The Fractal Debate

Since the introduction of fractals by Benoit Mandelbrot, the fractal nature of the universe has become a hotly debated topic. On the one hand, the standard model of cosmology requires that matter be evenly distributed throughout the cosmos. This allows cosmologists to model the universe using Einstein’s theory of general relativity. On the other hand, matter in the universe does appear to clump together in a self-similar, fractal manner. As such, a truly fractal universe has not been ruled out.

First it must be said that there are no tools or methods that can be used to directly detect “fractality” with any certainty. The box counting method, for instance, can only be used to calculate the fractal dimension of a given distribution of data, whether it be fractal or not fractal. For example, one can use the “box counting” method to calculate the fractal dimension of the digits of PI, but that does not mean that the digits of PI are fractal.  The same can be said for counts in spheres, a method used in astronomy to quantify the “clumping” of matter. It also should be noted that all “space filling” fractals will look mathematically homogeneous at some very large scale. In this manner, “fractality” need not contradict relativity. In other words, the universe could be isotropic, homogeneous AND fractal.

Instead of asking the question, “IS the universe a fractal” which cannot be answered with any mathematical certainty, maybe we should be asking different questions. CAN the universe be fractal? What does fractal geometry buy us? Fractals are usually generated using very simple formulae. Does there exist a simple formula for generating a Universe? CAN this formula reproduce the very specific morphologies of planetary nebula, galaxies and galaxy clusters? CAN this same formula tell us something about gravity, dark matter and dark energy? CAN this same formula explain what we observe at the quantum scale. A truly fractal theory of the Universe must be applicable to all scales of Organised Matter including the biological scale. The goal of my research is put an end to the fractal debate by demonstrating the fractal nature of the universe, at all scales of organised matter, beyond a reasonable doubt.

Embrace the Fractal Paradigm


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