############################################################################
#
#	File:     cquilts.icn
#
#	Subject:  Program to create "chaotic square quilts"
#
#	Author:   Ralph E. Griswold
#
#	Date:     March 14, 1995
#
############################################################################
#
#   This file is in the public domain.
#
############################################################################
#
#  This program creates square quilting patterns as described in
#  "Symmetry in Chaos", Michael Field and Martin Golubitsky, Oxford
#  University Press, 1992.
#
#  Instead of plotting an image, the values are computed and saved
#  in "numerical carpets" for off-line plotting.
#
#  The following options are supported:
#
#	-i i	Save carpet files every i iterations; default 100000
#
#	-p s	Prefix for carpet file names, default q_
#
#	-t i	Terminate execution after i iterations; default no limit
#
#  Warning:  This program takes a long time to go through enough iterations
#  to produce nice results.
#
#  Note:  This is an unfinished work, supplied for interest only.
#
#  There are several sections of parameter values below.  All but one
#  is commented out.  Change this to get other patterns.
#
############################################################################
#
#  Requires:  Version 9 graphics
#
############################################################################
#
#  Links:  matrix, options, writecpt
#
############################################################################

link matrix
link options
link writecpt

global pi_2
global pi_4
global pi_6

$define Size 200

procedure main(args)
   local x, y, xnew, ynew, lambda, alpha, beta, gamma, omega, ma, shift
   local mcount, sx, sy, xp, yp, max, min, i
   local count, prefix, iter, opts, interval, limit

   pi_2 := 2 * &pi
   pi_4 := 4 * &pi
   pi_6 := 6 * &pi

   iter := 0
   count := -1

   opts := options(args, "i+p:t+")

   interval := \opts["i"] | 100000
   prefix := \opts["p"] | "q_"
   limit := \opts["t"]

   xnew := x := 0.1
   ynew := y := 0.334

# Sugar and Spice

#  lambda := -0.59
#  alpha := 0.2
#  beta := 0.1
#  gamma := -0.27
#  omega := 0.0
#  ma := 0.0
#  shift := 0.5

# Emerald Mosaic

#  lambda := -0.59
#  alpha := 0.2
#  beta := 0.1
#  gamma := -0.33
#  omega := 0.0
#  ma := 2.0
#  shift := 0.0

# Sicilian Tile

#  lambda := -0.2
#  alpha := -0.1
#  beta := 0.1
#  gamma := -0.25
#  omega := 0.0
#  ma := 0.0
#  shift := 0.0

# Roses

#  lambda := 0.25
#  alpha := -0.3
#  beta := 0.2
#  gamma := 0.3
#  omega := 0.0
#  ma := 1.0
#  shift := 0.0

# Wagon Wheels

#  lambda := -0.28
#  alpha := 0.25
#  beta := 0.05
#  gamma := -0.24
#  omega := 0.0
#  shift := 0.0
#  ma := -1.0

# Victorian Tiles

#  lambda := -0.12
#  alpha := -0.36
#  beta := 0.18
#  gamma := -0.14
#  omega := 0.0
#  shift := 0.5
#  ma := 1.0

# Mosque

#  lambda := 0.1
#  alpha := 0.2
#  beta := 0.1
#  gamma := 0.39
#  omega := 0.0
#  shift := 0.0
#  ma := -1.0

# Red Tiles

#  lambda := -0.589
#  alpha := 0.2
#  beta := 0.04
#  gamma := -0.2
#  omega := 0.0
#  shift := 0.5
#  ma := 0.0

# Cathedral Attractor

#  lambda := -0.28
#  alpha := 0.08
#  beta := 0.45
#  gamma := -0.05
#  omega := 0.0
#  shift := 0.5
#  ma := 0.0

# Gyroscopes

#  lambda := -0.59
#  alpha := 0.2
#  beta := 0.2
#  gamma := 0.3
#  omega := 0.0
#  shift := 0.0
#  ma := 2.0

# Cats Eyes

#  lambda := -0.28
#  alpha := 0.25
#  beta := 0.05
#  gamma := -0.24
#  omega := 0.0
#  shift := 0.5
#  ma := -1.0

# Flowers with Ribbons

   lambda := -0.11
   alpha := -0.26
   beta := 0.19
   gamma := -0.059
   omega := 0.07
   shift := 0.5
   ma := 2.0

   mcount := create_matrix(Size, Size, 0)

   repeat {

      # iterate
      sx := sin(pi_2 * x)
      sy := sin(pi_2 * y)
      xnew := (lambda + alpha * cos(pi_2 * y)) * sx - omega * sy + beta *
         sin(pi_4 * x) + gamma * sin(pi_6 * x) * cos(pi_4 * y) + ma *
         x + shift
      ynew := (lambda + alpha * cos(pi_2 * x)) * sy + omega * sx + beta *
         sin(pi_4 * y) + gamma * sin(pi_6 * y) * cos(pi_4 * x) + ma *
         y + shift
      if xnew > 1.0 then xnew -:= integer(xnew)
      else if xnew < 0.0 then xnew +:= integer(-xnew) + 1
      if ynew > 1.0 then ynew -:= integer(ynew)
      else if ynew < 0.0 then ynew +:= integer(-ynew) + 1
      x := xnew
      y := ynew

      xp := integer(Size * x)
      yp := integer(Size * y)
      mcount[xp + 1, yp + 1] +:= 1
      iter +:= 1
      if iter % \interval = 0 then {
         max := 0
         min := 2 ^ 31
         every i := mcount[1 to Size, 1 to Size] do {
            max <:= i
            min >:= i
            }
         if min < 0 then min := 0
         write_cpt(prefix || right(count +:= 1, 3, "0") || ".cpt",
            mcount, min, max)
         }
      if iter >= \limit then exit()
      }

end