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Author Topic: very simple sierpinski triangle in conways game of life  (Read 6552 times)
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cKleinhuis
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« on: April 11, 2014, 11:10:20 PM »

recently i am playing with a game of life simulator, because i stumbled over a very huge game of life pattern collection,
but what i wanted to discuss/publish is a simple sierpinski generator that is very easy to reproduce

use golly for simulation:
http://golly.sourceforge.net/


so, the thing is, draw a very long line
running the simulation yields a sierpinski triangle

and this is a nice wiki about game of life patterns:
http://www.conwaylife.com/wiki/Main_Page



* sierpinskilife.jpg (106.5 KB, 998x868 - viewed 946 times.)
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Dinkydau
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« Reply #1 on: April 20, 2014, 02:18:53 PM »

That's very cool. I didn't know so much was possible with the game of life, but I never actually played it before either. It's interesting that at first a sierpinski triangle indeed appears, but it becomes distorted as time goes on, until it's stable.
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youhn
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« Reply #2 on: April 20, 2014, 09:02:54 PM »

Check out replicator.rle in Golly !

Code:
#C All patterns in this rule replicate.
x = 13, y = 6, rule = B1357/S1357
b2o3bo2bo2bo$o2bo2bobo3bo$o2bo2b2o4bo$o2bo2bobo3bo$o2bo2bo2bo$b2o3bo2b
o2bo!

Watching it move is better than the slideshow. But to get an impression:















Dinkydau,
Thanks for brining this to our attention!
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cKleinhuis
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« Reply #3 on: April 20, 2014, 09:26:29 PM »


Dinkydau,
Thanks for brining this to our attention!


that menger replicator is cool, but it was me sad smiley
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youhn
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« Reply #4 on: April 20, 2014, 09:45:16 PM »

Oh, sorry  embarrass .. my bad. Thanks cKleinhuis!
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Dinkydau
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« Reply #5 on: April 20, 2014, 09:52:05 PM »

I've decided to make a line of length 2^16 = 65536 and let it iterate for a while. It took a very long time. The result is a better approximation:

Also the two triangles fit nicely together because of that power of 2.
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cKleinhuis
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« Reply #6 on: April 20, 2014, 11:32:17 PM »

it is very symetric, indeed, how did you count it ? i was unable to get the scripting running sad
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Dinkydau
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« Reply #7 on: April 21, 2014, 06:31:10 PM »

Golly displays the amount of living cells as the population. If you only have a line, the length of the line is the population. I drew the line with the pencil tool which was also quite difficult to do.
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cKleinhuis
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« Reply #8 on: April 21, 2014, 07:19:32 PM »

ah, sure, smiley
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marius
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« Reply #9 on: April 21, 2014, 10:04:12 PM »

ah, sure, smiley

.rle is also pretty easy to hack manually. I'd wager something like:

Code:
#draw line.
x = 65536, y = 1, rule = B3/S23
65536o$!

I added bunch of .lif lifeforms to boxplorer2 a while back, just running brute-force /w gpu.
And only at screen resolution. And with wrap-around.

Still, mesmerizing to watch how some of the more complex structures self-destruct.
E.g.
Code:
./boxplorer cfgs/syntopia/life/  --lifeform=fermatprimecalculator_106.lif
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knighty
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« Reply #10 on: April 23, 2014, 01:07:30 PM »

Crazy Mandelbrot set in gollycrazy eyes
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TheRedshiftRider
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« Reply #11 on: July 13, 2014, 03:49:25 PM »

Very interesting.

Ive also tried this:

I iterated this rule on four cell:

B2/S12345678

And this was the result, it looks like this is a fractal.


« Last Edit: July 13, 2014, 03:53:38 PM by Toofgib » Logged

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TheRedshiftRider
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« Reply #12 on: July 13, 2014, 04:29:47 PM »

And I found an other simple rule to make a siepinski triangle with a single dot:

w22
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kram1032
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« Reply #13 on: July 13, 2014, 09:01:04 PM »

Toofgib that's an awesome pattern! Nicely in between man-made corners and organic patterns. I really like the texture of it.
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TheRedshiftRider
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« Reply #14 on: August 17, 2014, 11:44:46 AM »

With these rules its also possible to create fractal patterns using the same method:

B2/S01234H
B3/S012345
B178/S124567
B12/S1234567
B13/S1234567
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