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XX. Fractal Infernal Temporal Seed Body


The word fractal is an adjective used to describe the form of an object with parts that resemble smaller copies of the whole over a range of scale. Often, a fractal object has a rough or fragmented geometric shape that one can subdivide into parts, each part being, at least approximately, a reduced-size copy of the whole. Self-similarity of part to whole means that as one peers deeper into a fractal form, one notices that shapes seen at one scale are similar to the shapes seen in detail at another scale.


Many mathematical structures are fractal objects. Sierpinski triangles, Koch snowflakes, Peano curves, Mandelbrot sets, and Lorenz attractors are examples of mathematical structures that are fractal objects. When mathematicians use fractal geometry to derive shapes, self-similarity between part and whole may extend over an infinite range of scales from infinitely large to infinitesimally small. As one zooms in and out, the same kind of shapes keep coming into view.


Fractal mathematics can also be used to describe the shape of many real-world objects, such as clouds, mountains, turbulence, and coastlines that do not correspond to simple geometric shapes. When nature uses fractal geometry to derive shapes, self-similarity is common over a finite range of scales. The cauliflower is perhaps a familiar example of the self-similarity of fractal geometry over a finite range of scales. If one breaks a cauliflower into many pieces, most if not all the pieces resemble a miniature version of a whole cauliflower. The same goes for many natural features such as trees, rivers, clouds, and mountains. As one zooms in one notices that the shape of smaller parts resembles the shape of the whole.


A system is a group of interacting parts functioning as a whole and distinguishable from its surroundings by recognizable boundaries. To describe a system as dynamic is essentially to describe a system as changing over time. To describe the behavior and or condition of a dynamic system as chaotic is to recognize that the group of interacting parts that make up the dynamic system each exert their own influence over the future condition of the whole.  Complexity of a chaotic dynamic system makes the precise prediction of the future condition of any one of itsí parts next to impossible.

          However, we may describe the future condition of any one of the parts contained within a chaotic dynamic system as falling within a range of possibilities often referred to as a strange attractor. Consider the shape of the path swept out by the Earth as it moves around the Sun . Seventeenth century astronomer and mathematician Johannes Kepler taught us that the shape of the path swept out by the Earth as it moves around the Sun approximates an ellipse on a plane bisecting the center of gravity of the Earth and Sun . The effect of combined gravitational forces of the Sun and Earth is to cause the Earth to fall towards the Sun . The effect of the linear momentum of the Earth relative to the Sun is to cause the Earth to fly away from the Sun . The result of the balance of these two effects is an elliptical path that strangely attracts the Earth. The balance of the action and or force exerted by each part on all other parts draws the whole of a dynamic system towards a strange attractor. Earth and Sun are but two parts of a larger chaotic dynamic universal system made up of a number, variety and diversity of interacting parts. Therefore, the effect of the sum total of all parts interacting with the Earth and Sun cause the shape of the path swept out to vary slightly each time the Earth orbits around the Sun . The slight variation in the shape of the path swept out each time the Earth orbits the Sun means that precise prediction of the future position of the Earth with respect to the Sun is not possible. However, we can predict that the position of the Earth with respect to the Sun will be within a range of possibilities.  A probability of occurrence may be associated with each possibility for the Earthís position with respect to the Sun . The shape and intensity of probability can be used to create a three dimensional graphic display of the possibilities and probabilities that the Earth is strangely attracted to over time.

A seed grows over time into a body. We cannot precisely predict the future condition of the body by analyzing the present and past condition of the parentsí bodies and or by analyzing the DNA that directs the future development of a seed body because the future development of a seed body is also dependent upon the influence of other parts of the universe around and within it. We can predict a range of possibilities and probabilities for the future condition of any given seed developing over time into a body. The range of possibilities and probabilities is the seed bodiesí strange attractor.


Fractal geometry tells the story of the wild things that happen to the form and shape of chaotic dynamic systems as these develop and evolve over time.  A fractal then, is the shape of a form created by a fracture in the geometry of the earth left by a quake or the winding coastline printed with the turbulence of the ocean and erosion. A fractal is shape of a form created by the branching structure of a fern that traces the process of its growth. A fractal is the shape of a form created by scrambled edges of ice as it freezes. A fractal is the shape of a form created by the spacing of stars in the night sky. A fractal is the shape of a form created by the clouds and plumes of pollution spreading out from a power plant.  Even the intricacy of snowflakes with a six-fold symmetry of crystals is the fractal result of a chaotic dynamic process of a crystal building itself over time. Because fractal geometry accurately describes the shapes of many natural structures, special effect artists can apply computer technology and knowledge of fractal geometry to the task of generating images of convincing alien landscapes.


The planet Earth itself is essentially a slow-moving glob of liquid iron surrounded by a slightly faster-flowing glob of liquid rock covered by a thin crust. On the ocean floor, some of the crust is being sucked into the cauldron beneath, while tectonic plates grind into each other, spawning volcanic eruptions and earthquakes: fractal and chaotic signs of the immense dynamism of the living place we call Earth. Since everywhere on Earthís thin crust, the natural landscape is being hewn by chaos into shapes with branches, folds and fractures, and detail inside detail, the immense intermeshing of dynamical forces constitutes the eternal, ever changing dissonance and harmony of nature that has attracted the attention of scientists and artists throughout the centuries.


As the universe explodes and expands, it leaves behind a fractal imprint of swirling turbulent gases, star fields, and repeating forms. The shape of the form created by each sub-atomic particle, atomic element, star, and galaxy is similar to every other of itsí kind in the fractal universe. Every life form of a given species is made in the fractal image of every other life form of a given species. The fractal universe exhibits self-similarity on scales of size. No matter how deeply we peer into space, more detail will always unfold that resembles details seen on a larger scale. From elementary particles to super clusters of galaxies we see parts collected to form "wholes'" and the latter collected into larger "wholes," and so on. Virtually all of the atomic mass of the known universe is lumped into stars, and virtually all stars collect into galaxies. In between atomic scale objects and stellar scale objects, there are many interesting classes of objects, including us, but these are quite rare relative to the dominant classes of objects. Therefore, to a first approximation, a discrete hierarchy organizes the portion of nature that we can directly observe. Given the strong stratification of the cosmological hierarchy, our universe at least has a very rudimentary self-similar organization: galactic "particles" are composed of stellar "particles", are composed of atomic "particles".


Fractal geometry is everywhere. The structure of our bodies with their branching of nerves, bronchial tubes, veins, and arteries, is replete with fractal geometry. Our cells are self-similar in that each contains a copy of the genetic blueprint of self. Our bodies exhibit self-similarity on a finite scale in that organelles contained within our cells function similar to the organs contained within our bodies. Therefore, perhaps it is only natural; that I should come to celebrate a model of existence that exhibits fractal geometry; and use the word fractal as an adjective to describe the quality of space inherent within our seed bodies and our universe.


I think of life as a synthesis of seed, body, soul, and spirit that forms a living, infernal, fractal entity or L.I.F.E. form.  Infernal is an adjective. An adjective describes a noun: a person, place, or thing. In this case, the adjective infernal describes the quality of the noun body as being of or relating to the lower world of the dead. The lower world of the dead is the universe because as far as I know no body comes out of this universe alive. Every body that grows from a seed within our universe is subject to a life cycle that ends in disease and death. Furthermore, the adjective infernal is similar to the noun inferno. The noun inferno describes a place or a condition suggestive of a place where burning generates heat. The body is a place where burning generates heat. The body uses oxygen to burn food and generate heat. Molten magma exists under the crust of the Earth. When and if this molten magma breaks through the crust and erupts on to the surface of Earth, we may observe by use of our senses burning and the generation of heat. The universe is a place where burning generates heat. The energy of the universe is composed of galaxies that are composed of stars that burn hydrogen and other heavier elements in thermonuclear reactions to produce heavier elements and heat. Therefore, I use the adjective infernal to describe the quality of both the noun body and the noun universe.  Scientists currently predict that eventually our bodies, life on earth, the stars, galaxies, and the burning of thermonuclear furnaces throughout our universe will end. Therefore, I use the adjective temporal to describe the longevity of the noun body and the noun universe.



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