Created
June 7, 2019 02:25
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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(n) | |
l = seq(n) | |
ns = n.to_s(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 { | |
'n' => n, | |
'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 graph(f, l2, t) | |
f.puts("$dat << eof") | |
f.puts(l2[0].keys.join("\t")) | |
j = 0 | |
l2.each_with_index \ | |
{ | |
|x, c| | |
l = x['l2'].flatten | |
w = x['n'].to_s(2).length | |
l.each_with_index \ | |
{ | |
|x1, i| | |
f.puts([i, x1, c].join("\t")) | |
} | |
f.puts | |
} | |
f.puts('eof') | |
f.puts("set title '#{t}'; set key top left; plot $dat using 1:2:3 with point linecolor palette lw 1 pt 5 ps 0.25") | |
f.puts('pause -1') | |
end | |
def dense3(w, d) | |
begin | |
ns = dense(w, d) | |
n = ns.to_i(2) | |
end while (n % 3 == 0) | |
return n | |
end | |
def dist(k) | |
s = {} | |
l = [] | |
1e4.to_i.times \ | |
{ | |
x = count(dense3(100, 0.5)) | |
next if (s.member?(x[k])) | |
s[x[k]] = nil | |
l << x | |
} | |
return l.sort_by { |x| x[k] } | |
end | |
def sample(l, c) | |
return l if (l.size < c) | |
r = l.size / c | |
l2 = *(0...l.size).select { |x| x % r == 0 } | |
l2[c..-1] = [] | |
return l.values_at(*l2) | |
end | |
def sample2(l, c) | |
s1 = l.size | |
l = sample(l, c) | |
s2 = l.size | |
$stderr.puts({'s1' => s1, 's2' => s2}.inspect) | |
return l | |
end | |
def trend2(x) | |
n = x['n'] | |
l = back(n) | |
l2 = l.map { |l1| sample(l1.map { |x| Math.log(x) }, 10) } | |
return {'l2' => l2}.merge(count(n)) | |
end | |
def process(f, l2, t) | |
l2.sort_by! { |x| x['cm'] } | |
graph(f, l2, t) | |
end | |
f = File.open('gnuplot.cmd', 'w') | |
c = 40 | |
process(f, (1..c).map { trend2(count(dense3(100, 0.5))) }, 'dist1') | |
process(f, sample2(dist('cm'), c).map { |x| trend2(x) }, 'dist2') | |
f.close | |
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