hi all. sometimes feel am going in circles with this collatz thing. seems infinitely slippery & impossible to get traction sometimes. have tried to think sideways/outside the box so many times it leads to circus contortions. or maybe that movie pi? or [less alarmingly, more comically] feels like the roadrunner, wile e. coyote, and ACME™ dynamite. back to the drawing board. deja vu all over again. but thats how its gonna be solved someday right? sometimes to console myself I try to remember that rome wasnt built in a day, theres a reason its unsolved, & *its only a matter of coming up with another idea/the next experiment.*

this following idea just occurred to me today. its utterly simple yet it looks promising at the moment, or nanosecond. what do you think? it has a nice backstory as usual, somewhat in line with the last thread of thoughts, may write it up sooner or later. *hint:* its a case of “reverse engineering” and asking whether where there’s smoke, theres fire. and, why didnt I think of this a long time ago?

**Cyber-Zen Question:** what does this plot imply?

def f(x)
c = 0
x2 = x
while (x2 >= x)
while (x2.even?)
x2 >>= 1
end
x2 = x2 * 3 + 1
c += 1
end
return c
end
n = 5
l = []
i = 0
m = 0
c = 0
mx = 0
loop \
{
x = f(n)
n += 2
m += x
i += 1
if (m > 1.125 * mx) then
puts([i, m].join("\t"))
$stdout.flush
mx = m
m = 0
i = 0
c += 1
break if (c == 100)
end
}

hint: its inspired partly by this idea, basically looking at “integrated noise at different scales”. the variation in noise at different scales shows the self-similarity/scale-invariant/power-law properties of the collatz problem & its link to fractal properties.

def f(x)
c = 0
x2 = x
while (x2 >= x)
while (x2.even?)
x2 >>= 1
end
x2 = x2 * 3 + 1
c += 1
end
return c
end
def add(j)
n = 5
i = 0
m = 0
c = 0
t = 2 ** (j + 1)
loop \
{
x = f(n)
n += 2
m += x
i += 1
if (i == t) then
puts([t, m.to_f / t].join("\t"))
$stdout.flush
m = 0
i = 0
c += 1
break if (c == 100)
end
}
end
10.times { |i| add(i) }

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