Chaos and Patterns

Randomness - Patterns

"chaos" means "a state of disorder". There is no universally accepted mathematical definition of chaos.

Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.

Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.

Patterns in living things are explained by the biological processes of natural selection and sexual selection.

Mathematics seeks to discover and explain abstract patterns or regularities of all kinds.

Visual patterns in nature find explanations in chaos theory, fractals, logarithmic spirals, topology and other mathematical patterns.


Chaotic behavior exists in many natural systems, such as weather and climate.

It also occurs spontaneously in some systems with artificial components, such as road traffic.

Science is more than facts and patterns. Everything should be explained and proved. You should understand how one fact follows from another and (ideally) you should be able to continue. It helps to see the whole picture and to find the shortest ways to solve problems.

Problems in Predictions

The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems — a response popularly referred to as the butterfly effect — rendering long-term prediction of their behavior impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable.This behavior is known as deterministic chaos, or simply chaos.

The theory was summarized by Edward Lorenz as: (1) Chaotic systems are predictable for a while and then 'appear' to become random. (2) Prediction depends on, how accurately its current state can be measured. (3) When meaningful predictions cannot be made, the system appears random.


This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.

Chaos theory has applications in many disciplines, including meteorology, anthropology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, and philosophy. The theory formed the basis for such fields of study as complex dynamical systems, edge of chaos theory, and self-assembly processes.

Chaos theory began in the field of ergodic theory. Later studies, also on the topic of nonlinear differential equations,

Pattern Matching

In computer science, pattern matching is the act of checking a given sequence of tokens for the presence of the constituents of some pattern.

Pattern Recognition

Pattern recognition is the process of classifying input data into objects or classes based on key features. There are two classification methods in pattern recognition: supervised and unsupervised classification.

Pattern Recognition is a mature but fast developing field, which underpins developments in areas such as computer vision, image processing, text and document analysis and neural networks. It is closely akin to machine learning, and also finds applications in fast emerging areas such as biometrics, bioinformatics, multimedia data analysis and most recently data science.

Humans are the most amazing pattern-recognition machines. They have the ability to recognize many different types of patterns. If you've ever watched a toddler learn words and concepts, you can almost see the brain neurons firing as the small child starts to recognize patterns for differentiating between objects. Intelligence, then, is really just a matter of being able to store more patterns than anyone else. We could build machines that could recognize as many chessboard patterns as a chess grandmaster.

Artificial intelligence pioneer Ray Kurzweil was among the first to recognize how the link between pattern recognition and human intelligence could be used to build the next generation of artificially intelligent machines. In his, How to Create a Mind: The Secret of Human Thought Revealed, Kurzweil describes how he is teaching artificially intelligent machines to think, based on the stepwise refinement of patterns. According to Kurzweil, all learning results from massive, hierarchical and recursive processes taking place in the brain. Take the act of reading – you first recognize the patterns of individual letters, then the patterns of individual words, then groups of words together, then paragraphs, then entire chapters and books. Once a computer can recognize all of these patterns, it can read and "learn."

Kevin Ashton analyzed “how experts think.” It turns out patterns matter, and they matter a lot. A star football quarterback needs to recognize all kinds of patterns – from the type of defense he’s facing, to the patterns his receivers are running, to the typical reactions of defenders. All of this, of course, has to happen in a matter of nanoseconds.

You can see patterns all around you. Getting to work on time in the morning is the result of recognizing patterns in your daily commute and responding to changes in schedule and traffic. Ex: driverless cars, which are able to recognize all of these traffic and schedule changes faster than humans. Diagnosing an illness is the result of recognizing patterns in human behavior.

The future of intelligence is in making our patterns better, our heuristics stronger. In his article for Medium, Kevin Ashton refers to this as "selective attention" - focusing on what really matters so that poor selections are removed before they ever hit the conscious brain.

Living things like orchids, hummingbirds, and the peacock's tail have abstract designs with a beauty of form, pattern and colour that artists struggle to match.

Symmetry is pervasive in living things. Symmetry has a variety of causes. Radial symmetry suits organisms like sea anemones whose adults do not move: food and threats may arrive from any direction. Spirals are common in plants and in some animals, notably molluscs.

Being able to recognize patterns is what gave humans their evolutionary edge over animals.

Accept Chaos in Life

Some Popular Quotes by Many


Plato, looking only at his work on natural patterns — argued for the existence of universals. Pythagoras explained patterns in nature like the harmonies of music as arising from number, which he took to be the basic constituent of existence. Leonardo Fibonacci, introduced the Fibonacci number sequence