1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
|
#!/usr/bin/gnuplot
# Copyright 2012, 2013 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-PlanePath is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
# Usage: gnuplot sierpinski-triangle-replicate.gnuplot
#
# Plot points of the Sierpinski triangle by a bitwise-and to decide
# whether a given X,Y point should be plotted. Points not wanted are
# suppressed by returning NaN.
level=6
size=2**level
# Return X,Y grid coordinates ranging X=0 to size-1 and Y=0 to size-1,
# as t ranges 0 to size*size-1.
x(t) = int(t) % size
y(t) = int(t / size)
# Return true if the X,Y coordinates at t are wanted for the
# Sierpinski triangle.
want(t) = ((x(t) & y(t)) == 0)
triangle_x(t) = (want(t) ? x(t) : NaN)
triangle_y(t) = (want(t) ? y(t) : NaN)
set parametric
set trange [0:size*size-1]
set samples size*size
set key off
plot triangle_x(t),triangle_y(t) with points
pause 100
|
