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Cellular Automaton done by an artist

Reinhard Danelzik
Posted 10 years ago

Three Years ago I came about Stephen Wolfram's book “A New Kind of Science”. It has taken me on a phantastic journey from which I returned with a vision to paint a cellular automaton, big in size and big in scope. I decided to generate and paint a one-dimensional, two nearest neighbours cellular automaton with 14 colors. The problem was, I have just rudimentary knowledge of programming and I knew that this task was beyond me. Taking a course in adult education and two educational books on this matter were to no avail. Then I bought Mathematica. Some Money for a risk. What, if I couldn’t handle it? Well I could, because of the excellent, interactive Help-section and that I could go to work just by using functions and brackets, no need to dive deeper into the realm of Mathematica. Also great the fast computation and visualization. What I had to do all by myself was to find in a set of 14(power14(power3)) the one rule which was worth to be painted. It took months of searching in colored deserts, no interesting structures to be found. Well, I think I finally found a good one, and I think it belongs to class three! (Right click on the image and select "View in new tab" to zoom.)

enter image description here

The direction of evolution of the automaton is horizontally from the left to the right for aesthetical reasons. I have been a printer and I paint with printing ink on aluminium printing plates. The painting is composed of 12 Plates, overall size 2.1 x 4 m, The image is composed of photos of the 12 plates, which are not easy to take pictures from because of their glossy surface.

Editor's Edit

Below is the painting and the painter kindly shared by the author upon requests below in the comments:

enter image description here
POSTED BY: Reinhard Danelzik
12 Replies
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This is a nice discovery. It appears to be mostly class 3 but it has some localized structures like class 4. There is also irregular boundary behavior, some of which makes me think it has a large radius.

It reminds me of some of the 3 color totalistic rules, which are discussed in the New Kind of Science book, like code 1635

enter image description here

and code 2049

enter image description here

Maybe with the right color scheme your rule can make a good tweet-a-valentine
POSTED BY: Todd Rowland

Reinhard this is a very nice work - thank you for posting! I have read about your painting and other work on your website too. I must advise other people curious that one can right-click on the painting and "View in new tab" or "Download" to examine it better because you uploaded it in high resolution. At highest zoom it looks like:

enter image description here

I have a few questions if you do not mind answering:

  1. Was the number 14 for the colors an arbitrary choice ?

  2. The painting is quite big - 2.1 x 4 meters. How long did it take to paint?

  3. If you have a chance could you post a photo of yourself standing right by your painting? It would help us to grasp the size and also it would be very nice to see the artist and his painting together.
POSTED BY: Vitaliy Kaurov

Hello Vitaliy, thanks for your reply, I like your animated version of my painting, and no I do'nt mind to.answer.

  1. The choice of the numbers and the kind of colors are not arbitrary, indeed they are the same I used in an earlier painting: Nr. 131 "Gaussian Gradient" from 2006. You'll find it on my website in Paintings 2. with an explanation of the concept of construction. In short: the color of each square has been fixed by arbitrarily under the restriction of values of probability, given by 14 functions of Gaussian distribution (1 for each color) lying over each other. I choose the colors from CIE-Lab Color-space: black and white from the orthogonal axis, 12 hues from outer border of the a/b plane.

  2. I needed about 684 hours for painting only. It took some time of getting accustomed to Mathematica and it took months to find the Chosen Rule. As I browsed through the universe of the rules I saw either trivial or simple CA and vast deserts of colorful boring ones. I was afraid, that the great number of colors could be the reason for not finding class 3 or class 4 CA.

  3. I like to do that. And I beg your pardon for the Quality of the shot. My paintings are so difficult to take fotos from. The Painting is hanging on the Wall in my Living room and the lighting is all but ideal, and to compare the size I'm a man 1,65m. To see high-resolution image use THIS LINK

enter image description here
POSTED BY: Reinhard Danelzik

At last I want to add the code of my CA:

ArrayPlot[
 CellularAutomaton[{\
9447782812769403966940947080229848294189494277470937627589735727672493\
7981067026725274780735839744267123165239631223751000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
0000000000000000000000000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000000000000000815, 
   14}, {7, 6, 12, 7, 4, 7, 4, 10, 0, 7, 4, 5, 5, 8, 6, 11, 7, 7, 3, 
   8, 13, 8, 5, 6, 5, 11, 13, 8, 9, 10, 2, 13, 10, 6, 0, 6, 10, 2, 7, 
   8, 8, 0, 9, 3, 0, 11, 4, 5, 13, 1, 8, 12, 6, 4, 1, 1, 10, 9, 4, 6, 
   0, 3, 5, 5, 13, 5, 9, 8, 12, 13, 13, 11, 12, 13, 4, 5, 7, 9, 11, 
   13, 4, 3, 6, 5, 7, 10, 10, 0, 13, 0, 11, 12, 11, 1, 3, 3, 1, 6, 12,
    9, 9, 0, 3, 13, 2, 3, 8, 13, 4, 12, 2, 6, 1, 6, 2, 3, 2, 7, 13, 
   12, 7, 7, 2, 8, 4, 2, 0, 0, 2, 12, 0, 4, 3, 6, 5, 9, 6, 12}, 264], 
 ColorRules -> {0 -> White, 1 -> Yellow, 2 -> {Hue[.13, 90, 1]}, 
   3 -> Orange, 4 -> Red, 5 -> Magenta, 6 -> {Hue[.8, 1, .9]}, 
   7 -> {Hue[.75, 1, .7]}, 8 -> Blue, 9 -> Cyan, 10 -> Green, 
   11 -> {Hue[.23, .9, 1]}, 12 -> {Hue[.2, .9, 1]}, 13 -> Black}]
POSTED BY: Reinhard Danelzik

thanks for your comment on the question of the classes into which my CA would fit. What I would have liked to know, when I was searching for the rule, are there algorithms to filter rules according to a given class?
POSTED BY: Reinhard Danelzik

This is flabbergasting - I knew I need to see you posing close to the painting - and it worked - it is monumental! Thank you for taking and posting the photo! I recommend other readers to visit your website and read the explanation for the earlier painting Nr. 131 "Gaussian Gradient" as I did already.

What are you planning to do next? Any other potential computational art projects?
POSTED BY: Vitaliy Kaurov

Hello Vitaliy, I have to give more information on the painting “Gaussian Gradient”: It is accompanied by a print copy multiple as you can see here "Gaussian Gradient"Multiple Gaussian Gradient I did the the big painting with MS-Excel, Programming the Multiple was beyond my ability. I got a professional to do it. I lost the code of the multiple, when two years ago my website had been hacked and I had to build a new site in a more secure environment. So the next computational art project is the restitution of the multiple in Mathematica.![Multiple Gaussian Gradient][1]
POSTED BY: Reinhard Danelzik

Awesome rule number - this is how approximately big it is:

N[%, 2]

enter image description here

I understood that the color selection was the essential part of the work. But here for the pure sake of experiment the same rule in some default color schemes (if your rule is defined as RULE):

ArrayPlot[
     CellularAutomaton[{RULE, 14}, {7, 6, 12, 7, 4, 7, 4, 10, 0, 7, 4,
        5, 5, 8, 6, 11, 7, 7, 3, 8, 13, 8, 5, 6, 5, 11, 13, 8, 9, 10, 
       2, 13, 10, 6, 0, 6, 10, 2, 7, 8, 8, 0, 9, 3, 0, 11, 4, 5, 13, 
       1, 8, 12, 6, 4, 1, 1, 10, 9, 4, 6, 0, 3, 5, 5, 13, 5, 9, 8, 12,
        13, 13, 11, 12, 13, 4, 5, 7, 9, 11, 13, 4, 3, 6, 5, 7, 10, 10,
        0, 13, 0, 11, 12, 11, 1, 3, 3, 1, 6, 12, 9, 9, 0, 3, 13, 2, 3,
        8, 13, 4, 12, 2, 6, 1, 6, 2, 3, 2, 7, 13, 12, 7, 7, 2, 8, 4, 
       2, 0, 0, 2, 12, 0, 4, 3, 6, 5, 9, 6, 12}, 264], 
     ColorFunction -> #, PixelConstrained -> 1] & /@ 
   ColorData["Gradients"] // Partition[#, 5] & // 
 Grid[#, Spacings -> {0, 0}] &

enter image description here
POSTED BY: Vitaliy Kaurov

Beautiful painting of a complex 14 colors CA!
POSTED BY: Bernat Espigulé

We do quite often searches like this in the Wolfram Science Summer School. There are a few approaches and you can look through the resources page for code samples, for example in "Conducting Searches" by Paul-Jean Letourneau. Generally in a very large rule space - as you have - you would do random rule sampling checking for some criteria. It is possible to make an algorithm to catch complex glider collisions and also check for some measures such as entropy or informational compressibility. For example, it is hard to compress (with built in Compress or JPG image compression, etc.) type-3 evolution from random initial conditions. While type-1 and type-2 will be highly compressible. So type-4 will be somewhere in between and based on a particular rule space and compression method - needs a bit of experimenting. Also refreshing on Chapters 2 and 6 of the NKS Book would inspire some thinking. Perhaps someone else will give some more ideas.

POSTED BY: Vitaliy Kaurov

Awesome for me is, how little code it takes to show 50 color shemes. And do I get this right, "RULE" takes its input from my post above yours? .And what did I do wrong, that the code in my above post stays inactive? I took the code from the notebook by copy as input.
POSTED BY: Reinhard Danelzik

"RULE" is the huge number you used for the CA rule - I just did not want to paste it in order to make code compact. Of course in the notebook you have to use the actual number. I am not sure what you mean by "code in my above post stays inactive". I copy-pasted your code from the post to the notebook and it worked.

POSTED BY: Vitaliy Kaurov
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