Proceedings of the 51st Annual Meeting of the ISSS - 2007, Tokyo, Japan, Papers: 51st Annual Meeting

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Fractal Universes

luis sancho


A fractal is a form which repeats itself when we grow or diminish in scale by a certain factor.
The Universe is made of fractal structures, whose forms reproduce into multiple clonic forms that latter re-organize themselves, giving birth to macro-forms similar to the original ‘cell’. The most obvious fractals are those created by the iterative, repetitive nature of geometrical space. For example, a salt or ice crystal is a chemical fractal - a triangular or cubic crystal that reproduces its form as it grows in scale and recomposes itself into huge tetrahedrons and cubes. On the other hand, mathematical fractals are iterative equations, which plotted in the same space-time plane, repeat their form when we grow or diminish their scale.
But fractals are not only fixed, geometrical forms that repeat in spatial scales. There are also fractal, temporal cycles: logic, organic functions that repeat themselves in different scales, at different time intervals.
For example, a human being is a fractal organism, made of fractal cells, whose organic functions repeat themselves at the individual macro-scale in a longer time-interval: the feeding, reproductive, informative (sensorial), and social behaviour of human beings are a macro-repetition of the same cycles that take place in cells. Cells feed on energy, absorb information, reproduce themselves and form social groups, as human beings do, at a smaller, faster scale. The fractal sum of those cellular cycles create a human being. And then, the fractal sum of human cycles at a bigger scale create socio-biological organisms, called nations and civilizations. Thus, if a crystal or mathematical equation is a geometrical, spatial fractal; a human being is an organic, bio-logic, temporal fractal.
Finally minds are also fractal systems that replicate the forms and movements of the Universe in a smaller scale, through the syntax and semantics of a certain language that orientates the organism who perceives in that bigger Universe.
Thus it is possible to describe mathematical, physical, biological and metaphysical species with the same forms and functions of fractal structures.
Moreover, since Aristotle’s we know that temporal functions are always related to certain spatial forms: ‘Function is form’. So we can establish a relationship between fractal forms and fractal functions. For example, all systems that process information, from DNA nuclei, to eyes, to brains, have similar cyclical or spherical forms; because a sphere stores the maximum amount of information in minimal space. On the other hand, all moving bodies are lineal in form, because a line is the fastest, shortest distance between 2 points. So fast felines, F-1 cars, light beams and rockets are lineal in form. Thus, unlike the simplest mathematical fractals concerned only with spatial form, the real fractals of the Universe combine a geometrical form and a parallel, temporal, cyclical function. And both, function and form repeat themselves in the bigger scale.
So we talk of 2 essential forms/functions, which are the iterative units of the fractal Universe: the lineal form of energy and the cyclical form of information. For example, in Physics, lineal strings and cyclical strings are the iterative forms that gather together in lineal and cyclical branes of electromagnetism and gravitation.
Thus 3 elements are essential to describe any fractal, real system:
- The fractal forms and functions that repeat themselves in all Universal Systems. Which are lineal energy and cyclical information.
- The networks and processes that reproduce and reorganize the fractal unit into a macroform whose functions and forms are similar to the original cell.
- i: The iterative scales at which the fractal unit emerges into a macroform.
Thus we can define the Universe in fractal terms:
‘The Universe is a fractal super-organism made of networks of lineal, spatial energy and cyclical, temporal information, whose functions and forms repeat themselves in decametric scales’.
In that sense, as Leibniz affirmed, every fractal piece of the Universe is a small Universe in itself, with the same elements of the whole. And we talk of infinite ‘i-universes’, where ‘i’ is the scalar parameter that defines both, the size of the relative i-Universe and also the relative science that studies it, specialized in a certain scale. For example, Chemistry studies fractal molecules; Biology, fractal cells and History fractal, human societies. So it is possible to postulate the existence of a Science of Sciences, dedicated to the formal study of all fractal structures in the Universe, and the description of its species with those common functions and forms.

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