Introduction to Fractals in a Time-Space Continuum
by Michael Peragine
A "Fractal" is a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole, a property called self-similarity. The origins of fractals can be traced back to geometric functions by Karl Weierstrass, Georg Cantor and Felix Hausdorff in studying functions that were continuous but not differentiable. The term ''fractal'' was coined by Benoit Mandelbrot in 1975 and was derived from the Latin ''fractus'' meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.
The mathematics behind fractals began to take shape in the 17th century when mathematician and philosopher Gottfried Leibniz considered recursive self-similarity. Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Thus, examples include clouds, snow flakes, crystals, mountain ranges, lightning, river deltas, cauliflower or broccoli, neural networks, systems of blood and pulmonary vessels, sea shells, pine cones, leaves of a fern, branches of a tree and galaxies can all be considered fractal in nature.
The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and for being a complicated structure arising from a simple definition, and is one of the best-known examples of mathematical visualization. Many mathematicians, including Mandelbrot, communicated this area of mathematics to the public. Fractals of all kinds have been used as the basis for digital art and animation. Starting with 2-dimensional details of fractals, such as the Mandelbrot Set, fractals have found artistic application in fields as varied as film and video graphics, plant growth simulation and landscape generation. In 1999, certain self similar fractal shapes were shown to have a property of "frequency invariance"; the same electromagnetic properties no matter what the frequency; from Maxwell's equations.
Fractal Analysis is the modeling of data by fractals. It consists of methods to assign a fractal dimension and other fractal characteristics to a signal, dataset or object which may be sound, images, atomic structure, molecules, networks, numerical, or other data. Fractal analysis has been introduced to financial market analysis, medicine, construction methods, engineering, and is now widely used in all areas of science.
In physical cosmology, "Fractal Cosmology" is a set of minority cosmological theories which state that the distribution of matter in the Universe, or the structure of the universe itself, is fractal. More generally, it relates to the usage or appearance of fractals in the study of the universe and matter. A central issue in this field is the fractal dimension of the Universe or of matter distribution within it, when measured at very large or very small scales. Fractals can be demonstrated in observational cosmology. The first attempt to model the distribution of galaxies with a fractal pattern was made by Luciano Pietronero and his team in 1987, and a more detailed view of the universe’s large-scale structure emerged over the following decade, as the number of cataloged galaxies grew larger. Pietronero argues that the universe shows a definite fractal aspect, over a fairly wide range of scale, with a fractal dimension of about 2. The ultimate significance of this result is not immediately apparent, but it seems to indicate that both randomness and hierarchal structuring are at work, on the scale of galaxy clusters and larger.
The use of fractals to answer questions in cosmology has been employed by a growing number of serious scholars close to the mainstream, but the metaphor has also been adopted by others outside the mainstream of science, so some varieties of fractal cosmology are solidly in the realm of scientific theories and observations, and others are considered Fringe science, or perhaps metaphysical cosmology. These various formulations enjoy a range of acceptance and legitimacy.
In Classical Mechanics, Newton's concept of "relative, apparent, and common time" can be used in the formulation of a prescription for the synchronization of clocks. Events seen by two different observers in motion relative to each other produce a mathematical concept of time that works pretty well for describing the everyday phenomena of most people's experience.
"Time" has been defined as the continuum in which events occur in succession from the past to the present and on to the future.
Einstein (''The Meaning of Relativity''): "Two spacetime events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to K, which register the same simultaneously. "Einstein wrote in his book, ''Relativity'', that simultaneity is also relative, i.e., two events that appear simultaneous to an observer in a particular inertial reference frame need not be judged as simultaneous by a second observer in a different inertial frame of reference.
Graphic timeline animations visualize the different treatments of time in the Newtonian and the relativistic descriptions. At heart of these differences are the Galilean and Lorentz transformations applicable in the Newtonian and relativistic theories, respectively. The vertical direction indicates time. The horizontal direction indicates distance, and the curve is the spacetime trajectory "world line" of the observer. Small dots indicate specific past and future events in spacetime. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer.
"The magical power of the subconscious mind". To believers who think that they need to convince their subconscious mind to make the changes that they desire, all spirits and energies are projections and symbols that make sense to the subconscious. A variant of this belief is that the subconscious is capable of contacting spirits, who in turn can work magic. "The Oneness of All." Based on the fundamental concepts of monism and Non-duality, this philosophy holds that magic is the application of one's own inherent unity with the universe. That personal realization, or illumination, is that the self is limitless, one may live in unison with nature, seeking and preserving balance in all things.
Time has historically been closely related with space, the two together comprising spacetime in Albert Einstein's special relativity and general relativity. According to these theories, the concept of time depends on the inertial spatial reference frame of the observer, and the human perception as well as the measurement by instruments such as clocks are different for observers in relative motion. The past is the set of events that can send light signals to the observer, the future is the set of events to which the observer can send light signals. The brain's judgement of time is known to be a highly distributed system, including at least the cerebral cortex, cerebellum and basal ganglia as its components. One particular component, the suprachiasmatic nuclei, is responsible for the circadian (or daily) rhythm, while other cell clusters appear to be capable of shorter-range (ultradian) timekeeping.
From the age of Isaac Newton to Albert Einstein's profound reinterpretation of the physical concepts associated with time and space, time was considered to be "absolute" and to flow "equably" (to use the words of Newton) for all observers. The science of classical mechanics is based on this Newtonian idea of time.
Einstein, in his special theory of relativity, postulated the constancy and finiteness of the speed of light for all observers. He showed that this postulate, together with a reasonable definition for what it means for two events to be simultaneous, requires that distances appear compressed and time intervals appear lengthened for events associated with objects in motion relative to an inertial observer.
Einstein showed that if time and space is measured using electromagnetic phenomena (like light bouncing between mirrors) then due to the constancy of the speed of light, time and space become mathematically entangled together in a certain way (called Minkowski space) which in turn results in Lorentz transformation and in entanglement of all other important derivative physical quantities (like energy, momentum, mass, force, etc.) in a certain 4-vectorial way.
A "Theory of Everything" is closely related to unified field theory, but differs by not requiring the basis of nature to be fields, and also attempts to explain all physical constants of nature.
String theories and supergravity (both believed to be limiting cases of the yet-to-be-defined M-theory) suppose that the universe actually has more dimensions than the easily observed three of space and one of time. The motivation behind this approach began with the Kaluza-Klein theory in which it was noted that applying general relativity to a five dimensional universe (with the usual four dimensions plus one small curled-up dimension) yields the equivalent of the usual general relativity in four dimensions together with Maxwell's equations (electromagnetism, also in four dimensions). This has led to efforts to work with theories with large number of dimensions in the hopes that this would produce equations that are similar to known laws of physics. The notion of extra dimensions also helps to resolve the hierarchy problem, which is the question of why gravity is so much weaker than any other force. The common answer involves gravity leaking into the extra dimensions in ways that the other forces do not.
In the late 1990s, it was noted that one problem with several of the candidates for theories of everything (but particularly string theory) was that they did not constrain the characteristics of the predicted universe. Fractal cosmology is essentially a visualization technique to diagram the universe in multiple dimensions as well as cosmological constants simultaneously. Even the "standard" ten-dimensional string theory allows the "curled up" dimensions to be compacted in an enormous number of different ways (one estimate is each of which corresponds to a different collection of fundamental particles and low-energy forces. This array of theories is known as the string theory landscape.
A modal phenomena of an oscillating cymatic system is a pattern of motion in which all parts of the system move with the same frequency and in phase. The frequencies of the normal modes of a system are known as natural frequencies or resonant frequencies. A physical object, such as an architectural structure, a transmitting antenna or molecule, has a set of normal modes that depend on its structure, materials and boundary conditions. When relating to music, normal modes of vibrating instruments such as strings, pipe organs, or drums, produce what are known as "harmonics" or "overtones". The most general motion of a system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. The concept of normal modes also finds application in wave theory, optics, quantum mechanics, and molecular dynamics.
Fractals are identified not as separate from the heavens but rather a force that acts and permeates throughout the Universe. Fractals demonstrate an indisputable connection between the invisible God and the visible heavens. Such a conception would, to the Western Scientist, be known as electromagnetic activity manifesting endless waves of probability. "Deus sive Natura", is the universal metaphysic. Perception of external objects are the result of both mental activities and external conditions. All the ultimate objects of knowledge, nature, thought, and deity, are known by us in the same way. Keeping our minds open to receive the necessary impressions can alone convey to us the causes of phenomena, the psychology of interpretation and their origin.
The "Holographic Principle" is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region, preferably a light-like boundary like a apparent gravitational horizon.
Digital holograms can be numerically multiplexed and demultiplexed for efficient storage and transmission. Amplitude and phase can be correctly recovered. The numerical access to the optical wave characteristics (amplitude, phase, polarization) made digital holography a very powerful method. Numerical optics can be applied to increase the depth of focus (numerical focalization) and compensate for aberration. Wavelength multiplexing of holograms is also possible in digital holography as in classical holography. It is possible to record on the same digital hologram interferograms obtained for different wavelengths.
Human History
For hundreds of thousands of years, man's evolution must be measured by his
stone tools. Then about 120,000 years ago, a different type of man appeared in different parts of the world. This was the Neanderthal man, named after the German valley where the first remains were discovered. At this time, earth was in it's final glacial period so Neanderthal men took to living in caves. He hunted animals such as reindeer, musk ox, woolly mammoth, and bear which lived at the edge of the glaciers.
Prehistory carried great stories with colorful parables to teach the young and entertain the elderly. Early man (40,000 B.C.), created legends of man-like beings that controlled nature. The sun always seems to be deified. The Sumerians, Egyptians, Mayan, and particularly the Greeks told complex tales to satisfy the unknowns of nature. Today, nature is understood partially or in full by science. Scientific methods using logic and reason developed into specialized branches that can accurately define, measure and analyze complete systems. The sun is a star, the earth evolves around the sun, and the moon effects tides, lightning and thunder are caused by electrically charged particles and so on.
In Sumer, Babylon, and ancient Egypt, the priests, astronomers, mathematicians, were often the same person, or employed by the ruling class. Mesopotamian people merged magic, science and religion. The myth reveals history, magic is applied to science and technology, and mystery becomes knowledge and reason. It is true the sun is not a god but it's real. We now know that the sun is simply a star of billions of stars in our galaxy. Consider the fact that all life of earth is the result of light and heat radiating from the sun. Without it there would be no life at all.
The '''Flower of Life''' is the modern name given to a geometrical figure composed of multiple evenly-spaced, overlapping circles. The five Platonic Solids are found within the symbol of Metatron's Cube, which may be derived from the Flower of Life pattern. They are arranged to form a flower-like pattern with a sixfold symmetry, similar to a hexagon. The center of each circle is on the circumference of six surrounding circles of the same diameter. It is considered by some to be a symbol of sacred geometry, said to contain ancient, religious value depicting the fundamental forms of space and time. In this sense, it is a visual expression of the connections life weaves through all sentient beings, and it is believed to contain a type of Akashic Record of basic information of all living things.
There are many spiritual beliefs associated with the Flower of Life, as with the symbols of the Vesica Piscis, an ancient religious symbol, and Borromean rings, which represents the Holy Trinity. These platonic solids are geometrical forms which are said to act as a template from which all life springs. They called it the Flower of Life because it looks like a flower and because it represents the laws and proportions for everything alive and even not alive; everything that's manifested. This is a significant example on how geometry allows us to understand how the mind and body are a unitary physical and causal system. The dreams of the human mind should be made a conscious activity tending towards the good of the human species.
When a person moves from believing to thinking, they move from the visible world to the intelligible world, from the realm of opinion to the world of knowledge. The state of mind that Plato calls thinking is characteristic of the scientist. The scientist works with visible things but not simply with his vision of them. Plato's theory of ideas have been refined and modified since they were originally written. Nevertheless, it represents an important advance in philosophy. "The Allegory of the Cave" is the first theory to seriously examine the problem of universals. Practical knowledge can be applied to daily routines to improve our quality of life. Although opinions are not as reliable as knowledge they exist as a motivational factor generating attraction and repulsion in biological organisms. Opinion is concerned with beautiful things, but knowledge is concerned with beauty in itself. People who are without a sense of spirituality can be compared to prisoners in a cave. Most people, according to Plato, are ignorant of the external world around them, and are preoccupied with belief, opinion, and sensory experience. Geometry is the transformation of appearance to the world to an understanding it's inherent and underlying ultimate reality.
Quantum Mechanics
Quantum mechanics challenges a simple materialistic view of the universe with the Uncertainty Principle, the Principle of Complementary and question, "is the electron a particle or wave?" Epicurus was generally correct in stating that atoms fall and recoil and some lock into each other and that motions have no observed beginnings because atoms and the void are the cause themselves. All our thoughts and sensations conscious or unconscious are caused by atomic (and molecular) relationships. Today we can trace thought to neurons and electrochemical impulses. The mind or soul is corporeal as far as quantum waves exist. The mind or soul exists within temporal-spatial limits and man lives within a spectrum of reality. Only a small band of visible light can be seen compared with the entire electromagnetic spectrum. As with our other senses, hearing, taste, smell and touch, scientific instruments act as tools to expand our senses, our reality, to find the answers to life, the universe and any supreme reality beyond that if it exists.
Picture a wave spreading out through space as though it were an ever-expanding sphere. It describes the probability that a certain event will occur. Physicists call this the quantum wave function. Any observer along the wave, anywhere in the universe, could discover its secrets; but only one will. The first to look at it is the first to collapse it into a single real event. For example, the wave function for a particular photon from a star will fold into a spot of light only on the retina of the first observer. Once seen, this event cannot occur anywhere else. Everyone within the reach of the wave, regardless of the distance from one another, is affected by this invisible quantum wave connection. Man discovers the big bang.
Human Nature
Inherent in man is his "Human Nature", a nature found in every man. Each man is an example of the universal conception of man. Whether he be a primitive native or part of the cultured bourgeois, they all have the same fundamental physical and emotional qualities. All men posses the same essence and their essence precedes their historic existence, which is learned through experience. The answer is their scientific and historical discoveries. Similar events have occurred to many great men in history. Aristotle (father of analytics and logic in the physical sciences), Spinoza (pantheistic philosopher), Darwin (discoverer of evolution), Gregor Mendel (father of genetics), Sigmund Freud (founder of modern psychology), Max Plank, Albert Einstein, Niels Bohr, Werner Heisenburg (the fathers of quantum physics).
People are inherently different. They are pluralistic in nature, with different economic opportunities, abilities and geographical differences as well. Politics on a local level is as important as global issues, however, what all people do have in common are the universal truths. These universal truths tend to follow natural laws, a social political animal forming a physical matrix of man-made laws and public architecture. How do live a simple natural lifestyle in such an increasingly complex world? One solution is creating network maps of data using fractal geometry. And applying metadata to index content and model web browsers and search engines to quickly organize and retrieve results. With these network mapping tools we can solve social problems with business, medical and engineering solutions based on fractal forms.
Human consciousness exists because of the division of hemispheres in our brain, the physical microcosms manifestation of reason and emotions. The Cortex acts as a bridge, an interface of the two halves, separate identities or modes of logic, perception, memory and recall. Synthesized, we emerge from a primitive ocean of pure skepticism and dogmatic solutions. The four major questions of men on our planet are: the creation of life, creation of the universe, the purpose of life, and finally, what happens after death.
Nature exists independently of what man thinks of it until we decide to change it. There are, however, an infinite amount of ways to interpret it. The differences of how we interpret nature, life, is what ultimately divide us, as we often work toward self interest. This is what causes differences in opinion; politically, socially, theological, but interesting enough, not scientifically. And law, of course, is there a "natural law" enshrined in the social contract of men?
What do all people desire? How do we achieve the feeling of happiness? By our ability to provide the necessary things to sustain life: air, water, food, shelter, and peace with other people and communities through friendship, love and understanding. Yet he can be challenged enough to satisfy man's insatiable scientific curiosity and ability for artistic expression. At first, scientists disagree on how this or that happens. Once the path is observed, upon discovering the cause and nature of a particular phenomena, it is generally accepted as fact. Sometimes man understands nature, sometimes he does not. That is not to say science is perfect or infallible. Science is a process. In searching for common ground of all cultures, the answer is twofold: nature and man's will. Science and mathematically expressed art forms.
The idea of the atom was first introduced to science by Democritus and Epicurus, more than 2,000 years ago. In humanities, artistic expression of reality and his emotional response to mystery, there is not one path to follow, there are many. Nature exists independently of what people think of it. There is only one reality but there is potentially an infinite amount of directions to interpret nature. This interpretation manifests as mathematics and may be used as a universal language. The language of physics provides substance, quality and regulation to organisms of all kind. The human animal part of an electromagnetic, biomechanic and electrochemical matrix. Consciousness in the form of memory, cognitive faculties, and emotions all originate from encoded cryptic seeds. Biological tides of a sea of electricity ripple as logarithms of opposing forces. Animate or inanimate, existence and reality are corporal, temporal-spatial cause and effect relationships. Existence precedes essence, in an existential world where people are self-governing and assume responsibility for their own actions. The theory of gravity, laws of thermodynamics, particles physics, genetic engineering, psychology, all form an impression, a signature of nature and life. Man's architecture is comparable to the electronic slaves he designs in anthropomorphic manifestations. Achievements of automation and mainframe computers can reconstruct time, space, financing, manufacturing and art, all digitized into a temporal world similar to Leibniz's monads. Digitized into reality.
Evolutionary Logic in Analysis and Design
Evolution is a fact. It still remains, however, a valid question to ask how do things evolve. The evolution of life, humankind, and of the universe, to the formation of amino acids, proteins, and DNA. These questions are answered by science and history. The first cell division, plant life, fish, birds, and mammals all follow fractal patterns. Man is not the final product of design. Darwin's metaphysic has continued to be the most influential scientific principle of the century. The original thesis of Darwin's theory was to confirm a biological natural selection in nature. As a general principle, evolutionary logic has a profound significance in all areas of scientific analysis and design. Cellular Automata, or the patterns of growth, are studied at Princeton. Evolution is a method of understanding everything that occurs in nature; the growth of cities, population densities, the history of human psychology, the cause of disease, computer graphics for video animation, the history of architecture or even the evolution of religion. Man emerged from the jungle and plains of Africa. He migrated North along the Nile River. Upon reaching the fertile delta at the mouth of the Nile, decisions were made that determined the future of the world. Some people stayed and founded Egypt, many others traveled further along the fertile crescent and divided. One group followed the sunrise to the East, while still others choose the sunset in the West. This migration is symbolic of the left and right hemispheres of the brain, Eastern and Western philosophy, reason and emotions. In the brain the Corpus Callosum acts as a bridge between the two hemispheres. The Sinai is the Corpus Callosum of the old world the internet the social neural network of the new world. Self actualized, transcending ethics and morality in an amoral universe. Judgment and value are also the logic of semantics. To educate is to facilitate understanding of language; whether that of a general medium, (Latin, English, BASIC, etc.) specialized as in computer sciences, medicine, engineering, business, or law. Fractal logic traces causality as one of the forms of general interdependence of phenomena in the objective world. In essence, cause and effect are only moments of interdependence in universal relation of the evolutionary connection of events; that are present in the chain of development of matter. There can be no phenomena without causes. All natural phenomena have natural and material causes.
Human Technology
Human technology can be defined a number of ways. It is a devotion to the humanities, that is education, music, art, poetry, philosophy, or it can be a lifestyle centered on human interests or values. Technology is a practical systematic treatment of applied science or art. It is what we are and why we do it. Imagine a computer planed society not without individual initiative, but rather one that grows like a unified biological organism, simultaneously creating a cellular "entity", a self-actualized being with expanding artistic value. Science and religion are concerned with different dimensions of life. Ancient religions thought of natural and social phenomena as manifestations of a god's will and wisdom. As science advanced some theological doctrines were proven unreasonable in their approach to nature and human affairs, and they were discarded as they became increasingly insufficient to explain the real phenomena of the universe. Each individual ought to find his or her own purpose in life. People are inherently different. They are pluralistic in nature, with different jobs, education, mental and physical abilities and geographical differences as well. Politics on a local level is as important as global issues, however, what all people have in common are the universal truths. These universal truths tend to follow natural laws, a social political animal forming a physical matrix of man-made laws and public architecture. People will mostly live in urbane complexes, surrounded by numerous machines (Automata). In particular the world wide web has linked central data banks and electronic libraries with fully automated access. A credit card economy in which cash will be virtually eliminated. Cell phones, MP3 players and other personal and mobile devices facilitate communications with persons everywhere.
Economic power is more important than military power in determining a nation's influence. The movement to worldwide free trade economic considerations transcending political consideration, developing telecommunications and an advancement of democracy and the spread of free enterprise. In Benoit Mandelbrot's 2004 book “The (Mis)behaviour of Markets”, fractal mathematics are used for modeling many aspects of the financial markets and changes the way we should consider risk. Fractal art is a direct way to correlate everything one has ever learned. By understanding how artistic styles modified the environment, one can achieve a better comprehension of past civilizations and emulate patterns in our present culture. Picasso, possibly the most important single figure in modern art, has constantly changed his personal style and has introduced intellectual and subjective elements of modern art into his work. He thus maintained his position as a creative and active force. To experience the initial illusion and the overcoming of illusion, the mind's self awareness is the achievement and return to the nature of reality. Weltgeist, the world mind of Hegel, the German idealist philosopher, extends beyond the confines of human experience. Human technology has dreams, purpose, function and form.
The Animation of Spirit
The kind of spirituality needed to relate man to the new technologically created environment is a spirit of synthesis and design. The animation of spirit lies within us, our desires scan the heavens, our collective memory, the seed of the new world. The essence of spirit is without mystery. Traditionally defined as the soul, it is now generally accepted by scholars and scientist to mean the part of human beings associated with the feelings and mind. The word spirit, originates from the Latin spirare, which means to breathe. The concept however, of soul and spirit has been the subject of theological debate for millennia, until the founding of modern psychology and medicine. George Hegel (1770-1831), the German idealist philosopher, translated "spirit" as "mind". Mental activity differs from nature in that the mind is an "I". Spirit or mind exist for itself. This consciousness recognizes three types of spirit: subjective, objective, and absolute. The philosophy of subjective spirit studies the individual in relation to his social relations and discusses such topics as consciousness, memory, thought and free will. The objective spirit deals with man's rights towards his fellow men. These rights suppose a legal sense founded in the study of ethics and political theory. The highest stage of spirit is the "absolute spirit", whose three parts are art, religion, and philosophy. According to Hegel, the study of absolute spirit has to do with spirit as "infinite", not spirit as something boundless, but as having returned to itself from self-alienation. That is to say that, at this stage of thought, one recognizes that subjective and objective are one. This absolute spirit can be experienced in the highest profundity level of the psychedelic experience, as noted by R.E.L. Masters and Jean Houston, two leading investigators in this area. Images journey the general history of human beings, animal evolution and rituals of passage. The most profound level, seldom reached is called the Integral level. Experience at this level are religious and mystical, often dealing with a confrontation with God. The individual may experience a union with nature. The feeling is profoundly religious and cannot be easily defined in verbal terms.
Our mind, thoughts and consciousness are electrochemically activated in the brain, specifically located in nerve cells or "neurons." There are neurons, a synapse (the gap between the neurons) and molecules that cross from one neuron to another. These molecules are called neuro-transmitters. Our memory, emotional characteristics and cognitive functions are encoded in a neuron or string or matrix of neurons in the brain.
The research of neuroscientist Efrain Azmitia of New York University demonstrates that the brain is an active, dynamic, ever changing structure, that, in fact, can be neurotronically engineered. Scientists speculate that alien civilizations may have already initiated the process of breeding a race beings whose brains are perfectly adapted to the computer. Hans Moravec, a computer scientist at Carnegie-Mellon University, believes that by the early part of the twenty-first century, it will be possible to dump the data from each neuron in our brains into a computer program, creating electronic clones that can merge with other forms of artificial consciousness. DNA can be digitized in binary form and reconstructed chemically in physical space.
Once in a very great while scientists' minds discover principles and put them to rigorous physical tests before accepting them as principle. "Acknowledging the mathematically elegant intellectual integrity of eternally regenerative Universe is one way of identifying God.", R. Buckminster Fuller. Fractal geometry opens a window to all the knowledge of the universe. Microcosmic and macrocosmic worlds formed by cymatic waves unified by a single event, perhaps. Fractals by definition are infinite time and space, absolute, pure, all knowledge: past, present and future.
The Mandelbrot set is a keystone in the study of the cosmos. It's cosmology requires all current scientific knowledge in the natural sciences. To know is to understand or be aware and recognize a truth or fact. Doing so by experience, directly through perception of our senses or indirectly with scientific instruments, or logic and reason. The universe is infinite. Numbers and knowledge are potentially infinite. The known universe is and probably always will be finite, from man's point of view. What mankind collectively knows is finite.
All rational men seek to understand nature or the universe, even if it is a small portion of the whole. In this sense all men, even the Atheist, seek to know God. The universe is constantly changing. Atoms, life and stars go through an evolutionary process. This definition has a great unifying force that can be shared by all people regardless of their political ideology. Arthur C. Clarke said, “The origin of the universe might be forever unknown, but all that had happened since obeyed the laws of physics”. Fractals unify laws and forces of nature as one and simplify the complex world so we can understand the beauty of it all.
Michael Peragine
12/21/2010
