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############################################################################
#
# File: sier.icn
#
# Subject: Program for generalized Sierpinski's triangle
#
# Author: Gregg M. Townsend
#
# Date: June 10, 2004
#
############################################################################
#
# This file is in the public domain.
#
############################################################################
#
# Originally inspired by the Nova television show on chaos.
# Colorization suggested by Kenneth Walker.
#
############################################################################
#
# This program constructs Sierpinski's triangle using an iterative
# method. An initial point is chosen (by clicking the mouse inside the
# triangle) and marked. Then, the program repeatedly moves half way to
# a randomly chosen vertex and plots a point in the color corresponding
# to the vertex.
#
# The polygon need not be a triangle. The number of sides may be given
# as a command line argument, or a digit 3 through 9 or 0 through 2 may be
# pressed to establish a new polygon of 3 to 12 sides.
#
# The S, G, E, and Q keys function identically to the Stop, Go, Erase,
# Quit pushbuttons.
#
############################################################################
#
# Requires: Version 9 graphics
#
############################################################################
#
# Links: button, evmux, random, graphics
#
############################################################################
link button
link evmux
link random
link graphics
$define BevelWidth 2
$define WindowMargin 10
global win, bwin, vwin, vcolors
global m, w, h
global nsides, xpos, ypos, outline
global running, xcur, ycur
procedure main(args)
local i, vcolors
win := Window("size=400,400", "font=Helvetica,bold,14", "bg=pale gray", args)
nsides := integer(args[1]) | 3
if nsides < 3 then stop("sierpinski: need at least 3 sides!")
m := WindowMargin
h := WAttrib("height") - 2 * m # usable height
w := WAttrib("width") - 2 * m # usable width
# make a window (g.c.) for drawing in background color
bwin := Clone(win)
Fg(bwin, Bg(win))
# make a color for each vertex
vcolors := [
"deep green",
"dark red",
"dark blue",
"deep red-magenta",
"dark cyanish blue",
"dark red-orange",
"deep purple",
"deep cyan",
"deep brown",
"deep orangish red",
"deep purple",
"dark cyanish blue"
]
vwin := []
if WAttrib(win, "depth") > 2 then
every put(vwin, Clone(win, "fg=" || !vcolors))
else
put(vwin, win)
# configure and draw the polygon
configure()
erase()
# set up buttons and character handlers
button(win, "Go", setfill, 0, m, m, 50, 20)
button(win, "Stop", setfill, -1, m, m + 30, 50, 20)
button(win, "Erase", argless, erase, m + w - 50, m, 50, 20)
button(win, "Quit", argless, exit, m + w - 50, m + 30, 50, 20)
sensor(win, 'Gg', setfill, 0)
sensor(win, 'Ss', setfill, -1)
sensor(win, 'Ee', argless, erase)
quitsensor(win) # enable Q-for-quit etc.
sensor(win, '3456789012', setsides)
# set up sensor for drawing the curve
sensor(win, &lrelease, setfill, 1, m, m, w, h)
# process events
randomize()
i := 1
repeat {
while *Pending(win) > 0 | running < 0 do
evhandle(win)
every 1 to 100 do {
DrawPoint(vwin [i | 1], xcur, ycur)
i := ?nsides
xcur := (xcur + xpos[i]) / 2
ycur := (ycur + ypos[i]) / 2
}
}
end
# configure() -- set vertex points
procedure configure()
local a, da, i
local xmin, xmax, xscale, ymin, ymax, yscale
# ensure we have enough windows for the vertices
while *vwin < nsides do
vwin |||:= vwin
# get coordinates for vertices as points on a radius-1 circle
da := 2 * &pi / nsides
a := 1.5 * &pi - da / 2
if nsides = 4 then
a +:= &pi / 12
xpos := list(nsides)
ypos := list(nsides)
every i := 1 to nsides do {
xpos[i] := cos(a)
ypos[i] := sin(a)
a -:= da
}
# now scale to available window size
# also make coord list for drawing outline
xmin := xmax := ymin := ymax := 0.0
every xmin >:= !xpos
every xmax <:= !xpos
every ymin >:= !ypos
every ymax <:= !ypos
xscale := w / (xmax - xmin)
yscale := h / (ymax - ymin)
outline := [win]
every i := 1 to nsides do {
put(outline, m + xscale * (1.01 * xpos[i] - xmin))
put(outline, m + h - yscale * (1.01 * ypos[i] - ymin))
xpos[i] := m + xscale * (xpos[i] - xmin)
ypos[i] := m + h - yscale * (ypos[i] - ymin)
}
put(outline, outline[2])
put(outline, outline[3])
end
# erase(gc) -- erase the polygon and draw its outline
procedure erase(gc)
outline[1] := bwin
FillPolygon ! outline
outline[1] := \gc | win
DrawLine ! outline
running := -1
xcur := m + w / 2
ycur := m + h / 2
return
end
# setfill(win, n, x, y) -- start/stop filling points according to n
#
# n<0 stop
# n=0 start, from current point
# n>0 start, from (x,y)
procedure setfill(win, n, x, y)
if n > 0 then {
xcur := x
ycur := y
}
if n >= 0 then {
outline[1] := bwin
DrawLine ! outline # erase outline
}
running := n
return
end
# setsides(win, dummy, x, y, event) - reset the number of sides
procedure setsides(win, dummy, x, y, event)
nsides := integer(event)
if nsides < 3 then nsides +:= 10
erase(bwin)
configure()
erase()
end
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