Fractal Cosmology

[FractalWoman]

Abstract

   A fractal model of the cosmos is presented by demonstrating a self-similarity between the Universe and the infamous Mandelbrot Set iterated function system (Mset1). Current cosmological models involve numerous mathematical formalisms supported by a complex language of cryptic symbols often wrapped in  confusing or counter-intuitive theories. But what if there existed a model or system that required only “one” equation (or mathematical formula) with “zero” parameters and could reproduce “all” the observables of the Universe? And, what if we could solve this equation using only addition and multiplication, and no calculus?  According to Occum's Razor (?), this description of the Universe would be preferable, as long as it does not contradict observation or experimental fact. Using the computer as my telescope, microscope and particle accelerator,  I studied in great detail one of the simplest iterated function systems (IFS), Mset, and uncovered an unmistakable self-similarity between Mset and our Universe. In this framework, an analogy for gravity is presented leading to a new interpretation of  singularities, black holes and event horizons. The complex morphologies of galaxies and galaxy clusters are easily reproduced using the simple techniques outlined in this essay. Particle dynamics and magnetic fields are also strangely encoded into this strange attractor. The concepts of matter, antimatter and light are explained in the context of this new paradigm leading to a new interpretation of Planck's constant and it's associated units of length, mass and time. In short, the Mset-Universe analogy presented in this essay points a  self-similar fractal universe where all the forces in nature can be seen as emergent properties a very simple mathematical formalism in close alignment with the Mandelbrot Set iterated function system.

1 In this essay, the term Mset refers to the iterated function system z=z^2+c as applied to the points on the complex plane.

[weavers]

Behold morph not, think lot : Concentrate thee, child of the world into the dark, alone, you must be, answer will come to thee! Door shut Mind open! The confine that binds, will be broken!

Go growth with the force!