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위키데이터

• ID : Q848427

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1. z = z2 + c where c is another complex number that gives a specific Julia set.
2. After numerous iterations, if the magnitude of z is less than 2 we say that pixel is in the Julia set and color it accordingly.
3. The Julia set is named after the French mathematician Gaston Julia who investigated their properties circa 1915 and culminated in his famous paper in 1918.
4. Computing a Julia set by computer is straightforward, at least by the brute force method presented here.
5. The well known Mandelbrot set forms a kind of index into the Julia set.
6. A Julia set is either connected or disconnected, values of c chosen from within the Mandelbrot set are connected while those from the outside of the Mandelbrot set are disconnected.
7. View Julia set.
8. Though, it looks like there are some other interesting configurations in the centers of the Mandelbrot bulbs, where the corresponding Julia set has a pleasing symmetry.
9. The "filled-in" Julia set is the set of points which do not approach infinity after is repeatedly applied (corresponding to a strange attractor).
10. The true Julia set is the boundary of the filled-in set (the set of "exceptional points").
11. The equation for the quadratic Julia set is a conformal mapping, so angles are preserved.
12. Let be the Julia set, then leaves invariant.
13. The quantity c also is defined as a complex number, but for any given Julia set, it is held constant (thus it is termed a parameter).
14. z2 + c has little potential to create anything interesting—it is only by repeatedly iterating it that the Julia set can be defined.
15. There seems to be a little definitional confusion in the literature as to whether the boundary points (i.e., the Julia set) are themselves part of the prisoner set, but this must be the case.
16. Depending on the value of c selected, the resultant Julia set may be connected or disconnected—in fact, either totally connected or totally disconnected.
17. then the Julia set coincides with the filled-in Julia set.
18. Filled Julia set for c=-1+0.1*i.
19. In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function.
20. The complement of F(f) is the Julia set J(f) of f(z).
21. This means that f(z) behaves chaotically on the Julia set.
22. Although there are points in the Julia set whose sequence of iterations is finite, there are only a countable number of such points (and they make up an infinitesimal part of the Julia set).
23. The Julia Set Fractal is a type of fractal defined by the behavior of a function that operates on input complex numbers.
24. The Julia Set Fractal is dependent upon complex numbers - numbers which have both a real and 'imaginary' component i, i being defined as the square root of -1.
25. Pixel indexes to initialize z values of the Julia Set.
26. The applet draws the fractal Julia set for that seed value.
27. For a julia set, for each pixel apply an iterated complex function.
28. The points that remain in the circle forever, are the ones that belong to the Julia Set.
29. The more iterations, the more detailed the Julia set will look when zooming in deeply, but the more calculations are needed.
30. "Julia Set"); //make larger to see more detail!
31. We'll call the set of initial values whose iterates remain bounded the filled-in Julia set, or simply the Julia set for short.
32. We have begun to explore the complex Julia set for this function, but only just begun.
33. This was a quadratic function gave an interesting Julia set.
34. You can then click the Julia set to pick a complex seed \(z_0\) and view its orbit under the iteration of \(f_c\).
35. then \(z_0\) belongs to the filled-in Julia set.
36. If the chosen number \(c\) gives rise to a connected Julia set, then \(c\) belongs to the Mandelbrot set (see The Mandelbrot Set for more information).
37. When generating a filled-in Julia set, the distance to the origin after a maximum number of such iterations can be used to decide if a point belongs to the filled-in Julia set.
38. When generating a true Julia set, i.e. the boundary of the filled-in set, it's better to use a so called backwards orbit.
39. An explosion is a sudden change from a nowhere dense Julia set to one which is the entire complex plane.
40. A. Douady, Does a Julia set depend continuously on the polynomial?
41. I am working on julia set in java.
42. In julia set, i am generating RGB color using return value of iteration.
43. Clearly, this post doesn’t present the most efficient computation of a Julia set.
44. max_iteration then point is in filled-in Julia set, else it is in its complement (attractive basin of infinity ).
45. Modified binary decomposition of whole dynamical plane with circle Julia set.
46. Modified decomposition of dynamical plane with basilica Julia set.
47. In the numerous fractal dimension definitions, box-counting dimension is taken to characterize the complexity of Julia set since the calculation of box-counting dimension is relatively achievable.
48. In 1918, Julia Gaston, a famous French mathematician, discovered an important fractal set in fractal theory, when he studied the iteration of complex functions, which was named Julia set.
49. In fractal theory, Julia set is a set of initial points of the system that satisfy certain conditions.
50. With the same thought, we define the Julia set of Brusselator model.
51. program displays an ASCII plot (character plot) of a Julia set.

메타데이터

위키데이터

• ID : Q848427

Spacy 패턴 목록

• [{'LOWER': 'julia'}, {'LEMMA': 'set'}]