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############################################################################
#
# File: fstars.icn
#
# Subject: Procedure to produce traces of fractal stars
#
# Author: Ralph E. Griswold
#
# Date: May 23, 1996
#
############################################################################
#
# This file is in the public domain.
#
############################################################################
#
# This procedure produces traces of fractal "stars". For a discussion of
# fractal stars, see
#
# Fractals; Endlessly Repeated Geometrical Figures, Hans Lauwerier,
# Princeton University Press, 1991, pp. 72-77.
#
# and
#
# Geometric and Artistic Graphics; Design Generation with
# Microcomputers, Jean-Paul Delahaye, Macmillan, 1987, pp. 55-63.
#
# The arguments are:
#
# x, y, n, p, r, incr, extent
#
# x x coordinate of the initial point, default 0
# y y coordinate of the initial point, default 0.5
# n number of vertices, default 5
# p number of phases, default 5
# r reduction factor, default 0.35
# incr angular increment factor, default 0.8
# extent extent of drawing, 1.0
#
# Chosing values for these arguments that produce interesting results and
# centering the star in the window is somewhat of an art. See fstartbl.icn
# for some good values.
#
############################################################################
#
# Links: gobject
#
############################################################################
link gobject
global size
procedure fstar(x, y, n, p, r, incr, extent, xinit, yinit) #: fractal stars
local angle, i, h, m, dist, xloc, yloc
/size := 500
/x := 0
/y := 0.5 * size
/n := 5 # defaults
/p := 5
/r := 0.35
/incr := 0.8
/extent := 1.0
/xinit := 0
/yinit := 0.5
incr *:= &pi # scaling
extent *:= size
xloc := xinit * size
yloc := yinit * size
n -:= 1 # computational convenience
p -:= 1
# suspend Point(x + xloc, y + yloc) # initial point
angle := 0
every i := 0 to ((n + 1) * n ^ p) do {
m := i
h := 0
until (m % n ~= 0) | (h >= p) do {
m /:= n
h +:= 1
}
dist := extent * r ^ (p - h)
xloc +:= dist * cos(angle)
yloc +:= dist * sin(angle)
suspend Point(x + xloc, y + yloc)
angle +:= incr
}
end
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