Smallest block duplicator ever.

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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Alegend
Posts: 31
Joined: October 5th, 2009, 3:20 pm

Smallest block duplicator ever.

Post by Alegend » October 17th, 2009, 5:14 pm

Here it is:

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x = 10, y = 10, rule = B3/S23
$8bo$7bo$6bo$5bo$4bo$3bo$b2o$b2o!
Here comes a simlar one:

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x = 18, y = 18, rule = B3/S23
$16bo$15bo$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$b2o$b
2o!
And another:

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x = 26, y = 26, rule = B3/S23
$24bo$23bo$22bo$21bo$20bo$19bo$18bo$17bo$16bo$15bo$14bo$13bo$12bo$11bo
$10bo$9bo$8bo$7bo$6bo$5bo$4bo$3bo$b2o$b2o!

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x = 34, y = 34, rule = B3/S23
$32bo$31bo$30bo$29bo$28bo$27bo$26bo$25bo$24bo$23bo$22bo$21bo$20bo$19bo
$18bo$17bo$16bo$15bo$14bo$13bo$12bo$11bo$10bo$9bo$8bo$7bo$6bo$5bo$4bo$
3bo$b2o$b2o!

Sokwe
Moderator
Posts: 2859
Joined: July 9th, 2009, 2:44 pm

Re: Smallest block duplicator ever.

Post by Sokwe » October 17th, 2009, 5:53 pm

It generally is not considered a block if it is directly connected to the rest of the pattern. What you've come across is a fuse that leaves a block at one end, and leaves another block if the length of the pattern is divisible by 8. This has the disadvantage that it is difficult to synthesize, and so has few practical uses (at least that I can see). Also, two sparks are sufficient to create four blocks via lumps of muck:

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oo...
.....
..oo.
..oo.
.....
....o
-Matthias Merzenich

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