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Emergence, Week 4
Welcome to the on-line forum associated with the Biology 361 = Computer Science 361 at Bryn Mawr College. Its a way to keep conversations going between course meetings, and to do so in a way that makes our conversations available to other who may in turn have interesting thoughts to contribute to them. Leave whatever thoughts in progress you think might be useful to others, see what other people are thinking, and add thoughts that that in turn generates in you.
As always, you can leave whatever thoughts occurred to you this week. But if you need something to get you started ...
Statistical randomness versus "randomness"? Further thoughts about the importance of context for emergence models? Initial reactions to one-dimensional cellular automata?
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Rule 91
The rule that I thought was interesting was Rule 91.
Simply, it takes whatever initial (be it random or single) squares at the beginning (in any shape or size) and drags them down the screen infinitley. You end up getting a very different looking striped wallpaper so to speak (when using random, or making your own) and with single, it is simply a straight line. I thought this would also be a good rule to model to get a good grasp of NetLogo's code.
The capabilities of this rule include (when playing with turning other rules on & off), making the lines go slanted, inversing the colors, etc. An explanation of this rule in regards to the real world could be the outline of rain, the outline of many natural things.
Rule 117
Rule #: 117
Results:
When you run rule 117 you end up getting a distorted pattern of green and black parallel lines. When one green square is turned on it then turns on one square to its top left and one square to its bottom right. Then the squares next to these two turn on until they form distorted parallel green lines. The squares immediately below these green lines are turned off forming distorted black parallel lines. When you use random setup the distorted parallel lines produces a wave-like effect. I thought at first that the rule switched between two stable states but if you change the max-pxcor and max-pycor to 200 then you can see that this isn't the case.
Capabilities:
Changing the density when using the random setup allows you to produce different wave-like patterns. The places where there are parallel likes could represent crests and the distorted lines could represent troughs.
World Explanation:
This rule is interesting because it can have a number of real-world applications. For example the wave-like effect produced when you use random setup at a certain density allows you to represent things like sound waves, light waves, radio waves, microwaves and earthquake waves. We can maybe also use it to model trends that have a wave-like pattern. Some other rules that were similar to rule 117 were rules 11 and 59.
A couple of thoughts...
I am still trying to figure out a way of categorizing rules. At first, I thought that I could differentiate the different rules by whether or not they were statistically random, but I soon realized that too many of them contained this element of statistical randomness after presenting ordered patterns for a couple of clicks.
One thing that I am still thinking about is the statement, “cellular automata are capable of producing anything the universe is capable of producing”…
An initial thought is that cellular automata are capable of producing ordered structures and contain both randomness and predictability, so in that sense they can be linked to the real world in which both of these elements exist. On that same note, cellular automata are also capable of producing both simple and complex patterns. Do these elements then make cellular automata capable of producing anything the universe is capable of producing? Not sure that I’m convinced, yet. It seems too simplistic, but at the same time appealing because it is a different and simpler way of viewing the universe. It was similarly difficult for some of us to accept the idea of our universe as a deterministic system in which we questioned whether or not then it was possible for us to be sitting here again doing the same exact thing if the big bang were to repeat.
From the different rules, I was initially struck at how many different patterns one is able to get. However, the more I played with the different rules, the more I realized similarities between different patterns. However, one thing that remained was the unpredictability between rules. There does not seem to be a pattern between rules. There was more of a pattern every other rule. This is apparent in Rules 129-134 in which rules 130, 132, 134 contain one line and 129,131,133 contain a large shape of a triangle in the center...
What surprised me even more what this: http://www.wolframscience.com/nksonline/page-55. Many of the rules are strikingly similar and seem to be repetitive. As a result, when I see the pattern again in another rule, it does not seem as “interesting”.
Rule 204
Rule: # 204 (11001100)
Results: Regardless of the setup, cells that are on stay on and others stay off (giving vertical lines of 'on' cells)
World Explanation: At first I thought this was a really boring rule, but then I started thinking about how it gave a pattern that looks like a barcode. By changing the background and foreground colors, I made it look even more like a barcode. I suppose a barcode isn't really something about the world to understand, but it is a way of encoding information about the world. By manipulating the starting condition, this rule could be used to generate any one-dimensional barcode.
Additionally, I suppose you could see this rule as demonstrating Newton's first law of motion: A body at rest stays at rest and a body in motion remains in motion unless acted upon by an unbalanced external force.
Interesting?: I don't know if I would call this rule interesting-it's the kind of straightforward thing that could be demonstrated in much simpler ways, but if you're going to attempt to explain the universe with a finite (and, in fact, quite small) set of rules, you're going to have to make each one count, and each is going to have to explain much more than one thing.
Rule 127
I played with a whole bunch of rules and found rule 127 really interesting. I will try to stick to Steph's criteria in discussing it:
Rule # 127
Results:
With the single setup, horizontal strips of green and black are produced and they keep repeating. When the setup is random, vertical green lines appear on top of the horizontal lines at random locations depending on the density that is set.
Capabilities:
When density is 1, no vertical lines appear at all. Only the horizontal strips are seen. When the density is set to really low (between 2% and about 20%) very few to no vertical lines appear. The vertical lines start to get denser and denser when the density is increased, especially from about 40% to 80%. After that, the lines once again start to appear less and less frequently, until at 100% density, there are no vertical lines again.
World Explanation:
I think this is a perfect representation of “too many cooks spoil the broth.” We can consider the vertical lines a measure of productivity. When there are few people and it is not enough for a project, then little to nothing gets done over a certain period of time. When there is an optimum number of people, the most work gets done. Then when there are too many, it ruins the work and productivity goes down once again.
In fact, it works for any scenario that is represented by the bell curve. Take the total utility curve for instance. Utility increases as an individual gets more and more of a good or service up to a certain point. After that, utility starts to decrease.
Interesting?
Yes, it represents so many different real-life situations!
I currently don't have my
I currently don't have my notebook so I can't post the rules I tested with the results. However, in my search to find rules that are interesting, I began to ponder what indeed made one rule more interesting than another. At first I classified interesting rules as those that produced designs with triangular patterns. However, many rules I tested began producing these similar patterns. For me, this made the rules that produced these triangular patters less interesting. After testing numerous rules, the one rule I tested that was unlike all others I felt at the end was most interesting (the particular rule produced nothing similar to the first rule). When I get my notebook, I'll discuss particular rules....
What's "Interesting"?
I've been running as many of the rules as I can and coming up with brief descriptions of all of them, and I'm also having a hard time coming up with a good standard for classifying a rule as “interesting.” The more rules I run, the more I realize that many of them do very similar things. In fact, many of the simpler ones appear to do the exact same thing when running off of a single cell. The random setups tend to vary more, even if the overall outcome is the same. Having run so many rules, I am becoming more interested in the relationships between different rules. I haven’t observed any predictable pattern of numbers of rules that produce similar outcomes yet, which is frustrating. I feel like there should be some correlation between number and outcome. An interesting relationship I’ve observed is that some rules produce similar outcomes with inverted colors, such as #6 and #155 or #22 and #129. I also think it’s interesting when the single setup and the random setup yield noticeably different outcomes, such as #109, or when the result is seemingly random but also symmetrical, like #73. I think my favorite rule is #122, which begins as a checkered triangle on black and then becomes an alternating series of Sierpinski triangles, because it’s the only one I’ve found that does two sets of different outcomes in one rule.
A question that I’m wondering about: should we concentrate on the ultimate stable outcome of the rule, or should be also take into account the first few lines? I’ve found that many rules with similar general outcomes have rather different beginnings, such as #78 and #79 (which are also interesting in that they have similar outcomes and are sequential.)
Post your information here - Class Collaboration
Hi, everyone. Please post to me your rules with the following criteria. Thanks! I can't wait to put all of our work together.
My chart criteria is as follows:
Rule #:
Results:
Your NetLogo Model File Name (for this rule, if you've created one--i.e. Rule10.nlogo):
Capabilites:
World Explanation (What fraction of the world can we explain with the findings of this rule?):
Interesting?:
Less Interesting?: