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I have heard the notion of randomness being able to create patterns but it seems that in every case of this, it is more of a perceived pattern more than anything. Every “pattern” usually ends up being imperfect, wishy washy, or a “half pattern” with no set rule.

The others are coincidences that upon closer inspection, usually do end up displaying imperfections which seem to display characteristics of randomness. So the question is: does randomness create patterns?

Theoretically, one can imagine things like fair coins landing on all heads many, many times. But these posits are usually theoretical. In every case of a consistent pattern that we’ve observed, it ended up occurring because of a law. And not randomness.

So is there anything in the world that exhibits patterns but is caused by a random process?

thinkingman
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    Numberphile has a quote along these lines, that “randomness is patterns on patterns on patterns” – J Kusin Aug 31 '23 at 07:09
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    "it ended up occurring because of a law. And not randomness" - physical laws apply to everything physical. So I don't think you'd be able to find any physical result of randomness (whether pattern or not) that doesn't arguably occur "because of a law". – NotThatGuy Aug 31 '23 at 07:59
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    Randomness is subjective. You might interpret a random behavior what I interpret as an organized behavior. And you might see an organized result where I see chaos. In such case, all behaviors are organized, and all result into patterns. Even if we can't perceive them. – RodolfoAP Aug 31 '23 at 10:12
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    Your notions of “patterns” and "randomness" are even more washy washy than the "patterns" you are complaining about. How are you deciding whether something is occurring "because of a law and not randomness" when both are present, which is always? Even a fair coin has a "law" - it is fair. Still, let me introduce you to the [law of large numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers), [central limit theorem](https://en.wikipedia.org/wiki/Central_limit_theorem) and [self-organizing structures](https://en.wikipedia.org/wiki/Self-assembly) in physics. – Conifold Aug 31 '23 at 10:41
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    Do you consider a bell curve a pattern? – Vaelus Aug 31 '23 at 17:21
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    Randomness can still be lawful. This is the whole basis of the field of statistics. See this toy for a compelling example of the ubiquity of the Gaussian distribution arising from the addition of many random independent events: https://galtonboard.com/ – Michael MacAskill Aug 31 '23 at 21:19
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    Mandatory Dilbert strip: https://www.reddit.com/r/programming/comments/6jzsi/dilbert_explains_random_numbers/ – armand Sep 01 '23 at 00:06
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    'Randomness' means too many different things to give a simple answer. If you mean are there physical processes that we conventionally describe using stochastic models that give rise to patterns, then yes for sure. – Bumble Sep 01 '23 at 01:02
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    Someone write an answer about Ramsey theory please (sorry i don't have time right now) – Alexander Woo Sep 01 '23 at 04:12
  • The first [definition of "random" given by dictionary.com](https://www.dictionary.com/browse/random) is "proceeding, made, or occurring without definite aim, reason, or pattern". *By (this) definition*, then, randomness excludes patterns. If you mean to use a different definition then do, please, tell us which. – John Bollinger Sep 01 '23 at 16:27
  • @RodolfoAP in fact, this property is the foundation of modern cryptography. The encrypted text must look like a random garbage to anyone who doesn't know the key. – Dmitri Urbanowicz Sep 02 '23 at 09:45

10 Answers10

13
  • Evolution
  • Thermodynamics
  • Quantum mechanics
  • The Poisson distribution for times between random events
  • A Galton board
  • The normal distribution
  • Using the Chaos Game to plot points of the Barnsley fern
  • A Boltzmann machine
  • Hawking radiation
  • Neutron emission during a fission explosion
  • Monte Carlo integration
  • Las Vegas algorithms
  • Ripples in sand
  • Brownian motion
  • Weather
  • Life
causative
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    The thing that creates patterns in Evolution is precisely _not_ the part that is random. – Jack Aidley Aug 31 '23 at 15:54
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    @JackAidley Both random variation *and* selection are necessary for evolution to work. Both, therefore, contribute to the creation of the patterns. (And selection is also a pretty random process.) – causative Aug 31 '23 at 16:08
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    The game of Scrabble doesn't work without patterns (words) emerging from randomly selected letters. –  Aug 31 '23 at 17:51
  • The implied assertion that Evolution has anything to do with randomness is a bold one if I may say so. – csstudent1418 Aug 31 '23 at 18:05
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    I don't understand the objection to Evolution being included in your list. No one objected to weather being random and environmental conditions exert a strong influence over the product of an evolutionary process. I'd argue the future evolutionary state of any organism is as predictable as a very long range weather prediction . –  Aug 31 '23 at 18:13
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    People object because the half-false "evolution increases order and this works because Earth is not a closed system" has bigger meme muscles than the true "evolution is an example of a dissipative process, a direct consequence of the tendency of systems to tend towards their locally highest entropy state" for whatever reasons memes have muscles. – g s Aug 31 '23 at 19:39
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    Maybe also Ramsey Theory? – Charles Sep 01 '23 at 01:08
  • https://en.wikipedia.org/wiki/Ulam_spiral – Blackhawk Sep 01 '23 at 20:06
  • These are all powered by the Central Limit Theorem, so they require certain extra assumptions besides "randomness", which might not necessarily be incompressible noise. Ramsey theory is a better answer. – Corbin Sep 02 '23 at 20:16
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Snow crystals are all different and they are formed randomly, but they still follow the hexagonal pattern. The same tree structure is repeated in all six arms.

Pertti Ruismäki
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    Snowflake pattern generation might seem random, because their growth is based on a set of complex rules that intertwine and are not fully understood, but are not random. There was a scientist that had an example of a snowflake creator, where he could "design" snowflakes by adjusting things like pressure, humidity, etc. in his generation chamber. – Beska Aug 31 '23 at 15:51
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    @Beska If a physicist had a perfectly controlled chamber, they could choose the result of a dice roll. Is a dice roll random? – Jack Aidley Aug 31 '23 at 15:54
  • @JackAidley At that level, no. We treat dice rolls as random generally because we don't have a way to predict them...but as you say, if you understand the physics, and can control the input perfectly, then you'll get a predictable result (minus any quantum level perturbations, which can probably be ignored for this example.) The fact that snowflakes have the same gross structure in all six arms is a good indicator that the generation is *not* random. – Beska Aug 31 '23 at 15:59
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    @Beska if you want to define away macroscopic randomness that's fine. Running single particles through a double slit setup produces a pattern from quantum mechanical randomness. – Dave Aug 31 '23 at 17:48
  • Snowflake "design" is random, because no-one deliberately designs them. – Pertti Ruismäki Aug 31 '23 at 19:56
  • @Dave Yep, agreed; that's a good example that fits the OP's question; I upvoted Causative's answer that is in a similar vein. I wasn't saying "randomness exists nowhere" or "there are no patterns that occur from randomness". Just a comment that I didn't think snowflake generation was the best example for it. – Beska Aug 31 '23 at 21:25
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    @PerttiRuismäki You're saying that anything that doesn't have a human designer is "random"? That seems like it's probably not the definition of random that OP was thinking of. – Beska Aug 31 '23 at 21:28
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    I think all of this goes to show that the original question could use a solid definition for what is meant by "random" and what constitutes a "pattern". – Beska Aug 31 '23 at 21:41
  • @Beska Yes. An intentional selection of one of multiple possibilities is called a deliberate *choice*. An unintentional selection of one of multiple possibilities is called a random *chance*. – Pertti Ruismäki Sep 01 '23 at 04:34
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    @PerttiRuismäki Hmm. I disagree. There can be cases of an "unintentional selection of multiple possibilities" that might appear random at a glance...but that, with enough knowledge, can be accurately and completely predicted. That's not what I would consider "random" for many discussions. But, again, until the OP defines what qualifies as "random" for the question, we can probably just leave it at "well, I guess we define random differently by default." – Beska Sep 01 '23 at 12:06
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    @Beska Random has different meanings in different contexts. In statistics it means "unpredictable". In physics it means "inaccurate". In philosophy and in common speech it means "not intended". This is a philosophical context and the OP asks if patterns can emerge without anyone designing them. – Pertti Ruismäki Sep 01 '23 at 12:50
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    @PerttiRuismäki, the OP presents coin flipping as an example of the kind of randomness they are talking about. That seems to align with the definition of "random" that you attribute to statistics, not the one you attribute to Philosophy. They contrast that with the result of application of a law (from context, a physical law), not with human action or decision making. This is not about human design or lack thereof. – John Bollinger Sep 01 '23 at 15:36
  • @JohnBollinger All the definitions boil down to the core idea that no-one decides random outcomes. That makes them completely unpredictable as there is no agent whose behaviour could be anticipated. – Pertti Ruismäki Sep 01 '23 at 17:24
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Radioactive decay is random

However at the macro level the randomness averages out to give us the ability to determine the half life of different elements

This rate of decay can also be plotted on a chart over time, which shows us this pattern

Peter Bridger
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Gravity Sorting

Fill a bucket with rocks of varying sizes. Shake the bucket randomly for a long time. Inspect the bucket. You will notice that the smallest rocks end up on the bottom and the largest end up on the top. That's because it's easy for small rocks to fall in between larger ones. The final state of the bucket has a lower entropy than the initial state, which by any reasonable definition constitutes a "pattern".

You could also shake the bucket in an extremely periodic manner and achieve the same result. It doesn't matter how you shake the bucket, as long as you provide enough momentum to shift the relative positions of the rocks.

Definitions

Your question is ill-posed because you don't actually define a "random process" or a "pattern". And this allows you to reject any candidate that you like. We can be precise about the gravity sorting example in this way:

  • Slice the bucket vertically into N strata. In each stratum, compute the average diameter of the rocks in the stratum. The bucket is "N-sorted" if the average diameter in each stratum is non-decreasing from the bottom to the top. We count a rock in a stratum if any part of the rock exists in that stratum. Thus, rocks may be counted multiple times, but since we are just computing the average rock size, this is ok.

  • We can formalize the shaking as a sequence of impulses, or force vectors, applied to the bucket over some time period. We can concatenate these vectors to form a single number, S. The Kolmogorov complexity of S, K(S) tells us how "random" it is. The larger the complexity, the more complicated it is to describe. Periodic shaking will have a short description and thus a low K(S).

  • My claim is that for sufficiently long S, N-sorting will be achieved no matter how large K(S) becomes, for N approaching the scale of the smallest rocks. In plain English, no matter how randomly you shake the bucket, the rocks will be sorted if you shake it long enough (and I could give relatively tight bounds on "long enough" so that this is reasonable, but if you are going to object to that, you're being obtuse).

There are some silly edge cases involving irregularly shaped rocks. We could solve them by requiring the rocks to be spherical, but hopefully this is not necessary.

Lawnmower Man
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  • This relies on gravity, which provides a gradient. In the absence of a gradient, do patterns still emerge? – Corbin Sep 02 '23 at 20:16
  • @Corbin well you can't remove gravity, so you are no longer talking about something "in the world". This is part of the problem in underspecifying a "random process". You could invent a mathematical universe and take care to ensure there are no forces which might introduce order, but that would be a different question than asked. – Lawnmower Man Sep 03 '23 at 00:41
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I think that the probability integral transform (PIT) theorem is worth considering. All probability distributions with an invertible cumulative distribution function have a mapping to the standard uniform distribution which is the maximum entropy distribution on the interval [0,1].

And going in another direction we have Sklar's theorem that shows that any joint distribution can be constructed via a map from such inverted distributions as we obtained from PIT.

Randomness does not create patterns per se. Systems are "random" in the sense that to some extent we do not know how to predict them, and it is such systems that in some sense 'create patterns'. So it is the systems, not the description of them being random, that create what we would describe as patterns.

Community
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Galen
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If by pattern you mean essentially order or repeated structure, then yes, definitely. Imagine having a set of Scrabble tiles, one for each letter in the alphabet, and employing an absolutely random process—perhaps involving quantum mechanics—to draw tiles one at a time (and without replacement). So you are essentially shuffling the tiles.

In how many possible ways can this shuffling process turn out? Exactly

 26 * 25 * 24 * … * 2 * 1 = 26!,

which is roughly 400 million billion billion. And one of those myriad outcomes—one which is exactly as likely as any of the others—is

 A, B, C, D, …, X, Y, Z

and there surely is order in that outcome. Another is

 A, Z, B, Y, C, X, …, M, N

which is a folding of the previous outcome. So once again, order and structure.

But bear in mind, too, that the notion of pattern is in a sense subjective. As an example, what may appear to me as a meaningless, “random” string of characters may be instantly recognized as a very meaningful word by a speaker of some other language. And for another example, if there is a sweepstakes drawing for an enormous prize, then there is no rational reason for the winner to be amazed at perceived good fortune. After all, somebody had to win, by construction. The issue was never whether a huge payout would take place, but only to whom it would be awarded.

Paul Tanenbaum
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My two cents ... for what they're worth.

I tried an online random number generator a sol ago. Unfortunately, I do not recall the exact outputs, but suffice it to say that a sequence within the random numbers generated possessed a pattern. To illustrate:

0, -1, 3, 9.01, 9.02, 9.03, 23, 0, 7.4, ...

The pattern [T(n+1) = Tn + 0.01] has been bolded for easy identification.

Is it possible, could it be, , that we can map the order we see in the universe to the pseudopattern 9.01, 9.02, 9.03?

"Order is just a phase in chaos" ~ Numerius Negedius.

Agent Smith
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    Correct. That's why it is so complex to generate random numbers in a computer: in final terms, random numbers just follow very complex patterns. – RodolfoAP Aug 31 '23 at 10:15
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    @RodolfoAP computers can't generate random numbers at all, they can only produce numbers which are unpredictable enough to appear random – Alan Birtles Aug 31 '23 at 15:23
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    ["When Apple released its Shuffle feature for iPods, users were deceived by the true randomness of its playback; songs from the same album or artist were often grouped by chance. Complaints led Steve Jobs to alter the device’s programming and begin offering Smart Shuffle, which allowed users to adjust the likelihood of hearing similar songs in a row. 'We’re making it less random,' he said, 'to make it feel more random.'”](https://www.laphamsquarterly.org/luck/miscellany/making-it-less-random) – Simon Crase Sep 01 '23 at 07:02
  • @AlanBirtles The descriptor "random" depends on the information available to the system making the prediction. If you sent me numbers generated by [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_Twister) but did not tell me where they came from or what the seed number was then that data generating process will be random for me even if it isn't random for you. – Galen Sep 02 '23 at 15:06
  • @Galen no, unpredictable for you, not random. that's why mersenne twister is called a pseudo-random number generator – Alan Birtles Sep 02 '23 at 18:05
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Brain-Based Model (Added Material)

Pattern recognition is the product of a cognitive process. If the Universe is in essence a random process then it is random in a way that pattern recognition and randomness arise as pattern recognition in the human brain.

What is signal and what is noise? - Youtube

https://youtu.be/sJR5igJUGIA

Video notes that initially the detection of the residual cosmic microwave background radiation was considered noise! Then it was interpreted as evidence of the big bang!

Random Processes - Introduction - Youtube

https://youtu.be/QVB5aJUL0Kw?t=83

The products or attributes of a random experiment or random process include the generic pattern called the signal and the noise. Metaphorically the continuous random process is described as a bag of signals, and when we sample the continuous process, we pick a particular signal and noise sample out of the bag! The bag in theory holds an infinite possible set of signal and noise sample combinations! Scientists and engineers even use statistical methods to characterize the attributes of random noise! So even the random noise can fit to a recognized pattern!

SystemTheory
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From a mathematical perspective, the answer is a clear "no". If process is random, it means that it cannot be predicted, which precludes the existence of a pattern - if there were a pattern it could be used to make predictions.

I rather like the definition of randomness used in algorithmic information theory: A sequence of bits (which may represent a sequence of heads or tails, dice rolls, scrabble tiles pulled from a bag etc.) is random if it is shorter than the shortest computer program that can generate it. In other words it is compressible.

"Aha" you say, "but a sequence of coin flips may give you a sequence of 32,768 (my favourite integer power of two) alternating heads and tails". This is true, however in reality the way this sequence would be generated would be for someone to repeatedly flip a coin for a very long time, while someone else monitors the sequence and raises the alarm when they detect a suitably compressible sequence. So it isn't a random process, each of the 32768 coin tosses were random (i.e. unpredictable) but it is the deterministic component (post-hoc pattern selection) that gives rise to the "pattern generator" and the compressibility of the sequence.

On a more philosophical point - there is arguably no such thing as randomness in the macroscopic world (and it hasn't been ruled out in the quantum world either). We use "randomness" to make phenomenological models for deterministic systems that are either chaotic (strongly dependent on unknown initial conditions) or involve too many variables for us to model the deterministic physics directly (e.g. statistical mechanics). Fortunately the properties that can be modeled this way are often useful, even if they ignore the actual mechanism. Note that nothing is "explained" by random chance - if we say that something is "due to random chance" it is basically saying "we don't know the causal mechanism by which this happened". So even if "randomness generates patterns", it is still the result of deterministic behaviour.

The real problem here is the question is too badly posed to have a really solid answer. The question doesn't adequately define what is meant by "randomness" (and I think if it did it would be self-answering) but also there are so many vague conditions on what defines a pattern that any example could be accepted or rejected arbitrarily.

Dikran Marsupial
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Sufficiently large objects have inevitable inner structure, regardless of how those objects were constructed. The classic example is Ramsey theory: a sufficiently large group of randomly-selected individuals (say, people at a gathering) will always be related by any binary relation in certain ways.

Corbin
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