Authors: Blair D. Macdonald
In a recent publication it was discovered trees growth rate accelerates with age. Trees are described as being clear examples of natural fractals. Do fractals offer insight to the accelerating expansion? In this investigation the classical (Koch snowflake) fractal was inverted to model the growth of a fractals seen from a fixed – new growth – perspective. New triangle area sizes represented new branch volume; these new triangles were held constant allowing earlier triangles in the set to expand as the fractal set iterated (grew) through time. 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. It was discovered that the area(s) of earlier triangles expanded exponentially, and as a consequence the total snowflake area grew exponentially. Distances between points (nodes) – from any location within the fractal set – receded away at exponentially increasing velocities and accelerations. For trees, if the new growth branch volume size remains constant through time, its supporting branches volumes will grow exponentially to support their mass. This property of fractals may account for the accelerating volumetric growth rates of trees. A trees age can be measured not only by its annual (growth ring) age, but also by its iteration age: the amount of iterations from trunk to new growth branch. Thought the findings have obvious relevance to the study of trees directly, they may also offer insight into the recently discovered observation of the accelerating growth rate of the universe.
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[v1] 2015-03-28 14:56:48
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