in the 2.5x2.5 region of the complex plane
# whose s-w corner is -1.5-i1.25. The display will be 400x400 pixels.
#
# The program has been tested on a Sun 4 using the Icon compiler, and 
# on a Sequent Symmetry running Version 5 Unix using both the
# compiler and translator.
#
############################################################################
#
#  Links:  random, wopen
#
############################################################################
#
#  Requires:  Version 9 graphics
#
############################################################################

link random
link wopen

procedure main(args)
   local a, b, c, colours, coords, events, gap, i, k, n, r, size
   local startc, startr, t, x, xmand, y

# check the number of arguments - if it's not 4, select 4 arbitrary values
if *args == 4
then {startr:=args[1]
      startc:=args[2]
      size:=args[3]
      n:=args[4]
      n:=integer(n)}
else {startr:=-1.5
      startc:=-1.25
      size:=2.5
      n:=200}

# set max size to 400
if (n>400) then n:=400

# calculate 'size' of each pixel
gap:=size/n

# open window
xmand:=WOpen("label=xmand", "height="||n+40,
   "width="||n+40) | stop("Can't open xmand")

# set colours to be 5 cycles of alternating black & white - this for the
# benefit of those with monochrome screens, or (like me!), a crummy palette.
colours:=["black","white"]
colours:=colours|||colours|||colours|||colours|||colours

# write image info in window
GotoXY(xmand,20,35+n)
writes(xmand,startr," ",startc," ",size," ",n)

# this bit coupled with counting y *downwards* later, effectively means that
# the image in the X-window is 'right way up' for those who live in a 
# cartesian world.
startc+:=size

# set up co-ordinates, one for every point in the display and randomize
coords:=list(n*n,0)
every i:=1 to n*n
do coords[i]:=i-1
randomize()
every !coords:=:?coords

# main loop
every i := 1 to n*n
do {t:=get(coords)

# compute random x,y value from co-ordinate
    x:=(t/n)
    y:=(t%n)

# compute value of this x,y point in complex plane - count downwards in
# y direction to get image 'right way up'
    r:=startr+x*gap
    c:=startc-y*gap
    a:=0
    b:=0

# and calculate if point is in set or not
    every k:=1 to 100
    do {t:=a*a-b*b+r
        b:=2*a*b+c
        a:=t
        if (a*a+b*b) > 4.0 then break}

# scale final value of k to one of range of colours
# subtract 1 to put in range 0->99; divide by 10 to put in range 0->9
# add 1 to put in range 1->10 - I have 10 'colours' selected
# this scaling gives fairly unexciting displays, is there a better scaling
# (eg: logarithmic, square root, w.h.y)?
    k-:=1
    k/:=10
    k+:=1

# and display
    Fg(xmand,colours[k])
    DrawPoint(xmand,(x+20),(y+20))

# this bit bales out of loop if left button is pressed
    if (events:=Pending(xmand)) & (*events > 0)
    then if Event(xmand)==&lpress
            then break}
WFlush(xmand)

# just close the window and exit when it is finished
Event(xmand)

end