x = 36, y = 36, rule = B3/S23
b2o$o$bo$2bo2bo$2bo2bo$4bo2$5b2o$5b4o2b2o$9b2o$8b2o$14bo$10bo3bob3o$
11bobo$12bo3bo$15bo$14b2o$13bo9bo$14b2o7bo$15b2o4bobo$16b2ob2o$17bobo
3b2o$18bo3bo$21bo5bo$22bo4bo$23bo2bo$25b2o$25bobo$27bo$27b2o$27b2o2b2o
$30bo2$31b2o2bo$33bobo$34bo!
137ben wrote:the "smallest spaceships" page at PD is outdated--a smaller c/6 diagonal spaceship was posted on these forums earlier
x = 23, y = 23, rule = B3/S23
20b2o$20b2o$19bo2bo$16b2obo2bo$22bo$14b2o3bo2bo$14b2o5bo$15bob5o$16bo
3$13b3o$13bo$11b2o$5b2o4bo$5b3o3bo$3bo4bo$3bo3bo$7bo$2b2obobo$2o5bo$2o
4b2o$2b4o!
quintopia wrote:... the sequence of ships which are slower than all smaller ships.
To considering this, one would need to order the spaceship velocities (is c/4 diagonal faster than c/4 orthogonal?).
I would like a sorting that is neither L-infinity nor Manhattan metric.
Mats wrote:quintopia: I'm having trouble following your argument. Is it an argument for L_1 or for L_inf? Or is it a mixture of both? You wrote: "Thus, the glider's travel is always less than or equal to the LWSS's travel time." In L_inf it's "less than" and in L_1 it's "equal". Exactly what do you mean by "always less than or equal"?
My sorting order gives c/2_ort > c/4_dia > c/4_ort. I find that intuitively correct. L_1 gives c/2_ort = c/4_dia and L_inf gives c/4_dia = c/4_ort. That's why I think it's worthwhile to consider other choices than L_inf and L_1.
Mats wrote:I guess this would be "L-very large but not infinity".
HartmutHolzwart wrote:IMHO the matter is settled for CGoL:
The most appropriate metric is L_1! This is because the proof of the speed limit is based on the fastest possible advance of a diagonal line. Please look up the details in other forum threads.
In that sense the glider is as fast as an LWSS.
I'm sorry but I'm still having problems understanding your argument. After substitution you get: "the glider's travel is always less than or equal to the c/4 ortogonal spaceship's travel time." In L_1 the glider is faster than a c/4 ortogonal spaceship.quintopia wrote:Substitute "a c/4 orthogonal spaceship" for every occurrence of LWSS and it should make more sense.
Why would you need a normed space to sort spaceship speeds?quintopia wrote:makes absolutely no sense. L_p is a set of normed spaces. There is no norm that satisfies your lexicographical ordering.
IMHO the matter is settled for CGoL:
The most appropriate metric is L_1! This is because the proof of the speed limit is based on the fastest possible advance of a diagonal line. Please look up the details in other forum threads.
In that sense the glider is as fast as an LWSS.
but the Euclidean metric doesn't really mean much in a Moore neighborhood.
Another counter example (you might need to View Image to see the right hand section):but the Euclidean metric doesn't really mean much in a Moore neighborhood.
x = 4, y = 3, rule = B3/S345
2o$2o$b3o!
# Draw a circle on the Golly plane
# Author: Tony Smith (ts@meme.com.au), July 2009.
# Single on state, all midline crossing cells on, assumes centred on ( -1/2, -1/2 )
use strict;
use warnings;
use POSIX;
my @line = ( 0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9 );
my $params = g_getstring("Enter the radius and thickness of the desired circle:",
"100 10", "Draw circle");
my ( $r, $t ) = split( /\s/, $params );
my $outer = $r + $t/2;
my $inner = $r - $t/2;
my $outer2 = $outer * $outer;
my $inner2 = $inner * $inner;
my ( @lines, $long );
for ( my $y = 0; $y < floor( $inner ); $y++ ) {
my $y2 = $y * $y;
my $xi = floor( sqrt( $inner2 - $y2 ) );
my $xo = ceil( sqrt( $outer2 - $y2 ) );
$long = $xo - $xi;
push( @lines, -1-$xo, $y, $long, $xi, $y, $long, -1-$xo, -1-$y, $long, $xi, -1-$y, $long );
}
for ( my $y = floor( $inner ); $y <= ceil( $outer ); $y++ ) {
my $y2 = $y * $y;
my $xo = ceil( sqrt( $outer2 - $y2 ) );
my $l = $xo + $xo + 1;
$long = $l if $l > $long;
push( @lines, -1-$xo, $y, $l, -1-$xo, -1-$y, $l );
}
my ( @long, $this );
while ( $long-- ) { push( @long, $this++, 0 ) }
while ( @lines ) {
my $x = shift @lines;
my $y = shift @lines;
my $l = shift @lines;
my @line = @long[ 0 .. 2*$l + 1 ];
g_putcells( \@line, $x, $y, 1, 0, 0, 1, 'or');
}
This shows B3/S345 run to 30,000 iterations from a small asymmetric seed:
Return to Other Cellular Automata
Users browsing this forum: onw and 2 guests