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Examples of the the word, fractal , in a Sentence Context

The word ( fractal ), is the 15731 most frequently used in English word vocabulary

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  1. A straight Euclidean line) is formally self-similar but fails to have other, fractal ,characteristics; for instance, it is regular enough to be described in
  2. Or one or two-dimensional molecular movement. In these situations,a, fractal ,Michaelis-Menten kinetics may be applied. Some enzymes operate with kinetics
  3. Irregularity is constant over different scales (" self-similarity" ) is a, fractal ,(for example, the Koch curve or" snowflake ", which is infinitely long yet
  4. Purposes. Complexity of the Tree of Life The cladistic tree of life is a, fractal ,:" The tree of life is inherently fractal -like in its complexity, .... Look
  5. His fame as" celebrity beyond the academy" and lauds him as the" father of, fractal ,geometry. " Honors and awards A partial list of awards received by Mandelbrot:
  6. Cladogram of the tree of life. The tree of life is a quasi-self-similar, fractal ,; that is, the deep reconstruction is not as regular as the shallow
  7. Is generally known as" Hofstadter's butterfly ", which was the first, fractal ,ever found in physics, and it has recently been confirmed in transport
  8. Set, Julia set, the Burning Ship fractal , the Nova fractal and the Lyapunov, fractal , The 2d vector fields that are generated by one or two iterations of
  9. Exercises. Fractals and regular roughness Although Mandelbrot coined the term, fractal , some of the mathematical objects he presented in The Fractal Geometry of
  10. Of them were based on recursion, leading to the popular meaning of the term ", fractal ,". Examples A class of examples is given by the Cantor sets, Sierpinski
  11. Strange attractors and Julia sets typically have a fractal structure, and a, fractal ,dimension can be calculated for them. Minimum complexity of a chaotic system
  12. Above characteristics, such as when it is possible to zoom into a region of the, fractal ,that does not exhibit any fractal properties. Also, these may include
  13. But is best known as the father of fractal geometry. He coined the term, fractal ,and described the Mandelbrot set. Mandelbrot extensively popularized his work
  14. Physics and quantitative finance, but is best known as the father of, fractal ,geometry. He coined the term fractal and described the Mandelbrot set.
  15. Of 1),a result proved by Mutsuhito Shishikura in 1991. A closely related, fractal ,is the Julia set. Generation Five common techniques for generating fractal s are
  16. Observations by discovering regularities such as repetitions and symmetries and, fractal ,self-similarity. Whenever the observer's learning process (which may be a
  17. The Face of War had given him" the intuition about the transcendence of the, fractal ,geometry when making intelligible the omnipresent similitude in the forms of
  18. Examples of this type are the Mandelbrot set, Julia set, the Burning Ship, fractal , the Nova fractal and the Lyapunov fractal . The 2d vector fields that are
  19. Curves and Surfaces Consisting of Parts Similar to the Whole described a new, fractal ,curve, the Lévy C curve. Georg Cantor also gave examples of subsets of the real
  20. Energy versus magnetic field) that is a self-similar ( fractal ) shape. This, fractal ,structure is generally known as" Hofstadter's butterfly ", which was the
  21. Such as the branching of the circulatory and bronchial systems proved to fit a, fractal ,model. Chaos was observed by a number of experimenters before it was recognized
  22. Are dense everywhere. ) Self-similarity The Cantor set is the prototype of a, fractal , It is self-similar, because it is equal to two copies of itself, if each copy
  23. The tree continues to recreate itself by bifurcation, a series of events called, fractal ,evolution. Every single speciation event, including all the species that are
  24. Were continuous but not differentiable; however, the term. Characteristics A, fractal ,often has the following features: * It has a fine structure at arbitrarily
  25. File for other programs to play. Some of these simple programs are based on, fractal ,geometry, and can map midi notes to specific fractal s, or fractal equations.
  26. Paradox (the" dark night sky" riddle),demonstrating the consequences of, fractal ,theory as a sufficient, but not necessary, resolution of the paradox. He
  27. Sky even if the Big Bang had not occurred. In 1975,Mandelbrot coined the term, fractal ,to describe these structures, and published his ideas in Les objects fractal s
  28. Julia sets depended on the complex parameter μ he studied the Mandelbrot set, fractal ,that is now named after him. (Note that the Mandelbrot set is now usually
  29. Dimensions. Networks and dimension Some complex networks are characterized by, fractal ,dimensions. The concept of dimension can be generalized to include networks
  30. Is a variant of the same idea. In general, there exist more definitions of, fractal ,dimensions that work for highly irregular sets and attain non-integer positive
  31. S work was finished, Benoît Mandelbrot invented a new branch of mathematics, fractal ,geometry, to describe just such non-rectifiable complexes in nature as the
  32. Mg 1804b. JPG|Benoit Mandelbrot, MS 1948,Engineering 1949,father of, fractal ,geometry, namesake of the Mandelbrot set Image: Frank Capra. JPG|Frank Capra
  33. Form more bonds than nitrogen, their lighter analogues on the periodic table. A, fractal ,has been defined as" a rough or fragmented geometric shape that can be split
  34. Are based on fractal geometry, and can map midi notes to specific fractal s, or, fractal , equations. Although such programs are widely available and are sometimes seen
  35. Generated by one or two iterations of escape-time formulae also give rise to a, fractal ,form when points (or pixel data) are passed through this field repeatedly. *
  36. Curve, and Koch curve. Additional examples of fractal s include the Lyapunov, fractal ,and the limit sets of Iranian groups. Fractals can be deterministic (all the
  37. Work by Lewis Fry Richardson. Finally, in 1975 Mandelbrot coined the word ", fractal ," to denote an object whose Hausdorff–Besicovitch dimension is greater than its
  38. It is possible to zoom into a region of the fractal that does not exhibit any, fractal ,properties. Also, these may include calculation or display artifacts which are
  39. See attractor). Objects in the parameter space for a family of systems may be, fractal ,as well. An interesting example is the Mandelbrot set. This set contains whole
  40. Field form a graph (energy versus magnetic field) that is a self-similar (, fractal ,) shape. This fractal structure is generally known as" Hofstadter's butterfly
  41. This type are the Mandelbrot set, Julia set, the Burning Ship fractal , the Nova, fractal ,and the Lyapunov fractal . The 2d vector fields that are generated by one or two
  42. Group theory and probability. It has applications to enumeration combinatorics, fractal ,analysis, theoretical computer science, automata theory and linguistics. While
  43. Star field emulations, fading effects and calculated images, such as Mandelbrot, fractal ,animations. There are now many tools and programs that can transform raster
  44. Of the new figure serving as the basis for his study is: A key property of the, fractal ,is self-similarity; that is, at any scale the same general configuration
  45. Or" snowflake ", which is infinitely long yet encloses a finite space and has, fractal ,dimension equal to circa 1.2619,the Merger sponge and the Sierpinski gasket).
  46. Not until 1872 that a function appeared whose graph would today be considered, fractal , when Karl Weierstrass gave an example of a function with the non-intuitive
  47. Identified L with a non-integer form of the Hausdorff dimension, later the, fractal ,dimension. Rearranging the right side of the expression obtains:: \franc \dot
  48. Epsilon where Find must be the number of units ε required to obtain L. The, fractal ,dimension is the number of the dimensions of the figure being used to
  49. As strange repellers. Both strange attractors and Julia sets typically have a, fractal ,structure, and a fractal dimension can be calculated for them. Minimum
  50. Is the number of the dimensions of the figure being used to approximate the, fractal ,: 0 for a dot,1 for a line,2 for a square. D in the expression is between 1

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