My Math Forum Creating chaos through colors

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 June 28th, 2018, 07:47 AM #1 Newbie   Joined: Jun 2018 From: Groningen Posts: 14 Thanks: 0 Creating chaos through colors Hi everyone, I created a quite easy but quite insightful sequence that seems to create chaos (when viewing them together). I used colors to make the patterns visible, and I believe it can give many insights. However, I am not sure whether this thing is actually chaos, and whether it coheres with the theories on it. I would love to get some feedback on it! Here is the link to my website: The chaos of colors â€“ chaos shown through colors – JUSTIN TIMMER Thank you very much!
 June 28th, 2018, 05:27 PM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 502 Thanks: 280 Math Focus: Dynamical systems, analytic function theory, numerics The pictures are cool but I would hesitate to call it "chaos" since this has a specific meaning in math. In particular, there is no definition for a picture being chaotic. If you instead mean that the dynamics which generated the pictures are chaotic then this requires quite a bit more work. There is no indication how you generated those pictures or any mathematical description of the pictures. Could you elaborate on what you mean by "I believe it can give many insights"? What can? Insight into what?
 June 30th, 2018, 03:42 AM #3 Newbie   Joined: Jun 2018 From: Groningen Posts: 14 Thanks: 0 Thanks, but you are right. I am not sure to call this chaos. I am not a mathematician and have no clue how to make a formal mathematical description of this. First of all, because it seems like multiple formulas below each other. Maybe some matrix calculations? I don't know. I was hoping someone here could help me or have something to say about it. I don't really know what kind of knowledge there is. Although, I am quite curious on what you guys work on! Regards to my comment that it gave give many insights; well the basics of the structure is sequential learning/pattern recognition (A -> B -> C, and on). If you could argue we use sequences quite often in our daily lives, then you could argue that simpler patterns become chaotic at an earlier phase than more complex patterns, when you compare several patterns. Secondly, a longer (more difficult) sequence seems to be similar to the sequences around it. Whereas a simpler sequence fits better with the other simple sequences around it. If you would exchange sequences/patterns in behavior, then you might be more likely to fit your patterns with similar patterns of others (preferential attachment). Lastly, I am quite intrigued by the diagonal lines. You might argue that from a different perspective (sideways) you could find a fitting pattern too (although it is the absolute wrong perspective). I know I am just implying stuff on just a few color patterns. And I dont know whether its chaos. But you asked for it
 July 1st, 2018, 04:13 AM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,734 Thanks: 605 Math Focus: Yet to find out. No no.. How did you generate the picture exactly! You didn't really answer SDK's questions. Also, have you ever looked at 'chaotic images' before? (e.g. a phase space diagram of a chaotic system) What do you see when comparing with your figures?
July 2nd, 2018, 12:40 AM   #5
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Okay, the first part I did it manually in Excel. I wrote down the formula using the method I described earlier, then assigning a color to it (although I couldn't assign the colors randomly as I mention in the post). On the larger structure, a friend helped me with the very neat formula =MOD(COLUMN(),ROW()). Then, I used conditional formatting to assign the colors.

Yes, I have looked often at phase space diagrams, bifurcation diagrams etc. I see each row oscillating over time, like 0,1,0,1,0,1 (columns). With every row, I see a bifurcation at the end of the sequence. Where one new "phase/color" is added to the previous sequence (like a 2), but the old row continue's to oscillate, and the new sequence/row finds his own oscillation pattern (0,1,2,0,1,2).

Below I added a graph of the first 50 sequences over time (columns) (where the darker lines are the simpler sequences, and the lighter ones the more complex sequences. I don't know how to make a phase space diagram (and if I could do that using this data). It seems that the diagonal lines try to find stability on some level, while others do it on other levels.

Thanks!
Attached Images
 Chaos through colors over time.jpg (19.5 KB, 10 views)

 July 3rd, 2018, 06:11 PM #6 Senior Member     Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: non-euclidean geometry I'm not sure how you're doing what you're doing, but the images are reminiscent of a type of cellular automata. https://www.math.ucdavis.edu/~gravner/edge/ Stephen Wolfram wrote a book on this called "A New Kind of Science." Thanks from justintimmer
 July 10th, 2018, 07:27 AM #7 Member   Joined: Oct 2017 From: Japan Posts: 62 Thanks: 3 The post makes some interesting points but I would refrain from using any specific maths jargon since it has little to do with chaos. I may be wrong but I am almost sure there are patterns also within the highlighted triangle, you may want to apply a simple software to find them.
July 12th, 2018, 05:12 AM   #8
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Quote:
 Originally Posted by rudimt The post makes some interesting points but I would refrain from using any specific maths jargon since it has little to do with chaos. I may be wrong but I am almost sure there are patterns also within the highlighted triangle, you may want to apply a simple software to find them.
Thanks! But do you have any idea what kind of software?

July 18th, 2018, 06:53 AM   #9
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Quote:
 Originally Posted by justintimmer Thanks! But do you have any idea what kind of software?
The software would have to be written, I would start by focusing on one colour only and find all its locations inside and outside the triangle. Once you know the location of the colour you can start looking for a pattern, maybe the colour appears at position n,n+d, n+cd, n+c^4d, etc...If you can't find the pattern straight away, I would apply some basic math(subtraction, division between consecutive positions for example) to see if a pattern emerges.

September 13th, 2018, 06:02 AM   #10
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Quote:
 Originally Posted by rudimt I am almost sure there are patterns also within the highlighted triangle, you may want to apply a simple software to find them.
100% sure there is a pattern, it basically is a pixelated representation of colored lines that are stored in a triangle which is sheared by whatever amount. The pixelated representation just can't handle the steep angles, because the density of information is way too high in those areas.

Reminds me of "seemingly" complicated patterns that appear when you look at moire patterns (open the link), it's all scaled hexagons, but when you rotate too much, it seems like it isn't, because the initial pattern can't handle the representation of those small hexagons:

https://www.openprocessing.org/sketch/306748

Also: When you rotate the triangular pattern, there has to be a hexagon in the rotational center at all times, in the link there is no sign of that, because the pixels aren't that accurately calculated, there is anti-aliasing etc going on.

Last edited by theHeavyLobster; September 13th, 2018 at 06:06 AM.

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