Hello,
Thanks for your interest about the 8-bits binary counter.
I share that point of view about the strange fact that the binary
counter cannot apparently be as compact as the trinary counter is.
Sad also to see that the basic principle of using tunnels in my
counter restrict to 8 bits (the limited number of tunnels available
in LT) any binary counter based on that principle.
Is the perfect binary counter still to find ?
That level is also not as clean-looking as I hoped, as Donald found
shortcuts that were to be eliminated.
Was the reset also avoidable ? I don't know but thanks again to
Donald for finding an elegent automatic reset.
A sexagesimal counter would be interesting to build a clock.
For that, given a binary and a trinary counter, a "quinary" counter
would be necessary.
To generalize, "p-inary" counters, with p prime, could be used to
built counters of any base.
The idea of using cellular automata ideas with LT is obviously very
tempting and I could not help have a thought on how to extend the
Game of Life into LT particularly.
Building oscillators of any period is easy.
One can also guess what a ship or a glider can look like, starting
with a simple movable block.
But what would a period-n gun look like ? a rake, or a puffer ?
How can a global population grow ?
LT seems limited in the fact that birth on a square seems
necessairily linked to death on another square.
The very nice level "a very long week", seen at maximum speed,
resembles very much a cellular automata, but is it one ? What are
the rules ?
A difficult chalenge, now : can one build a universal turing machine
with LT (supposing the grid is not limited to 16x16) ? Or can one
demonstrate it is not possible ?
I like to think it is possible, considering what LT can do.
But I will not dare search for one. ;-)
Finding a universal Turing machine whould place LT among those other
fascinating objects "that can do everything".
Alexis Monnerot
Thanks for your interest about the 8-bits binary counter.
I share that point of view about the strange fact that the binary
counter cannot apparently be as compact as the trinary counter is.
Sad also to see that the basic principle of using tunnels in my
counter restrict to 8 bits (the limited number of tunnels available
in LT) any binary counter based on that principle.
Is the perfect binary counter still to find ?
That level is also not as clean-looking as I hoped, as Donald found
shortcuts that were to be eliminated.
Was the reset also avoidable ? I don't know but thanks again to
Donald for finding an elegent automatic reset.
A sexagesimal counter would be interesting to build a clock.
For that, given a binary and a trinary counter, a "quinary" counter
would be necessary.
To generalize, "p-inary" counters, with p prime, could be used to
built counters of any base.
The idea of using cellular automata ideas with LT is obviously very
tempting and I could not help have a thought on how to extend the
Game of Life into LT particularly.
Building oscillators of any period is easy.
One can also guess what a ship or a glider can look like, starting
with a simple movable block.
But what would a period-n gun look like ? a rake, or a puffer ?
How can a global population grow ?
LT seems limited in the fact that birth on a square seems
necessairily linked to death on another square.
The very nice level "a very long week", seen at maximum speed,
resembles very much a cellular automata, but is it one ? What are
the rules ?
A difficult chalenge, now : can one build a universal turing machine
with LT (supposing the grid is not limited to 16x16) ? Or can one
demonstrate it is not possible ?
I like to think it is possible, considering what LT can do.
But I will not dare search for one. ;-)
Finding a universal Turing machine whould place LT among those other
fascinating objects "that can do everything".
Alexis Monnerot
--- In [email protected], "Steve" <stephen.ryan@3...> wrote:
>
> Donald & Alexis-
> "Horst Ledpeddle" is indeed interested in the new binary levels,
> don't get me started, oop too late.
>
> Very nice. How appropriate that it is two people that share the
new
> world binary record of "256" for binary counting in LT.
> Congratulations!
>
> Your new levels resemble the architecture of an IC (integrated
> circuit). It's interesting that the binary math done on LT is (so
> far) large and clunky and not automatic (it requires complex user
> input), but the trinary cells are more compact and the levels are
> either automatic or require only simple input. I never did find an
> automatic binary counter or other bases except trinary. Maybe
> someday...
>
> here's the other base number systems-
> 2 binary
> 3 ternary/trinary
> 4 quaternary
> 5 quinary
> 6 senary
> 7 septenary
> 8 octal
> 9 nonary
> 10 decimal
> 11 undenary
> 12 duodecimal
> 16 hexadecimal
> 20 vigesimal
> 60 sexagesimal
>
> If you think binary and trinary are fun, then the sexagesimal
system
> must be a real blast! (nudge, wink)
>
> Hey, what about "unary"!? What would this level look like? In base
> one, there is only one state, so it would require a level that
could
> not change, like a tank with 255 solid blocks. what a fun level
that
> will be - hours and hours of fun! you couldn't even die.
>
> To my knowledge, only binary and trinary/ternary have been
> demonstrated in LT. But, since base 2 and 3 have been done, then,
by
> definition, bases for combinations of these have been done, ie.
base
> 2, 4, 8, 16 up to 256, and base 3, 9, 27 up to 3^30. Also, with
some
> fiddling, one could create an adapter and "plug" a small binary
> counter into a small trinary counter and start to get some multi-
base
> math going, eg. (count to 8) x (count to 9) = (base-72 math), or
> 3x4=12 (duodecimal).
>
> I haven't seen his calculations, but Eric Schmidt wrote:
> "30-trit counter based on Trinary Counter VI.
> 10,122,384,296,788,923 moves, 4 shots"
> (Trinary Counter VII)
> (#27, Special-I_No-LPB.lvl)
> (Eric Schmidt)
>
> I have also been working on a calculation that will give the
> theoretical upper limit that can be counted by any level in LT,
i.e.
> the number of states possible in a non-repeating series of states.
> The playing surface is finite, there are a finite number of
objects,
> and LT is completely governed by cause and effect. This means that
> there is a finite number of possible states, each with exactly one
> resulting state for each of a finite number of actions. Seems a
> little sad, for some reason...
>
> Another topic is that of complexity arising from simple initial
> conditions (chaos from order). There is at least one extremely
> interesting technique that may be able to produce some very large
> numbers:
>
> "A very long week"
> (#352, Special-I.lvl)
> (Indybob@y...)
>
>
> "A very long week (Mod.)"
> (#17, Special-I_No-LPB.lvl)
> (Indybob@y...)
> (mod. by Suyono)
>
> "A Long Wait"
> (#21, Special-I_No-LPB.lvl)
> (Jay B)
>
> The lpb (2 moves) for "A very long week" (#352, Special-I.lvl) can
be
> watched very much speeded up with "f8" and sound "off" to see the
> progression to the end in just a few minutes. The reason it is
> interesting is because the cells are small and many (movable
> mirrors), the number of states are large, and it
resembles "cellular
> automatons", a term from the field of "artificial life" (different
> from "artificial intelligence"). The most famous and successful
> example was "Conway's Life" originally played on paper, and now a
> program available widely on-line. The math of this approach is
> difficult, and the level itself becomes the calculator. I made my
own
> lpb, but perhaps Donald would like to put the lpb on the playback
> page?
> http://pages.globetrotter.net/lasertank/LT_Utility/playback.htm
> Indeed, "A very long week" looks very much alive using "f8".
>
> -steve