Thanks Steve
I don't understand all that's in your message but
that's surely very interesting for math lovers.
I had a lot of fun watching the pattern on http://www.ibiblio.org/lifepatterns/ (Conway's Life)
I had a lot of fun watching the pattern on http://www.ibiblio.org/lifepatterns/ (Conway's Life)
and yes I'll add the LPB if you send it to
me.
Donald
----- Original Message -----From: SteveSent: Sunday, February 06, 2005 12:42 PMSubject: Re: If you like MATH
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)
([email protected])
"A very long week (Mod.)"
(#17, Special-I_No-LPB.lvl)
([email protected])
(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