Authors: Blair D. Macdonald
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 of accelerated expansion is not unique to the universe, but is also evident with tree (plant) growth. As trees are fractals: do fractals offer an explanation and insight to the accelerating expansion property of the universe? An experiment was undertaken on the classical Koch snowflake fractal. The snowflake was inverted to model observations from within an iterating fractal set – as if at a static ‘measured’ position. Unlike with the fractal snowflake formation, new triangles sizes were held constant allowing earlier triangles in the set to expand as the set iterated. Using classical kinematic equations velocities and accelerations were calculated for both the area of the total fractal, and the distance between points within the fractal set. The inverted fractal was also tested for the 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 increasing velocities and accelerations. The model was consistent with the standard ΛCDM model of cosmology and demonstrated: a singularity ‘Big Bang’ beginning; homogeneous isotropic expansion consistent with the CMB; Hubble's Law – with a Hubble diagram and Hubble's constant; and accelerating expansion with a ‘cosmological’ constant an expansion rate consistent with, and capable of explaining the early inflation epoch of the universe. It was concluded that the universe behaves as a general fractal object. Thought the findings have obvious relevance to the study of cosmology, they may also offer insight to all things fractal: the recently discovered accelerating growth rate of trees.
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