Fractals and the Cantor Set Fractals are remarkable designs noted for their infinite self-similarity. This means that small parts of the fractal contain all of the information of the entire fractal, no matter how small the viewing window on the fractal is. This contrasts for example, with most functions, which tend to look like straight lines when examined closely. The Cantor Set is an intriguing example of a fractal. The Cantor set is formed by removing the middle third of a line
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an
The Application of Fractal Geometry to Ecology Abstract New insights into the natural world are just a few of the results from the use of fractal geometry. Examples from population and landscape ecology are used to illustrate the usefulness of fractal geometry to the field of ecology. The advent of the computer age played an important role in the development and acceptance of fractal geometry as a valid new discipline. New insights gained from the application of fractal geometry to ecology
Fractals, a Mathematical Description of the World Around us In being characterized with fractional dimensions, Fractals are considered to be a new division of math and art, which is perhaps why the common man recognizes them as nice-looking and appealing pictures that are valuable as background on computer screens and art patterns. But they are more meaningfully understood by way of the recognition that many of nature’s physical systems and a lot of human works of art are not standard geometry forms
My infatuation in fractals began freshmen year at Greeley after taking a Seminar with one of the seniors. I’m not sure exactly when simple interest turned to a kind of obsession, but during that lesson something seemed to click. It seemed as if this was the universe’s answer to everything; the mystery was solved, however complex the answer was to understand. I’m still not sure if I was misunderstanding the lesson, or if I had somehow seen it for what it really was; a pattern to describe the way the
When one thinks of fractals, what comes to mind may be the pretty, intricate images associated with backgrounds and screensavers. But would you ever think of cancer? The truth is, there is so much more to fractals than what meets the eye. For years, the mathematics behind these "pretty images" has been applied in fields of nature, technology, computer graphics, and most recently - in cancer research. Cancer, like many other aspects of the natural world, cannot be described using the standard
Evaluation of the Fractal Dimension of a Crystal Abstract The purpose of this experiment was to determine the effects of voltage and molarity changes on the fractal dimension of a Cu crystal formed by the re-dox reaction between Cu and CuSO4. Using the introductory information obtained from research, the fractal geometry of the Cu crystals was determined for each set of parameters. Through the analysis of data, it was determined that the fractal dimension is directly related to the voltage
Fractals: A New-Age Mathematics to Explain Our World Fractal art is a new-age art that tantalizes the eyes and mind with patterns, shapes, colors, and abstract imagery. Artists have once again found a way to harness the abstractedness of mathematics and integrate it into their work. So where does this new art form of fractal design stem from? The reality is that fractals themselves are relatively young in the mathematical world. Of course since the beginning of art and history and mathematics
Chaos and Literary Comparison Abstract: I will show how chaos is can be found in art, specifically in literature, and analyze John Hawkes's Travesty to show the similarities between literature and chaos. John Hawkes describes the "artistic challenge" as conceiving the inconceivable. In accordance with that thought, Wallace Stevens says, "Imagination is the power that enables us to perceive the normal in the abnormal." It is arguable that chaos, deterministic disorder, is both abnormal
measuring a coastline physically but also the idea that tides are constantly changing and waves are breaking so the point of where sea meets land is unclear also makes physically measuring a coastline difficult. Coastlines are considered to be fractals. A fractal is an image that contains self-similarity which is described as something that is exactly or similar to a part of itself [5]. They usually have complex detail at every scale and are difficult to measure when in the shape of a coastline therefore
paper, I will attempt to explain the nature of Fractals. Both natural and computer generated fractals will be explained. At the end, I hope the reader has a rudimentary sense of fractals in terms of both art and geometry. Most people live in a state of semi-chaos. Isn't your cluttered desk an example of the chaos in the world? The words chaos and pattern seem to be a dichotomy, but fractals are both of these things. Basic definitions of fractals include the words self-similar, chaotic, and infinitely
Fractals are a geometric pattern that are repeat over and over again to produce irregular shapes and surfaces that cannot be classical geometry. It is also, an innovative division of geometry and art. Conceivably, this is the grounds for why most people are familiar with fractals only as attractive pictures functional as backdrop on the PC screen or unique postcard design. But what are they really? Most physical structures of nature and lots of human artifacts are not normal geometric shapes of the
The Sierpinski Triangle Deep within the realm of fractal math lies a fascinating triangle filled with unique properties and intriguing patterns. This is the Sierpinski Triangle, a fractal of triangles with an area of zero and an infinitely long perimeter. There are many ways to create this triangle and many areas of study in which it appears. Named after the Polish mathematician, Waclaw Sierpinski, the Sierpinski Triangle has been the topic of much study since Sierpinski first discovered it in
application, fractals, “offer a better model for some natural structures than do traditional mathematics” (413). After she made this statement, she showed the connection to Arcadia within her second heading, “Chaos Theory in Arcadia”. She states that Thomasina, a main character in the play, understands that regular geometry cannot accurately describes “natural objects” and shapes; she knows that an iterated equation, a fractal, would describe it more accurately (414). Having already outlined fractals within
behave by precise unbreakable law. Stochastic behavior is the opposite of deterministic it has no finite laws, it is totally dependant upon ch... ... middle of paper ... ...are self-similar; in that case at higher and higher magnification the fractal image resembles the original. The stock market is indeed chaotic and also self similar. It is truly random, but shows an orderly trend. It is highly dependant upon initial conditions, but because it is nearly impossible to describe those initial
This allows person B to remove the lo... ... middle of paper ... ...nown for his creation of the Mandelbrot set fractal, which is also in appendix a, he created the fractal using computer software. Fractals can be used to store pictures. The idea is to take a few colored pixels, and create a fractal generator program that would result in the picture. Storing a simple fractal generation program and a few pixels, would be infinitely more efficient than storing an entire .JPG image. In conclusion
M.C. Escher occupies a unique spot among the most popular artists of the past century. While his contemporaries focused on breaking from traditional art and its emphasis on realism and beauty, Escher found his muse in symmetry and infinity. His attachment to geometric forms made him one of modernism’s most recognizable artists and his work remains as relevant as ever. Escher’s early works are an odd mix of cubism and traditional woodcut. From these beginnings, one could already note Escher’s fondness
economic system works in order to benefit from it. When Benoit Mandelbrot created fractals they were used in various ways, to measure nature and various systems throughout the world. Proven in the video, fractals were used to translate a small piece in the real world to a larger scale involving multiple complex systems. We see this demonstrated when one single tree in the rainforest was observed breaking down into fractals and using the geometrical math in order to predict the amounts of C02 the entire
Theory Description The chaos theory is a part of the broader Systems Theory. The systems theory simply states that small systems are a part of a larger, complex system. Being that they are open rather than closed, the smaller systems are able to continuously interact with each other making them interdependent. Open systems allow for chaos to exist because boundaries are always changing and being defined and redefined (Bussolari & Goodell, 2009). Chaos Theory is a relatively new theory to the Social
collaboration of drawing and computing. ÒBy the mid-1970s and throughout the 1980s, computer graphics improved tremendously, and a new kind of imaging was possible: visualizations of complex mathematical functions, three-dimensional graphics, and fractal imagery no artis... ... middle of paper ... ...eating classical art has been and will continue to be a portal for artists to create masterpieces. Works Cited 1. Software: Jasc Paint Shop Pro 8 ©copyright 1996-2003, Amazon.com