#!/usr/bin/gnuplot # Copyright 2012 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 . # Usage: gnuplot sierpinski-triangle-replicate.gnuplot # # Plot points of the Sierpinski triangle by replicating sub-parts of # the pattern according to parameter t in ternary. # # The alignment relative to the Y axis can be changed by what # digit_to_x() does. For example to plot half, # # digit_to_x(d) = (d<2 ? 0 : 1) # # triangle_x(n) and triangle_y(n) return X,Y coordinates for the # Sierpinski triangle point number n, for integer n. triangle_x(n) = (n > 0 ? 2*triangle_x(int(n/3)) + digit_to_x(int(n)%3) : 0) triangle_y(n) = (n > 0 ? 2*triangle_y(int(n/3)) + digit_to_y(int(n)%3) : 0) digit_to_x(d) = (d==0 ? 0 : d==1 ? -1 : 1) digit_to_y(d) = (d==0 ? 0 : 1) # Plot the Sierpinski triangle to "level" many replications. # "trange" and "samples" are chosen so the parameter t runs through # integers t=0 to 3**level-1, inclusive. # level=6 set trange [0:3**level-1] set samples 3**level set parametric set key off plot triangle_x(t), triangle_y(t) with points pause 100