Learning Ability Test (Now Idiot-Proof!)

[black_hat_guy]

For school, I have to conduct an experiment to determine the effect of age on learning ability. I will be testing people on their ability to become familiar with the rules of an elementary cellular automaton (Rule 90) and answer questions about it. If you are already familiar with Rule 90, please do not take the test.

Here is the material you will learn:
A state of the Rule 90 pattern consists of an infinitely long sequence of digits which can each be either 0 or 1. Because an infinitely long sequence cannot be represented in a finite space, any digit not specified is assumed to be a zero. The sequence 11010001, for example, is actually surrounded by zeroes on both sides. For each step in the automaton, the next state is determined by applying a few rules to the current one. The basic idea is that you start with an initial position, compute the next step, compute the step after that, and continue as long as you want to see what the results are. What a digit will change to depends on the current state (y) of the digit, the digit to its left (x), and the digit to its right (z) based on these rules:

xyz result
000 0
001 1
010 0
011 1
100 1
101 0
110 1
111 0

Commit these rules to memory using any technique you like, then take the test, which can be found here:
http://www.misterpoll.com/polls/555308 (For some reason, you can't view this page without disabling safe mode, but I promise there's no inappropriate content.)

You may use a pencil and paper to apply the rules, but please do not write down the rules or use anything you wouldn't be allowed to use in a real test. Your help is greatly appreciated.


Clarifications:

• A cell consists of one number.
• A digit is a 1 or a 0.
• A string is a sequence of digits.
• General familiarity with cellular automata is fine, but specific knowledge about Rule 90 is not.
• You CAN use a pencil and paper while taking the test.

[Yakk]

Define "familiar"? As in, I'm aware that there are numbered 2 dimensional cellular automata rules that can result in Turing complete operation, but I have never examined Rule 90 in particular before.

[Meem1029]

I took it as the first and only so far! I do have some background in cellular automata, although it is fairly limited and I haven't done this sort of thing before. To clarify rules, was I allowed to write things down on paper to figure stuff out? If not, you should probably go in there and clear my results.

[coyotebush]

Guess I was #2. Kind of fun.

[Bakemaster]

The instructions are somewhat lacking. You refer to digits, then you refer to cells without making explicit whether a cell is a digit or something else. A lot has to be intuited or assumed to catch on to what you're asking the subject to do with your groups of numbers. Add another digit to the end of a string? Create a new string the same length as the given string? Change digits within the string? You need to be more explicit and your instructions need to be more "idiot-proof" because to look at learning ability you want to minimize the effect of things like technical background and past experiences as they don't relate to your experimental variables.

[Meem1029]

That is actually a very good point that I forgot to bring up. in some of the "find the next term" questions I just filled in the new values for the values that were above, even if they probably should have expanded.

[Tirian]

I think this is an awesome experiment of how many people are willing to disable safe mode and visit a site based on the assurances of a user named black_hat_guy.

[Meem1029]

I think this is an awesome experiment of how many people are willing to disable safe mode and visit a site based on the assurances of a user named black_hat_guy.

Haha, yeah. The safe mode on that site isn't what you'd think of as a typical safe mode. Basically it's a sandbox where they check all the tests that they allow for safe mode to ensure that they are child friendly (remembering from a few days ago when I did the test).

[Tirian]

I think this is an awesome experiment of how many people are willing to disable safe mode and visit a site based on the assurances of a user named black_hat_guy.

Haha, yeah. The safe mode on that site isn't what you'd think of as a typical safe mode. Basically it's a sandbox where they check all the tests that they allow for safe mode to ensure that they are child friendly (remembering from a few days ago when I did the test).

Ah, I assumed that it was about disabling browser security. Carry on then.

[ElCarl]

That is actually a very good point that I forgot to bring up. in some of the "find the next term" questions I just filled in the new values for the values that were above, even if they probably should have expanded.

Just did it, I did what this guy did as well...

[black_hat_guy]

Well, many thanks to everyone who participated, especially those of you who suggested improvements. There appears to have been a technical problem, so I'll have to get the rest of the data from another source.

[Alex-J]

Just stumbled across this, and I was wondering
In your instructions you say the new state of the digit depends on the current state, the digit to the right and the digit to the left.

but when I rearrange the rules you gave:

xyz result
000 0
010 0

001 1
011 1

100 1
110 1

101 0
111 0

As far as I can tell the current digit's state, the one in the middle, has no bearing on the results. Whenever the x and z are zeros the result is zero, whenever one of them is one the result is one, and whenever both are ones the result is zero. The "y" digit doesn't affect the outcomes.

I assume the test link doesn't work anymore because you did this awhile ago, probably a good thing because I seem to be missing something. I'm just curious, would anyone explain what affect the current digit has?

[cesium14]

Just stumbled across this, and I was wondering
In your instructions you say the new state of the digit depends on the current state, the digit to the right and the digit to the left.

but when I rearrange the rules you gave:

xyz result
000 0
010 0

001 1
011 1

100 1
110 1

101 0
111 0

As far as I can tell the current digit's state, the one in the middle, has no bearing on the results. Whenever the x and z are zeros the result is zero, whenever one of them is one the result is one, and whenever both are ones the result is zero. The "y" digit doesn't affect the outcomes.

I assume the test link doesn't work anymore because you did this awhile ago, probably a good thing because I seem to be missing something. I'm just curious, would anyone explain what affect the current digit has?

Well, it affect its neighbors.

btw, how do you get 00110011?

[Sizik]

That's just the general description of a 1-D cellular automata. The rule number is obtained by taking the binary number obtained from putting the results in order based on the xyz value, i.e. the result of 111 is the most significant digit, 110 gives the next, down to 000 giving the least significant digit. Thus, the following rules:
xyz result
000 0
001 1
010 0
011 1
100 1
101 0
110 1
111 0

give 01011010, which is 90 in binary. This means that there are 256 different elementary automata, some more interesting than others.

You are correct that the value of the current cell doesn't affect the cell directly below it; this is actually one of the questions on the test (which I just took, btw).