Chaos in colors

Only when there is a pattern in something you can understand it. However, patterns are relative to the one who sees them. When I yell “Green, Blue” there is no pattern, but when I repeat yelling green and blue five times, a pattern emerges. And when I add “Red” after each sequence, at first it seems more random (suddenly there is a different color), but when you zoom out over many sequences, it is a clear pattern (Green Blue, Red). It is just like when A leads to B, and B leads to C, then C leads to D. When I push (A) my bottle (B), my bottle falls (C), and from falling it breaks (D), this results in fragments on the floor (E). In this chain of events, each element is connected, and therefore A is related to E, through B,C,D.

Suppose, you need to memorize a chain of events, and every time you make a mistake you need to start over. Like when learning the tables on primary school, retelling a story, memorizing a sequence in a deck of cards, or a roadmap to a certain goal. The first steps are always quite easy, because you repeat them quite often. Because when you make a mistake, you need to go back a few steps and start over. Once you reach the last (known) point in your sequence, you need to guess what do next. With the example of the bottle we know steps A->E, but we don’t know what comes after F. We need to guess. It is quite likely we make a mistake because this step doesn’t fit the pattern yet. But once you make a mistake you have two options.*

Option 1. Is to give up
Giving up means that you don’t want, or can’t learn a longer sequence, you might know “Green, Blue” but you can’t understand why “Red” follows. Thus, you go on with fitting “Green, Blue” everywhere. What means that you try to fit your known pattern into every pattern you see. Once you stop learning, you are only aware of a few patterns.

Option 2. Continue with learning
If you don’t want to give up, you try hard to learn the next “color” in the sequence. You learn that after “Green, Blue” comes “Red”, and if you go on learning, you’ll learn that “Yellow” follows after “Red”.

Making a colorized sequence
Below there is a picture which visualizes this process. We have the process horizontally, A (Green), B (Blue), C (Red), D (Yellow), E (Purple), and so on. The sequence starts easy (A->B), but with each row (from above to below), we have a more difficult sequence. Row 1 is “Green, Blue”, row 2 is “Green, Blue, Red”, row 3 is “Green, Blue, Red, Yellow” and so on. The colors were picked with the primary colors first, and followed by the other colors, (I am aware this isn’t perfect). Once you “give up” at the pattern “Green, Blue” you stay in row 1, and continue horizontally with the same pattern. You keep trying to fit this pattern (Green, Blue) on everything. However, when you are eager to learn new colors (a more difficult sequence), you go down a row (to “Green, Blue, Red”, and so on). This can go on forever, but in the next picture the sequence goes until row 24. I made this picture manually using MS Excel. I wrote down the formula into the cells (using the method I described earlier), and then assigned a color to it using conditional formatting.

A first glimpse of the structure

Understanding the world through the patterns you know
The main thing we all want, is that the world makes sense. Albeit through the patterns we know or through learning more difficult sequences. Once you want that the world makes sense through the patterns you know (roughly at the first few rows, because the world is quite complex), you want to find similar people who think in the same pattern. If everyone says the only pattern is “Green, Blue, Red” and there is nothing more to it, you don’t want people to say, but there is also Yellow, Purple, and even Orange! You didn’t want to learn more difficult patterns so you avoid these people. You try to find similar minded people who all think “Green, Blue, Red” and nothing more. Nevertheless, if you are forced to interact with people who know (or think about) more difficult sequences, most of it looks like pure randomness. You don’t know about these colors, when someone says “Purple, Orange, Brown” this doesn’t make any sense. And if you are really stubborn, you will say; “He’s wrong, it’s not “Purple, Orange, Brown” it is “Green, Blue, Red.”.”

Things that (kind of) make sense for the once who only want to/can understand the easy patterns are within the black squares.

Understanding the world through learning more difficult patterns
When you want to/are able to learn sequences/pattern, you might be at row 26 by having acquired the most difficult patterns with many colors. For you, the most patterns you see around you make sense, although you also have a difficult time learning even more difficult patterns. You can understand most things that are happening, nevertheless, it is quite difficult to you to predict the behavior of other people. For example, when someone in the first rows says “Green, Blue, Red” you won’t be sure what the next color will be. It might be “Yellow”, or “Green” again. If this is your only information, you have a 50/50% chance of guessing what he will do. If you guess “Green” but it is “Yellow”, that someone will be offended because you assumed he only knew the easier pattern. Thus, although you might know every pattern, you still have a hard time understanding everyone else’s pattern. Although patterns become clear after behavior takes place, you can’t predict them, except when you know exactly with who you are dealing.

An overview of the group
When I was making this picture, something weird emerges what I couldn’t give a place quite easily. On the diagonal of the picture, you see a “clear” pattern emerging (see picture below). Although many peoples’ patterns become more and more out of sync with each row, they make a pattern over the diagonal axes. But it’s not just the diagonal axes, the pattern starts vertically, but shifts towards a more and more diagonal pattern. I have drawn black lines across the each (first) green block of a pattern to show this “new” pattern more easily. What does this mean? It might be that when looking at a group with more complex patterns, the perspective of finding pattern should change to make sense of its behavior. Flipping your view vertically, diagonally, and eventually horizontally can help you to make sense of each pattern emerging in this picture of colors. I still need to understand this better and do more with this. I hope some blogs about this will follow.

The diagonal patterns emerge over the picture. The lines follow the first green square of each pattern.

Chaos among the rows
Although you see the diagonal pattern as depicted in the previous picture. It seems to me, when looking at the picture, that at the first rows chaotic patterns emerge quite quickly. There is hardly no pattern to be found in the triangle I placed on the figure. In the lower rows we see a nice diagonal pattern, but these don’t seem to be there in the first rows. Nevertheless, the nice diagonal patterns also emerged after a while, so the triangle is slowly shifting to the right as the patterns grow. The seemingly chaotic mess in the triangle probably becomes a pattern as well, when we add more patterns and colors horizontally and vertically. This means that there is structure in presumably noise, which is an important thing.

The triangle depicts a seemingly chaotic structure in the first rows

The structure on a large-scale (with fewer colors)
Below I inserted a picture of the same structure but on a large-scale (528 rows by 300 columns). For this larger structure, a friend helped me to program it using a very neat formula: =MOD(COLUMN(),ROW()). Then, I used conditional formatting to assign the colors. It was interesting for me to learn that even though, I expanded the structure for numerous of cells, the general outline of the figure remained the same. This made me think of some fractal structure within it. Furthermore, I think it is quite funny how excel created its own pattern by inserting some black dots/lines across the figure. I guess this has something to do with the numbers within the cells. Unfortunately, Excel could only make me use three shades of colors (as far is was able to). If I get some positive feedback/help on this idea in general, I am willing to spend more time on this idea and write some code to get a better picture of the structure.

The chaos structure using 528 rows and 300 columns


Structure over time
For some further information; I added a graph below of the first 50 sequences over time (columns) (where the darker lines are the simpler sequences, and the lighter ones the more complex sequences.

The patterns over time of the first 50 sequences. The darker lines are the simpler sequences, and the lighter ones the more complex sequences

* I do not imply with this post that intelligence/smartness is only based on the learning of sequences/patterns. There is more to intelligence/smartness than that. However, this is not part of this post.

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