Essay on self-similarity

Scaling by K, we would expect most stars to have radii ranging roughly from cm to cm. If cosmological self-similarity is verified, then it would seem more likely that additional scales underlie the atomic Essay on self-similarity and encompass the galactic scale.

On the observational front, it is known with a high degree of confidence that some mysterious population of "dark matter" objects does indeed dominate the masses of galaxies by at least a factor of New observational results, much to the surprise of astrophysicists, appear to have confirmed this unique cutoff at the predicted value.

Metcalf, Nature We might go on with further examples of self-similarity within our bodies, but perhaps we would like to expand our horizons a bit and explore the outer world for new examples of this remarkable design strategy.

But, for all their apparent differences, might not atomic, stellar and galactic systems be more self-similar than is currently thought? By far the most impressive example is the incomparable Mandelbrot set, with its infinite hierarchy of M-sets within M-sets within M-sets.

The two examples given above both involve spatial structures, but self-similarity can also occur in temporal processes. In the same category, there is a correlation between the angular momentum j of an atom and its magnetic dipole moment u. A main stem rises to a node from which many secondary stems radiate.

The definitive predictions of main peaks at 7x solar masses and 0. Not surprisingly, since a turbulence expert coined the term self-similarity, turbulent motion provides archetypal examples. In the language of geometric measure theory 2.

Since the galactic "particles" are undergoing such enormously energetic random motions, the only reasonable atomic scale analogues would be fully ionized atomic particles, i. If microlensing experiments verify the unique predictions mentioned above, however, we would still be faced with some important and very difficult questions.

Again this is correct; galactic radii typically are on the order of cm to cm. Happily such a test has been identified, the initial experimental results are in, and definitive results will soon be available.

In fact, were it not for this elegant design strategy, we would be dire straits for at least five reasons. Likewise the countless numbers of atomic ions that make up stars and their immediate environs are in high energy plasma states with rapidly shifting self-similar clustering.

On very small scales, there is chaotic Brownian motion wherein big molecules and microscopic particles are buffeted around by the smallest and fastest moving air molecules in erratic zigzag patterns that are self-similar on micrometer to nanometer scales.

On the other hand, pulsar-planet systems were anticipated by the self-similar cosmological model several years before this discovery. These fingers have even smaller fingers on their surfaces, and by now it should not surprise anyone that there are microscopic fingers on the fingers of the fingers.Fractals and Self Similarity.

FRACTALS AND SELF SIMILARITY Contents 1. Introduction 2 2.

Fractals and Self Similarity

Preliminaries 3 Sequences of Integers 3 Continue for 47 more pages» • Join now to read essay Fractals and Self Similarity and other term papers or research documents. Read full document Save.

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ESSAYS, term and research papers available for UNLIMITED access. Self-similarity is something looking the same over all ranges of scale, meaning a small portion of a fractal can be viewed as a microcosm of the larger fractal.

One of the simplest examples of a fractal is the snowflake. It is - In this essay the conic sections in taxicab geometry will be researched. The area of mathematics used is geometry. Self-similarity is the idea that as an object is magnified the original shape of the whole is repeated over and over again.

The self-similarity of the Sierpinski Triangle (created on Geometer’s Sketchpad) is evident by the repetition of the shape within the original triangle.

Fractals: How They Are Self-Similarity Essay Words 3 Pages Fractals are all around us, in our lungs, kidneys, blood vessels, plants, in the clouds, in the tress, in.

FRACTALS AND SELF SIMILARITY

Fractals: How They Are Self-Similarity - He saw mathematical equations as pictures in his head. Essay on the Art of Chaos - The Art of Chaos Abstract: In this paper, I will attempt to explain the nature of Fractals.

A Fractal Universe?

Both natural and computer generated fractals will be explained. At the end, I hope the reader has a rudimentary sense of.

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Essay on self-similarity
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