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Fractal Math, Chaos Theory & Research => General Discussion => Topic started by: cKleinhuis on April 11, 2014, 11:10:20 PM




Title: very simple sierpinski triangle in conways game of life
Post by: cKleinhuis 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/
(http://golly.sourceforge.net/ticker.gif)

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



Title: Re: very simple sierpinski triangle in conways game of life
Post by: Dinkydau 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.


Title: Re: very simple sierpinski triangle in conways game of life
Post by: youhn 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:

(http://i.imgur.com/wDMEkqm.png)

(http://i.imgur.com/csK5N6b.png)

(http://i.imgur.com/jzPn3ZG.png)

(http://i.imgur.com/udpAFpA.png)

(http://i.imgur.com/Dc5tV8Y.png)

(http://i.imgur.com/N1exQUb.png)

(http://i.imgur.com/c7MPzaG.png)

Dinkydau,
Thanks for brining this to our attention!


Title: Re: very simple sierpinski triangle in conways game of life
Post by: cKleinhuis 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 :( :)


Title: Re: very simple sierpinski triangle in conways game of life
Post by: youhn on April 20, 2014, 09:45:16 PM
Oh, sorry  :embarrass: .. my bad. Thanks cKleinhuis!


Title: Re: very simple sierpinski triangle in conways game of life
Post by: Dinkydau 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:
(http://i538.photobucket.com/albums/ff342/formule/life_sierpinski.png)
Also the two triangles fit nicely together because of that power of 2.


Title: Re: very simple sierpinski triangle in conways game of life
Post by: cKleinhuis 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 :(


Title: Re: very simple sierpinski triangle in conways game of life
Post by: Dinkydau 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.


Title: Re: very simple sierpinski triangle in conways game of life
Post by: cKleinhuis on April 21, 2014, 07:19:32 PM
ah, sure, :)


Title: Re: very simple sierpinski triangle in conways game of life
Post by: marius on April 21, 2014, 10:04:12 PM
ah, sure, :)

.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


Title: Re: very simple sierpinski triangle in conways game of life
Post by: knighty on April 23, 2014, 01:07:30 PM
Crazy Mandelbrot set in golly (http://cp4space.wordpress.com/2012/09/09/big-mandelbrots/).  :crazyeyes:


Title: Re: very simple sierpinski triangle in conways game of life
Post by: TheRedshiftRider 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.


(http://i.imgur.com/MgOTPnM.jpg)


Title: Re: very simple sierpinski triangle in conways game of life
Post by: TheRedshiftRider 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


Title: Re: very simple sierpinski triangle in conways game of life
Post by: kram1032 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.


Title: Re: very simple sierpinski triangle in conways game of life
Post by: TheRedshiftRider 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


Title: Re: very simple sierpinski triangle in conways game of life
Post by: M Benesi on August 19, 2014, 04:04:54 AM
Wow... cool stuff Christian.  I forgot about Golly.  :D


Title: Re: very simple sierpinski triangle in conways game of life
Post by: DarkBeam on January 21, 2015, 05:54:36 PM
That is very nice stuff guys  :beer: