What is a pattern?

Over the past year I have been quite obsessed and interested in patterns. I have written several blogs on the omnipresence of patterns, how patterns guide our behavior, habits as attractor patterns, and a few semi-related articles talking about patterns indirectly. But I never fully focused on the definition of a pattern itself. According to Wikipedia, a pattern is a regularity in the world, man-made design, or abstract ideas. The Wikipedia page does not much more than just showing some examples but is does not really talk about what a pattern exactly is. Therefore, defining a pattern from my perspective is the goal of this blog. I have quite some thoughts about this but haven’t really structured them, which I will do in this blog. I do use and compare sources of mathematics but don’t approach patterns exactly from this angle. Keep that in mind. Anyway, I hope you enjoy reading my blog as much as I did writing it!

Regularity of patterns
So patterns main feature are “regularity”, but what does this mean? Imagine we have a sequence of “1 1 1 1 1 1 1 1”, we can clearly find a regular pattern here. The 1 keeps repeating regularly and with each number, the initial value of the pattern returns making the pattern “start over”. The sequence “1 8 4 2 1 8 4 2” also contains a pattern but this pattern is less regular. Now, every four numbers the sequence repeats itself. The size of patterns makes patterns sometimes hard to find. Patterns that take years to repeat require a lot of data collection, while small patterns are quite easy to detect. We need also multiple patterns to confirm there is an actual regularity. The perspective you take on patterns influences thus how you perceive a pattern but we’ll come back to that. But it gets more complex, some patterns do really repeat themselves, while other don’t really repeat themselves truly.

Non-equilibrium and equilibrium patterns
When you see “1 2 3 4” in a sequence, you would expect the next number to be “5”. We also perceive a pattern in regular counting, but it is not a repeating pattern. It is a continuing patterns that steadily rises but it never comes back to the initial value of “1”. I call patterns that never repeat themselves in absolute values “non-equilibrium pattern”. Examples of other patterns are exponential sequences like “1 2 4 8 16 …” Or the Fibonacci sequence “ 1 1 2 3 5 8 13 …”. Here, there is a pattern in the way the numbers change, but they do not (really) loop around in the absolute values. They do loop around, but on a different scale (this relates to fractal patterns which we will talk about later). However, you can try to find a pattern in the differences between the values of non-equilibrium patterns. For example, in the sequence “1 2 3 4 5 ..”, the difference between the value’s is always “1”; a clear regular pattern. For exponents, this gets weird. I worked on that in this blog, and found some interesting stuff. For Fibonacci, the regularity is the balance between the numbers. Either way, the absolute values of the patterns never repeat themselves and they move on until infinity, so I call them “non-equilibrium patterns”. On the other side, we have “equilibrium patterns”, pattern that do get stuck in a loop. “1 2 3 4 1 2 3 4 1 2 3 4 (repeat)” is an example where the values start over again with its initial starting point, indicating it is in a loop. “1 1 1 1 (repeat)” and  “ 1 0 1 0 1 0 (repeat)” are another examples.

Temporal and spatial patterns
First we also have to talk about the fact that there are two types of patterns. With sequences like mentioned in the last paragraph, we talk about temporal patterns; these are values (or states) changing and repeating itself in some order (over time). In our daily lives we see many temporal patterns; our day-night rhythm, the way we walk, the days of the week, and so on. We could call the days of the week a temporal equilibrium pattern, because it repeats itself over again in time. I think the temporal non-equilibrium patterns are a very interesting topic to talk about, because they often resemble development, growth, and quests. For example, we see the Fibonacci sequence a lot in the growth of plants but also in animals and in our own human body. But we also see many exponential patterns in nature and computing. When we talk about spatial patterns, I mean patterns that you can see parallel in space. For example, spatial patterns occur when we see multiple cars next to each other. We also see spatial patterns when we look at “design” around us; in buildings, clothes, human bodies, plants, and much more. With spatial patterns you could also talk about non-equilibrium and equilibrium patterns but this turns also into a debate because it is also dependent on the perspective you take. For example, you could argue that there is clear spatial pattern in the tree’s in the forest. Trees are alike and we all know what a tree is. When patterns are exactly alike, this would bring them in an equilibrium state. However, when you zoom into the details of trees, you will find that every tree is a little bit different, bringing them out of their equilibrium state. This relates to my blog about “why it is impossible to separate things”, it is a matter of perspective.

An example of a spatial pattern: within space, there are several images re-occurring similarly

Perspective
Finally, we can talk about perspective. Over the past paragraphs we noticed how important the perspective on regarding a pattern is. This is because our perspective determines what a pattern is. When we talk about perspectives, we could look at patterns from a different angle, or from a different distance (zooming in and out). Several artists play with finding patterns from different perspectives, Escher is famous for it. In the painting below, he plays with making the walls the floors, and floors the roof from all different perspectives(thus patterns of what you expect change from perspectives). This makes the characters seem to defy gravity, but they also don’t (from certain perspectives). Moreover, these “3D trash structures” also show nicely how our perspective (angle) changes the way we perceive patterns. The other form of perspective is the distance from which we look at patterns (zooming in and out). For example, when you would zoom into my heart rate during a day (relatively zoomed in) you will probably find a pattern. But if you would zoom out and look at my heart rate from a year, you would find different patterns (of changing heart rates over the seasons (look at this blog)). More mathematical; “1 1 1 1” could be a simple sequence, but when you zoom out, the sequence could become “1 1 1 1 2 2 2 2”, and if you would zoom out even further, the sequence might become “1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1”. It is thus actually quite hard to determine when a sequence reaches its full loop and starts over again. Especially when you are zoomed in, you might make quite some wrong assumptions. But when zooming out, you could only see the large overall fluctuations of the pattern.

Here, Escher plays nicely with perspectives and the laws of gravity/buildings

Patterns in patterns
With the differences in the patterns we see while zooming in and out, we reach fractals patterns. Patterns could have patterns within them at several scales. From the largest- to the smallest scale we might see patterns. These patterns at different scales might have nothing to do with each other; meaning that the small scale patterns are different than the large scale patterns. But when patterns from the largest to the smallest scale align, we see “fractals. For example, if you look at the structure of a tree in its fullest, you see a trunk that branches out, but when you zoom into the branches, you see again a trunk that branches, this patterns goes on until the smallest scale. This phenomenon is called “scale in variance”, because the pattern is independent from the scale (the perspective you zoom in). We see a lot of fractal structures in nature and man-made structures, spatially but also temporally. Fractal patterns also never find their equilibrium. Anyhow, many objects also don’t have these fractal structures. If you look at a car from different scales, you won’t find fractal characteristics. This is related to the “growth” of different structures. But don’t forget, I do not try to argue that everything is fractal, but that you can search for the alignment and differences of patterns across different scales.     

An example of a fractal tree pattern

Shared (multi layered) patterns
Imagine you are looking at a random line moving across your computer screen. It moves so random, you couldn’t find a pattern within the movement of this line. He is doing crazy stuff but suddenly another line pops up on your screen. This second line starts to perform the same random movements and his pattern is thus aligning with the first line but then on a different place. This alignment makes the movements seem less random as more lines follow the same path. You start to learn from the movements and even though you don’t really grasp what is going on, you start to understand the pattern. This phenomenon occurs often with memes and trending challenges on the internet. We often don’t really know why people are doing such crazy stuff, but we see a pattern as many people are doing it. This often even leads us towards accepting the “random” pattern. But we also see multi-layered patterns in many other real life circumstances. When multiple dancers follow the same choreography, When birds flock together, when we start to understand difficult puzzles, or when an difficult plan “comes together”. There is thus a form of synchrony between the different layers. These patterns could be independent or could be adaptive to their peers. For example, when we walk in a busy area, we choose and adapt our path to the paths of other people around us. If you would look at these areas from above, you will find some interesting flowing patterns. There is much more interesting stuff to talk about on this topic but that would be too much for now.

Conclusions
I think it is quite crazy that we hardly know anything about patterns, although we work with patterns every day; in our daily life, in science, in design, in music, art, and read more in this blog. Writing this blog has structured my mind a little bit better on patterns and made me distinguish important differences. I am actually not sure how much about patterns is figured out in mathematics and physics. Probably a lot but in a different way. In this blog I haven’t talked about frequency, wavelengths, and other physics stuff but looked at patterns from my perspective. This might be quite limited but also refreshing as I try to connect it with real world phenomena.

Either way, I hope you learned something as well, because you already know a lot about patterns. Ever day, you effortlessly predict the patterns of speed, behavior, music, and language. But how conscious do you do this? By making patterns conscious you could work and develop new and better patterns, we know how important they are. Having more regularity in your patterns could be quite useful to be reliable, I wrote a blog about this: “how to be a linearity”. On the other side, having more complex and adaptive patterns could also be quite useful to cope with the environment. But this was not the topic of today, it was to discuss what a pattern is. I think I went on long enough talking about that. I could go on, so if you are interested, contact me!

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