Cosmology, the study of the origin and structure of the universe, has seen many schools of thought come and go over the centuries. Although the current widely accepted cosmology is based on general relativity and the Big Bang model, there are always minority views challenging the status quo. One lesser known but slowly growing branch of cosmology is fractal cosmology.

There are fractal patterns everywhere in nature - coasts, mountains, rivers, plants, and even the human body. According to fractal cosmology, the universe itself exhibits fractal scaling behaviour, contrary to traditional cosmological assumptions.

Even though fractal cosmology has been around since the 80s, it is still considered fringe and has failed to gain widespread acceptance. However, in recent years more scientists have been taking interest.

Key concepts in fractal cosmology include scale invariance, recursive patterns, and fractional dimensions. Instead of the universe being homogenous at large scales as predicted by the Cosmological Principle, it is proposed to be ** heterogeneous **at all scales. Matter is distributed in clusters within clusters, similar to a fractal branching pattern.

Such a hypothetical concept calls into question long-held assumptions and requires rethinking core questions about the universe. More research is still needed to test predictions of fractal cosmology against astronomical observations. But its mathematical simplicity and natural appeal are attracting curious minds.

## Fractal Patterns Throughout Nature and the Cosmos

Various recursive and branching structures are found extensively in the natural world and, proponents argue, in the cosmic scenery as well.

In nature, we see fractal-like patterns in the complex branching networks trees, circulatory systems, and lung airways. Fractals are evident in the swirling turbulence of fluids. Snowflakes, with their intricate six-fold symmetry, have spawned some of the most well-known fractal models.

When we observe our galaxy and others in the cosmos, we can discern similar fractal structures. The distribution of stars throughout galaxies reveals fractal clustering, with small clusters nested within larger clusters at larger scales. Analyses of galaxy distribution data have uncovered fractal regularity out to scales of many light years.

The cosmic microwave background radiation, relic of the Big Bang, contains temperature fluctuations that also exhibit a fractal pattern. Some theorists argue that the entire observable universe shows fractal self-similarity due to gravitational clustering.

So, from the smallest snowflakes to the largest mapped structures in the universe, fractal geometry seems ubiquitous. This scale-invariant property is a key inspiration for fractal cosmology models attempting to explain the origin and growth of cosmic structures.

Fractal cosmology was largely developed and popularized by the Italian astrophysicist Luciano Pietronero, who famously stated..

"The universe shows a definite fractal aspect over a fairly wide range of scales."

## Fractals & Fractal-Like Patterns

True fractals display exact self-similarity at all scales, have fractional dimensions, and are defined by simple recursive equations. But natural structures do not have this precise property. Their patterns are statistically self-similar rather than exactly identical. They are wide in scale but limited in scale. Research from the Sloan Digital Sky Survey has revealed fractal patterns across a range of 330 million light years.

Fractal-like patterns are sometimes informally referred to as "quasi-fractals". Quasi-fractals exhibit many of the characteristics of true fractals, such as self-similarity and complex, detailed structures at various scales, but they may not strictly adhere to all mathematical definitions of a fractal. These patterns often appear in natural systems and other contexts where the strict requirements of fractal geometry are relaxed or only approximately met, hence their other name, approximate fractals.

For example, the branches of a tree are not perfect copies of each other. Variability exists in the angles, thicknesses, and lengths.

But there is an overall recurrence of the branching structure at different scales that can be described as fractal-like. Coastlines appear very irregular up close but smooth at far distances in a fractal manner.

Though the smaller and larger versions are not exactly the same. This looser definition of fractals is more useful when modelling and pondering natural forms.

Fractal-like patterns may not have pure mathematical fractal qualities, but they exhibit similarities such as self-organization, recursion, and scale invariance.

Even though cosmologists proposing universal fractality are not implying true mathematical fractals, the fractal-like clustering observed astronomically can still inspire fruitful models of large-scale structure formation.

One example of a an approximate fractal is a galaxy, like the mighty Whirlpool Galaxy and even our own.

The distribution of stars within a galaxy is fractal-like, with small clusters nested within larger clusters.

However, the fractal dimension of a galaxy is not exactly 2, which is the dimension of a true fractal.

The reason why the universe is not a true fractal is because of the way it formed. As you may know, the universe began as a hot, dense soup of wee particles. As the universe expanded and cooled, those wee particles clumped together to form stars, galaxies, and other structures. Gravitational instability.

Gravitational instability is a non-linear process, which means that it is sensitive to initial conditions aka the butterfly effect, meaning that even wee changes in the initial conditions can lead to large changes in the final structure of the universe.

As a result of gravitational instability, the universe is not perfectly smooth. Instead, it has a complex, hierarchical structure. This structure is fractal-like over a range of scales, but not exactly at all scales. Limited.

The category of "fractal-like" structures provides a versatile method for explaining the complexity and similarity we observe empirically in the world. By understanding the principles that govern fractal-like patterns or approximate fractals, we can gain better insights into the formation and evolution of various natural and cosmic phenomena.

## The Butterfly Effect and Chaos Theory

According to the butterfly effect, a small cause can have a disproportionately large impact. A butterfly flapping its wings could eventually cause a tornado, the metaphor usually goes. Chaos theory studies complex, dynamic systems that are highly sensitive to initial conditions.

Chaos and fractals go hand in hand. The endlessly recursive patterns reflect nonlinearity and unpredictability in chaotic systems. Slight variations in starting parameters for a fractal equation lead to wildly divergent outcomes.

Several phenomena, including weather patterns and population growth, have been explained by chaos theory. Physicists have proposed that chaotic growth of fractal structures was influenced by the specific conditions of the Big Bang. Gravitational instability created cosmic webs of voids and filaments from tiny quantum fluctuations in density.

As the butterfly effect shows, there are always unpredictable variables in complex systems like the weather, stock market, and universe. Chaos and fractals provide insight into managing systems whose uncertainties are dramatically amplified.

An experiment using a double pendulum is a classic example of the butterfly effect. A simple pendulum can actually be predictably swung back and forth, but when a second pendulum is attached, the motion becomes chaotic. With two pendulums end to end, fractal patterns emerge over time, wildly sensitive to starting angles. Even simple nonlinear systems can display complex emergent behaviour reflecting underlying fractal patterns.

## The Predictable Unpredictability of Fractals

Fractals may exhibit sensitivity to initial conditions and chaotic behaviour, but there is also a predictability to their overall patterns. One can make useful predictions about a fractal's general properties and dimensions while accepting variability at the smallest scales. So, fractals have a certain amount of order within their randomness. Uncertainty in the details does not mean complete lack of predictability. A balance between order and chaos is characteristic of many natural systems.

Fractal cosmology seeks to explain both the predictability of large-scale structure and the unpredictability at galactic and stellar scales using fractal models tuned to observations. The goal is to better predict the overall distribution while accepting variability at smaller levels.

### not random

The double pendulum experiment is not random. It is a deterministic system, meaning that its future behaviour is completely determined by its initial conditions. However, the double pendulum is also a chaotic system, meaning that its behaviour is extremely sensitive to wee changes in its initial conditions, meaning that two double pendulums with the same initial conditions will eventually diverge and exhibit wildly different behaviours.

### Non Linear

Given the same initial conditions, it is impossible to predict with certainty what the motion of the double pendulum will be in the future.

This is because the double pendulum is a non-linear system. In non-linear systems, wee changes in the initial conditions can have a magnified effect on the system's behaviour. This is what makes the double pendulum chaotic.

### Weather

The double pendulum experiment is a simplified example of how we predict the weather. Satellite data is utilized to run models on supercomputers, which then generate weather forecasts for specific periods. The precision of these forecasts hinges on the accuracy of the models and the quality of the observations. However, they cannot predict with absolute certainty, which is why, despite predictions of dry weather today, it is raining.

## Future Outlook for Fractal Cosmology

The future of fractal cosmology looks promising thanks to computational, mathematical, and technological advances. More sophisticated data analysis will be possible with multifractal models. Improved algorithms for measuring fractal dimensions and properties will also be beneficial.

Interestingly, phenomena such as the butterfly effect in weather patterns and the presence of fractals in nature may indirectly support the principles of fractal cosmology. These natural occurrences hint at the potential underlying fractal structures in the universe, providing a compelling case for further exploration and validation of fractal cosmology theories. We predict that we may hear more fractal jargon being used in the general public in the years to come.

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