Cosmology, the study of the origin and structure of the universe, has seen many schools of thought come and go over the centuries. While 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, which proposes that the distribution of matter in the universe is fractal in nature.

Space Ponder actively engages with and supports fractal cosmology. We conduct research on this topic, draw conclusions, and share our findings publicly. We think that fractal jargon will become more common in the near future.

Fractal patterns, which repeat at every scale, are found everywhere in nature - in coastlines, mountain ranges, river networks, plants, and even in the human body. Proponents of fractal cosmology argue that the universe itself shows evidence of fractal scaling behaviour, contrary to the traditional view of cosmology which assumes a smooth distribution of matter.

While 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 as computational power increases and previously difficult calculations become feasible.

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.

This theoretical concept challenges long-held assumptions and requires rethinking foundational questions like the age and size of 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

Fractal geometry is characterized by self-similar patterns that repeat at every scale. These recursive and branching structures are found extensively in the natural world and, proponents argue, in the cosmic landscape 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 hundreds of millions of lightyears.

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 dynamics.

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 structure.

## Fractals & Fractal-Like Patterns

True fractals display exact self-similarity at all scales, have fractional dimensions, and are defined by simple recursive equations. However, natural structures do not have this precise property. Their patterns are statistically self-similar rather than exactly identical. Also known as quasi-fractals or pseudo-fractals, they are not self-similar like fractals, but they do exhibit fractal like geometry, which means that they have similar patterns at different scales.

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.

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

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

So, while 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 quasi-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 like the butterfly effect. This means 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.

The category of quasi-fractals gives us flexibility to explain the complexity we observe empirically in the world. By understanding the principles of fractal geometry, we can better understand the formation and evolution of the universe and grasp it.

## The Butterfly Effect and Chaos Theory

The "butterfly effect" refers to the idea that small causes can have disproportionately large effects. The flapping of a butterfly's wings might ultimately cause a tornado through a cascading chain of events, the analogy puts. This concept is part of chaos theory, which studies complex, dynamic systems that are highly sensitive to initial conditions.

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

Chaos theory has been invoked to help explain a range of phenomena from weather patterns to population growth. In cosmology, some propose that the specific initial conditions of the Big Bang may have led to chaotic growth of fractal structures observed today. Tiny quantum fluctuations in density grew through gravitational instability into the cosmic web of voids and filaments.

The butterfly effect highlights that in complex systems like the weather, stock market, or universe, we can never know all the variables or predict long-term outcomess. There is an inherent unpredictability when small uncertainties get dramatically amplified. Understanding chaos and fractals provides insight into managing such systems.

A classic example of the butterfly effect is the double pendulum experiment. A simple pendulum swinging back and forth is very predictable. But when a second pendulum is attached, the motion becomes chaotic. Two pendulums attached end to end will trace out a fractal pattern over time, wildly sensitive to the starting angles. This shows how fractals and chaos can emerge from very basic physics. Even simple nonlinear systems can display complex emergent behaviour reflecting underlying fractal dynamics.

## 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. Striking 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.

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. This means that two double pendulums with the same initial conditions will eventually diverge and exhibit wildly different behaviours.

In other words, the double pendulum experiment is not random, but it is unpredictable. 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.

The double pendulum experiment is a simplified example of how we predict the weather. The models are run on supercomputers, and they produce a forecast of the weather for a certain period of time. The accuracy of the forecast depends on the accuracy of the models and the quality of the observations.

## Future Outlook for Fractal Cosmology

Fractal cosmology has promising prospects for the future, thanks to anticipated mathematical, computational, and technological advances. Further development of multifractal models and related analytic techniques will provide more nuanced characterization of cosmic data. Improved algorithms for measuring fractal dimensions and properties will also be impactful. The next generation of supercomputers will allow running vastly more detailed simulations of universal evolution, incorporating fractal geometry and testing new principles. The likes of quantum computing could exponentially speed up fractal analysis and modelling.

I predict that we may hear more fractal jargon being used in the general public in the years to come.