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############################################################################
#
# 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
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