I would say in terms of complexity I will look for patterns and if I don’t find any obvious patterns (if it looks random) I would consider that as being a complex system, potentially irreducible.

Weather patterns, bubbles in boiling water, cream mixing with milk are examples that come to mind as potentially complex, computationally irreducible systems.

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In this module, we learned about the Principle of Computational Irreducibility and its relationship to scientific processes. For example, we examined the pigmentation patterns of mollusk shells (note image below) which, like a one-dimensional cellular automata, grow one line at a time. What other “simple” patterns do you come across that exhibit “complex” behavior? On what basis do you determine whether it is simple or complex?

Flocking behavior, herd immunity, cosmic web evolution. Based on Kolmogorov dimension, and to certain degree to Hausdorff as well.

Economic data patterns. Simplicity/ complexity is a question of the interpretation models applied.

Idk

Cow horn growth rings may be a similar event, but tree rings can be also deciphered.

Complexity occurs after the simplicity of line by line, or ring by ring. Complexity is the whole shell, horn, or tree made of the unified simplicities.

The cicle of natural reproduction, the birth, old age, sickness and death of life

If the patterns were organised, I would consider them simple; if they were random and chaotic, I would consider them complex. And I feel that rainfall over the ocean is an example of “complex” behaviour.

The pattern of tiger’s stripes are different from one to another. No two tiger have the same stripes. If you want to draw a tiger’s stripe it’s easy and seemingly simple yet in nature you won’t find the same patterns between 2 tigers.

I’ve always been fascinated by the idea that every human being that has ever existed has a unique fingerprint. Fingerprints are incredibly complex patterns that are abundant in curves and awesome patterns.

Ladies and Gentlemen,

The eyes also mimic the complexity of fingerprint data- eye or retina scans being used for registering citizens in Modi`s India.

👀👁️🐼🐨🐸🐌🦜

Patterns that exhibit complex behavior while arising from simple rules are abundant in various domains of science and mathematics. Some examples include:
Conway’s Game of Life: This is a classic example of a cellular automaton that starts with a few simple rules governing the states of cells on a grid, and it leads to the emergence of intricate patterns, including gliders, oscillators, and even structures resembling living organisms.
Fractals: Fractals are geometric patterns that exhibit self-similarity at various scales. The famous Mandelbrot set is generated from a simple iterative equation, yet it produces highly intricate and detailed patterns.
Diffusion-Limited Aggregation: This model simulates the aggregation of particles undergoing Brownian motion. It starts with a few particles and simple rules, and over time, complex branching patterns emerge that resemble natural structures like snowflakes and dendritic crystals.
Chaos Theory: Systems governed by deterministic chaos can exhibit complex and unpredictable behavior despite having simple underlying equations. The weather is a classic example, where small changes in initial conditions can lead to vastly different outcomes.
Turing Patterns: These patterns arise in reaction-diffusion systems, where simple chemical reactions and diffusion processes lead to the formation of intricate spatial patterns, often seen in natural phenomena like animal coat markings and vegetation patterns.
L-systems: L-systems are used to model the growth of plants and other organic structures. They are based on a few simple rewriting rules that, when iteratively applied, generate complex branching patterns.
Determining whether a pattern is simple or complex can be subjective and context-dependent. However, a few criteria often used to characterize complexity include:
Number of Rules: A pattern with a small number of rules is generally considered simple, while those with a large number of rules are often considered complex.
Emergent Behavior: If a pattern exhibits behavior that is not directly dictated by its individual components or rules, it is often labeled as complex. Emergent behaviors are usually unexpected and difficult to predict from the basic rules.
Hierarchy of Structures: Complex patterns often involve multiple levels of structures or components, with interactions between them leading to intricate behavior.
Unpredictability: If a pattern is highly sensitive to initial conditions or exhibits chaotic behavior, it’s often considered complex due to the difficulty in predicting its long-term evolution.
Information Content: Complex patterns tend to encode a significant amount of information in their structure, which may not be apparent from the simplicity of their rules.
In the case of the pigmentation patterns of mollusk shells or other similar examples, simplicity might refer to the underlying rules governing the pigmentation process, while complexity could pertain to the intricate and diverse patterns that emerge as a result of those rules interacting over time.

There are countless examples of such complicated behavior in nature. For example, predicting how a baby would evolve and how it would look like as an adult is very complicated.

Or simulating the sound of a forest at night.

This mining of programs in the computational universe to model systems in nature is indeed very fun and I’m really surprised why isn’t everyone doing this.

It is a kind of field where everyone can contribute no matter what who you are and has great applications for society.

Patterns that display intricate behavior despite originating from basic rules are prevalent across various scientific and mathematical realms. Examples include Conway’s Game of Life, a cellular automaton generating diverse patterns from simple grid cell states; fractals like the Mandelbrot set, characterized by self-similarity at different scales via iterative equations; Diffusion-Limited Aggregation, simulating particle aggregation through basic rules to form complex structures akin to natural formations; Chaos Theory, where deterministic chaos yields unpredictable outcomes despite simple equations, as seen in weather systems; Turing Patterns, arising from simple chemical reactions and diffusion to create elaborate spatial patterns as observed in natural phenomena; and L-systems, modeling organic growth via simple rewriting rules to produce intricate branching patterns. Determining complexity is subjective but often involves assessing the number of rules, emergent behavior, hierarchical structures, unpredictability, and information content encoded in patterns. In the case of mollusk shell pigmentation, simplicity may refer to basic pigment rules while complexity encompasses the diverse patterns arising from their interactions over time.