[draw a color based on the numeric value represented in binary by the cell's history] - A New Kind of Science: The NKS Forum

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draw a color based on the numeric value represented in binary by the cell's history

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Posted by: inhaesio zha

This may be more artistic or philosophical than pure, or it may be more pure, I'm not certain. Also, it may be completely useless (which would push it in the direction of pure, I suppose).

Anyway, it's something I was thinking about, so here it is:

What if you take the history of a 2-color CA and, when displaying it, instead of drawing a color corresponding to the cell's value, you draw a color based on the numeric value represented in binary by the last however-many moments of that cell's history?

These systems are drawn in such a way, using some of my {ant} systems as a starting point:

http://inhesion.com/zha/ca/snapshots/22dec2005/ant_dx/

They use an 8-bit strip of history to select a shade of gray to represent the cell.

The next step I think would be interesting is to view regularly-colored graphics side-by-side with their binary-history-colored ones...but I'm not sure it would be all *that* interesting, so I haven't found the motivation to do it.


Posted by: inhaesio zha

I'll say this, too: I arrived at this binary-coloring idea (which I don't think is all that useful or interesting) by asking a question that I think probably has many useful and interesting answers.

What is the definition of "eye"? Or how does an eye function? When I look at CA output, it seems interesting, and if I interpret cells in key positions in CA history, after having encoded numbers or other data in the initial rows of the CA, the function of a CA can have an interestingness (or usefulness) that is completely non-visual. I haven't read the explanation of how WolframTones works, but, clearly, that's an example of using a different kind of "eye" to view CA data (or in that case an ear). So this binary-coloring thing is an example of how some 1d CA output might look to a different type of visual eye.

What if 2-color CA history is interpreted as strings of instructions from a set of 2 possible instructions given to a display machine that _does something_ based on an input sequence of bits? (Something different than display a color based on the last input bit.) What if the display machine is a turtle that moves at a rate of one centimeter per moment, and it turns left when it gets a 0-bit and right when it gets a 1? A CA that is 12 cells wide would provide instructions to a family of 12 turtles wandering around the woods. Or maybe the turtles pay attention to their input in 16-bit words, and have a more complex array of abilities (they could do this vertically, from a single cell's history, or horizontally, from groups of cells, or a combination of both). Maybe we use the output of one CA to generate a string of programming instructions, and we use the output of other CAs or another part of the original CA to generate parameters that will be fed to those instructions? That CA output would be [seen as] the source code for a piece of software...maybe what the resulting program did would be interesting or useful.


Posted by: inhaesio zha

Here are some graphic outputs from a turtle system like I mentioned:

http://inhesion.com/zha/ca/snapshot...06/ant_turtles/

Each turtle follows instructions from a single cell of an {ant} CA throughout time (using every 2-moment binary pair to decide whether to move north, south, east, or west). The red path in the turtle diagram corresponds to the red-highlit cell in the CA history. The other paths are drawn in varying shades of gray to make them easier to individuate.

I'm attaching a sample turtle path diagram to this post, along with a partial history of the CA it corresponds to. I'll put a zip file with the complete CA history in a reply to this post.


Posted by: inhaesio zha

Here's a zip containing complete images of the CA history and turtle output partially shown in the previous post.


Posted by: inhaesio zha

..


Posted by: inhaesio zha

I'm referring to the first post in this thread. Take a 2-color CA, and when you plot it, don't plot black for a 0 and white for a 1, but instead plot a shade of gray based on the binary string formed by the last 8 moments in the history of that cell.

The resulting drawings are shaded nicely, but that's not the most fascinating thing about them. The most fascinating thing about them, to me, is that their output looks, subjectively/visually, basically like the simple 0=black, 1=white plottings of these systems. I mean the forms you see in these binary-number-shades-of-gray plots are the same types of forms you see in the simple/standard plots.

Even with such a sort-of weird and non-sensical display algorithm, the same [types of] visual patterns appear. The same thing happened when creating those multi-color plots suggested by Seth Chandler's questioning...what if you view a 2-color CA as a 4-color CA, by grouping the rows together and viewing groups of rows as binary numbers representing higher-color systems...when he suggested that, I imagined the plots of grouped-together systems would look entirely different than the "regular" plots. But that's not what happened. The 4- and 8-color plots of those systems have the exact same forms as the 2-color plots, just squished.

(http://inhesion.com/zha/ca/snapshot...smc_multicolor/)
(http://forum.wolframscience.com/sho...15&pagenumber=2)

I find that interesting.




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