#!/usr/bin/gnuplot
# Author: Ika
# Date: 12/02/2014

# last changes:
# 2018-01-28: (JoKalliauer) instead of 50 plots with one line one plot with 50 lines, and only the first has a key 

set term svg font 'Liberation Sans, 24'
set output 'envelope_string_art.svg'

# In this program, the envelope equation is x^2 - 2xy + y^2 -2kx - 2ky + k^2 = 0. 
# In other words, the family of the string lines is y = -(k-t)x/t + k-t. 
# Each line connects (0, k-t) and (t, 0).
# Here k takes value 1.
k = 1;
# n is the number of the trajectories
n = 51;

set multiplot
set samples 1000

set xrange [0:k]
set yrange [0:k]
set xtics 0.2
set ytics 0.2
set xzeroaxis lt -1 lc rgb "black" lw 1
set yzeroaxis lt -1 lc rgb "black" lw 1

unset label

set key on

#t = i*k*1.0/n;
# The following draws the lines iteratively.

plot -1*(k-(1*k*1.0/n))*x/(1*k*1.0/n) + k-(1*k*1.0/n) t "k = 1" lc rgb "red" lw 1, \
	for [i=2:n-1] -1*(k-(i*k*1.0/n))*x/(i*k*1.0/n) + k-(i*k*1.0/n) notitle lc rgb "red" lw 1;

unset multiplot

set term x11
set output