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############################################################################
#
# File: lorenz.icn
#
# Subject: Program to display Lorenz strange attractor
#
# Author: Ralph E. Griswold
#
# Date: December 5, 1995
#
############################################################################
#
# This file is in the public domain.
#
############################################################################
#
# This is a barebones version of a display of the Lorenz strange
# attractor. It has deliberately been left simple and free of options so
# that the basic idea is clear and so that it can be used as the basis of
# more capable versions.
#
# This program is based on material given in "Fractal, Programming in
# Turbo Pascal", Roger T. Stevens, M&T Books, 1990.
#
############################################################################
#
# Requires: Version 9 graphics
#
############################################################################
#
# Links: numbers, wopen
#
############################################################################
link numbers
link wopen
procedure main()
local col, color, colorlist, cx, cy, cz, d0_x, d0_y, d0_z, d1_x
local d1_y, d1_z, d2_x, d2_y, d2_z, d3_x, d3_y, d3_z, dt, dt2
local i, old_col, old_row, old_y, row, sx, sy, sz, x, x_angle
local xt, y, y_angle, yt, z, z_angle, zt
x_angle := rtod(45)
sx := sin(x_angle)
cx := cos(x_angle)
y_angle := rtod(0)
sy := sin(y_angle)
cy := cos(y_angle)
z_angle := rtod(90)
sz := sin(z_angle)
cz := cos(z_angle)
WOpen("label=Lorenz", "width=640", "height=350",
"fg=white", "bg=black") | stop("*** cannot open window")
colorlist := ["red", "blue", "green", "magenta", "cyan", "yellow"]
color := colorlist[1]
x := 0.0
y := 1.0
z := 0.0
old_col := round(y * 9 + 320)
old_row := round(350 - 6.56 * z)
dt := 0.01
dt2 := dt / 2
every i := 0 to 8000 do {
d0_x := 10 * (y-x) * dt2
d0_y := (-x * z + 28 * x - y) * dt2
d0_z := (x * y - 8 * z / 3) * dt2
xt := x + d0_x
yt := y + d0_y
zt := z + d0_z
d1_x := (10 * (yt-xt)) * dt2
d1_y := (-xt * zt + 28 * xt - yt) * dt2
d1_z := (xt * yt - 8 * zt / 3) * dt2
xt := x + d1_x
yt := y + d1_y
zt := z + d1_z
d2_x := (10 * (yt-xt)) * dt
d2_y := (-xt * zt + 28 * xt - yt) * dt
d2_z := (xt * yt - 8 * zt / 3) * dt
xt := x + d2_x
yt := y + d2_y
zt := z + d2_z
d3_x := (10 * (yt - xt)) * dt2
d3_y := (-xt * zt + 28 * xt - yt) * dt2
d3_z := (xt * yt - 8 * zt / 3) * dt2
old_y := y
x := x + (d0_x + d1_x + d1_x + d2_x + d3_x) * 0.333333333
y := y + (d0_y + d1_y + d1_y + d2_y + d3_y) * 0.333333333
z := z + (d0_z + d1_z + d1_z + d2_z + d3_z) * 0.333333333
col := round(y * 9 + 320)
row := round(350 - 6.56 * z)
if col < 320 then
if old_col >= 320 then {
color := get(colorlist)
put(colorlist, color)
}
else if col > 320 then
if old_col <= 320 then {
color := get(colorlist)
put(colorlist, color)
}
Fg(color)
DrawLine(old_col, old_row, col, row)
old_row := row
old_col := col
}
Event()
end
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