The expanding fractal

The expanding fractal

Abstract

One of the great questions in modern cosmology today is what is causing the accelerating

expansion of the universe – the so-called dark energy. It has been recently discovered this

property is not unique to the universe; trees also do it, and trees are fractals. Do fractals offer

insight to the accelerating expansion property of the universe and more?

In this investigation, a simple experiment was undertaken on the classical (Koch snowflake)

fractal. It was inverted to model and record observations from within an iterating fractal set as

if at a static (measured) position. New triangle sizes were held constant, allowing earlier

triangles in the set to expand as the set iterated.

Velocities and accelerations were calculated for both the area of the total fractal and the

distance between points within the fractal set using classical kinematic equations. The inverted

fractal was also tested for Hubble's Law.

It was discovered that the area(s) expanded exponentially, and as a consequence, the distances

between points – from any location within the set – receded away from the observer at

exponentially increasing velocities and accelerations. The model was consistent with the

standard ΛCDM model of cosmology and demonstrated a singularity Big Bang beginning,

infinite beginnings; homogeneous isotropic expansion consistent with the CMB; an expansion

rate capable of explaining the early inflation epoch; Hubble's Law – with a Hubble diagram and

Hubble's constant and accelerating expansion with a ‘cosmological’ constant. It was concluded

that the universe behaves as a general fractal object. Though the findings have obvious

relevance to the study of cosmology, they may also give insight into the recently discovered

the accelerating growth rate of trees, the empty quantum-like nature of the atom, and possibly our

perception value of events with the passage of time.

My Youtube presentation of fractal expansion (fractspansion).

In memory of Neil Armstrong who died on the day I published this entry. All pilots inspire (me), he was the greatest of them all.

FRACTAL ECONOMICS