Created
May 27, 2019 22:22
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def f2(n) | |
return n.odd? ? (n * 3 + 1) / 2 : n / 2 | |
end | |
def dense(w, d) | |
w2 = w - 1 | |
a = (0...w2).to_a | |
s = '0' * w2 | |
(1..(d * w - 1)).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' } | |
return ('1' + s) | |
end | |
def back(n) | |
l = [n] | |
return (1..20).map \ | |
{ | |
l = l.map \ | |
{ | |
|x| | |
l1 = [x * 2] | |
l1 << (x - 1) / 3 if ((x - 1) % 3 == 0 && ((x - 1) / 3).odd?) | |
l1 | |
}.flatten | |
l | |
} | |
end | |
def seq(n) | |
n1 = n | |
l = [] | |
begin | |
l << n | |
n = f2(n) | |
end while (n != 1) | |
return l | |
end | |
def remove(a, ks) | |
a = a.dup | |
ks.each { |x| a.delete(x) } | |
return a | |
end | |
def count(ns) | |
l = seq(n = ns.to_i(2)) | |
cm1 = (0...l.size).max_by { |x| l[x] } | |
cg = l.index { |x| x < l[0] } | |
cg = l.size if (cg.nil?) | |
cm = (0..cg).max_by { |x| l[x] } | |
npo = Math.log(l[ns.length]) | |
return { | |
'ns' => ns, | |
'cm' => cm, | |
'cm1' => cm1, | |
'ls' => l.size.to_f / 10, | |
'cg' => cg, | |
'nl' => Math.log(n), | |
'npo' => npo | |
} | |
end | |
def sum(l) | |
t = 0.0 | |
l.each { |x| t += x } | |
return t | |
end | |
def avg(l) | |
return nil if (l.empty?) | |
return sum(l) / l.size | |
end | |
def trend(n) | |
l = (l1 = back(n)).map { |x| {'mn' => Math.log(x.min), 'mx' => Math.log(x.max), 'r' => Math.log(x.max) - Math.log(x.min), 'av' => avg(x.map { |x1| Math.log(x1) })} } | |
mn = l.map { |x| x['mn'] }.min | |
mx = l.map { |x| x['mx'] }.max | |
rmn = l.map { |x| x['r'] }.min | |
rmx = l.map { |x| x['r'] }.max | |
return {'n' => n, | |
'n3' => n % 3, | |
'n2' => n % 2, | |
'mn' => mn, | |
'mx' => mx, | |
'rmn' => rmn, | |
'rmx' => rmx, | |
'rrmn' => mn / Math.log(n), | |
'l1' => l1, | |
'l' => l | |
}.merge(count(n.to_s(2))) | |
end | |
def graph(k, f, l2) | |
l2.sort_by! { |x| x[k] } | |
f.puts("$dat << eof") | |
f.puts(l2[0].keys.join("\t")) | |
j = 0 | |
l2.each_with_index \ | |
{ | |
|x, c| | |
l = x['l'] | |
w = x['n'].to_s(2).length | |
l.each_with_index \ | |
{ | |
|x1, i| | |
f.puts([i, x1['av'] / w, c].join("\t")) | |
} | |
f.puts | |
} | |
f.puts('eof') | |
f.puts('plot $dat using 1:2:3 with line linecolor palette lw 1') | |
f.puts('pause -1') | |
end | |
l2 = [] | |
100.times { l2 << trend(dense(100, 0.5).to_i(2)) } | |
# l2.each { |x| p([x['cm'], x['cg']].join("\t")) }; exit | |
f = File.open('gnuplot.cmd', 'w') | |
graph('cm', f, l2) | |
graph('cg', f, l2) | |
f.close | |
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