What do fractals teach us about patterns that occur again and again at different scales and sizes?

Patterns like weather, diseases, stock-markets, migration, technological development, traffic flow, and many others follow the self-similarity of fractals at different scales.

“Miracles happen, not in opposition to Nature, but in opposition to what we know of Nature”. — St. Augustine

Chaos (entropy) describes a system that has apparent randomness but, when more closely observed, the order is seen. Fractals are objects in which the same patterns occur again and again at different scales and sizes. In a perfect mathematical fractal — such as the famous Mandelbrot set, this “self-similarity” goes infinitely deep: each pattern is made up of smaller copies of itself, and those smaller copies are made up of smaller copies again, forever. Many natural phenomena are fractal to some degree.

The chaos and irregularity of the world — Mandelbrot referred to it as “roughness” — is something to be celebrated. It would be a shame if clouds really were spheres and mountain cones. Look closely at a fractal, and you will find that the complexity is still present at a smaller scale. A small cloud is strikingly similar to the whole thing. A pine tree is composed of branches that are composed of branches — which in turn are composed of branches.

A tiny sand dune or a puddle in a mountain track has the same shapes as a huge sand dune and a lake in a mountain gully. This “self-similarity” at different scales is a defining characteristic of fractals. Fractal geometry can also provide a way to understand complexity in “systems” as well as just in shapes. The timing and sizes of earthquakes and the variation in a person’s heartbeat and the prevalence of diseases are just three cases in which fractal geometry can describe the unpredictable.

“The ultimate purpose of life, mind, and human striving: to deploy energy and information to fight back the tide of entropy and carve out refuges of beneficial order.”— Steven Pinker

The disorder is not a mistake or a curse; it is our default. Order is always artificial and temporary. An autopoietic system is the regeneration of components within a boundary of its own making. We have to expend a lot of energy to keep things in an ordered state. What if the disordered state is by design or the desired goal or part of the plan. The energy needed to remain in a disordered state will be very less. Low entropy or complexity brings boredom and complacency and high entropy brings confusion and despair. Optimum entropy brings pleasantness, positivity, and surprise.

A higher degree of predictability leads to rigid, inflexible thinking associated with repetitive and ruminative disorders such as depression, addictions, and OCD. And while at the other end of the spectrum, too much entropy is associated with a psychotic detachment from reality. We recognise life as that is made by certain chemicals, which have come together. May it is plants, animals, humans, or bacteria they are the same basic chemicals. The question then is, are there any other chemical combinations that we don’t recognise as life…(and maybe they don’t recognise us as life)

The equilibrium in nature is dynamic. “What else, when chaos draws all forces inward to shape a single leaf” Conrad Aiken

Instead of seeing entropy as a form of destruction (things falling apart) it is to be seen as a state of active play. Can collapse or chaos/ disturbance be used for building the future? How definitions limit us, chaos or collapse is seen as negative but can be used for building the future making it positive. What if systems expend part of themselves to sustain and rest is consumed in disorder (entropy) or the rest collapses to form a preplanned or designed disorder that is essential for the future or is future-ready.

Imagine some part of the home items or furniture collapses due to entropy to become something, which is a future need or can be usable later. Collapse due to entropy becomes something useful later. This is how the natural system is. Something dies and becomes food or ingredients, a source of energy for someone else.

By studying extremes and self-similarities we can learn which systems and features are more sensitive to changes so that we can apply this knowledge to build new systems that are more resilient and symbiotic.

Entropy Series #6